Counterparty
Credit Risk:
Deep Dive Compilation
Compiled by
Gaby Frangieh
Risk Management, Finance and Banking – Senior Advisor
April 2025
https://www.linkedin.com/in/gaby-frangieh-1873aa11/
Counterparty Credit Risk
Deep Dive Compilation
Counterparty Credit Risk
Deep Dive Compilation
Compilation Contents
1. Guidelines for counterparty credit risk management, Basel Committee on
Banking Supervision, December 2024
2. Counterparty credit risk and the effectiveness of banking regulation by
Sînziana Kroon and Iman van Lelyveld, De Nederlandsche Bank and VU
University Amsterdam, 2018
3. Strengthening banks’ Counterparty Credit Risk (CCR) management
practices to meet increasing supervisory expectations by Deloitte
Supervisory Insights, 2024
4. A Guide to Modelling Counterparty Credit Risk by Michael Pykhtin and
Steven Zhu
5. Counterparty credit risk in OTC derivatives by Florian Balke, Andreas
Barthe, Arne Reichel and Mark Wahrenburg, 2019
6. Counterparty credit risk and the credit default swap market by Navneet
Arora, , Priyank Gandhi, , Francis A. Longstaf, Journal of Financial Economics,
2011
7. Counterparty Credit Risk in OTC Derivatives under Basel III by Mabelle
Sayah, Journal of Mathematical Finance, 2017
8. Efficient Monte Carlo Simulation for Counterparty Credit Risk Modeling
by SAM JOHANSSON, KTH ROYAL INSTITUTE OF TECHNOLOGY, SCHOOL OF
ENGINEERING SCIENCES
9. Counterparty Credit Limits: An Effective Tool for Mitigating Counterparty
Risk? by Martin D. Gould, Nikolaus Hautsch, Sam D. Howison and Mason A.
Porter, Centre for Financial Studies, Goethe University, 2019
10. A Study of Counterparty Credit Risk and Credit Value Adjustment by Dong
Shen, An essay submitted to the Department of Economics, Queen’s
University, Canada, 2013
Basel Committee
on Banking Supervision
Guidelines for
counterparty credit risk
management
December 2024
This publication is available on the BIS website (www.bis.org).
©
Bank for International Settlements 2024. All rights reserved. Brief excerpts may be reproduced or
translated provided the source is stated.
ISBN 978-92-9259-823-5 (online)
Guidelines for counterparty credit risk management
iii
Contents
Executive summary ........................................................................................................................................................................... 1
1.
Introduction ....................................................................................................................................................................... 2
2.
Scope, proportionality and risk-based application............................................................................................ 2
3.
Due diligence and monitoring ................................................................................................................................... 3
Information disclosure .................................................................................................................................................. 4
Onboarding ....................................................................................................................................................................... 4
Ongoing credit assessment......................................................................................................................................... 6
4.
Credit risk mitigation ..................................................................................................................................................... 7
Margining ........................................................................................................................................................................... 7
Guarantees and other risk mitigants ....................................................................................................................... 9
5.
Exposure measurement ..............................................................................................................................................10
Exposure metrics ...........................................................................................................................................................10
Potential future exposure ..........................................................................................................................................13
CCR stress testing and scenarios analysis ...........................................................................................................14
Limits ..................................................................................................................................................................................16
6.
Governance ......................................................................................................................................................................17
People and risk culture ...............................................................................................................................................17
Risk framework ...............................................................................................................................................................18
Management reporting ..............................................................................................................................................19
Limit governance and exception management ................................................................................................20
7.
Infrastructure, data and risk systems .....................................................................................................................21
Counterparty credit risk reporting..........................................................................................................................23
8.
Closeout practices .........................................................................................................................................................24
Watch list practices and default management protocol ...............................................................................24
Glossary ..............................................................................................................................................................................................26
iv
Guidelines for counterparty credit risk management
Guidelines for counterparty credit risk management
Executive summary
In 1999, the Basel Committee on Banking Supervision (BCBS) published Sound practices for banks’
interactions with highly leveraged institutions. 1 Publication of that report was principally motivated by the
collapse of the hedge fund Long-Term Capital Management and associated risk management failures. In
recent years, there have been additional cases of significant mismanagement of counterparty credit
risk (CCR), including events linked to the failure of Archegos Capital Management in March 2021, which
caused over $10 billion in losses across numerous financial institutions. Other cases include commodities
market volatility after the Russia-Ukraine conflict in 2022 (eg the London Metal Exchange nickel market
episode) and gilt market disruption in late 2022 and early 2023. These incidents have made it clear that
certain fundamental CCR practices remain inadequate relative to supervisory expectations. Weaknesses
pertain to due diligence, both at initial onboarding and on an ongoing basis; credit risk mitigation practices
such as margining; risk measurement practices related to potential future exposure (PFE) and stress
testing; and the governance and senior management oversight of CCR.
In response to recent CCR management failings, this document lays out guidelines for CCR
management. It builds on Sound practices for banks’ interactions with highly leveraged institutions, while
drawing on other relevant disciplines such as fundamental credit risk management and market risk
management. Although the guidelines discussed in this document are intended to be comprehensive, they
place particular emphasis on key practices critical to resolving long-standing industry weaknesses in CCR
management. These include the need to:
•
conduct comprehensive due diligence at both initial onboarding, as well as on an ongoing basis
in order to ensure banks have a full understanding of the risks they are taking before they make
key credit risk decisions, and also that they are able to act swiftly and with sufficient information
on the changing risk profiles of counterparties during times of stress;
•
develop a comprehensive credit risk mitigation strategy to effectively manage the inherent risk
of their counterparty exposures using robust contractual terms and tools such as risk-sensitive
margining;
•
measure, control and limit CCR using a wide variety of complementary metrics while ensuring
CCR metrics comprehensively cover the bank’s range of material risks, portfolios and
counterparties; and
•
build a strong CCR governance framework that leverages skilled individuals from across the
organisation who have a clear sense of the bank’s risk culture; is guided by clear risk management
processes, including limits and escalations; and is supported by informative and reliable reporting
that is integrated into decision-making processes.
The guidelines are intended to be applicable to a diverse range of banks and should be applied
on a proportionate basis depending on the size, complexity and materiality of the counterparty credit risk
profile of banks. The greatest potential benefits in terms of improvements in CCR management are
expected to be in cases where banks have high-risk exposures to non-bank financial intermediary (NBFI)
counterparties. However, the guidelines are designed to be broadly applicable and should therefore be
used to manage banks’ CCR exposures to all types of counterparty. Banks and supervisors are encouraged
to take a risk-based and proportional approach in the application of the guidelines, taking into account
1
See BCBS, Sound practices for banks’ interactions with highly leveraged institutions, January 1999.
Guidelines for counterparty credit risk management
1
the degree of CCR generated by banks’ lines of business and their trading and financing activities, as well
as the complexity of such CCR exposures.
1.
Introduction
These guidelines 2 set out critical aspects of effective management of banks’ counterparty credit risk (CCR)
and sound practices regarding what constitutes a robust CCR management framework. CCR is the risk that
the counterparty to a transaction could default before the final settlement of a transaction’s cash flows.
CCR is a multidimensional form of risk, affected by both the exposure to a counterparty as well as the
credit quality of the counterparty, both of which can be sensitive to highly dynamic and fast-moving
changes in financial markets. CCR is also affected by the interaction of these risks, for example the
correlation between an exposure and the probability of default of the counterparty, or the correlation of
exposures among the bank’s counterparties. Constructing an effective CCR management framework
requires a combination of risk management techniques across credit, market, operational and liquidity risk
disciplines.
Recent events, such as the default of Archegos Capital Management, highlighted broad-based
weaknesses in areas related to due diligence, risk measurement, risk management and governance. These
issues are particularly acute for high-risk counterparties, such as institutions with material concentrations,
opaque business activities, limited transparency or high leverage. The risks posed by these weak practices
may be exacerbated when competitive pressures in the industry drive a race to the bottom in activities
that mitigate risk, such as margining. The sound practices set out in these guidelines aim to address recent
CCR management failings. The guidelines build on the BCBS’s Sound practices for banks’ interactions with
highly leveraged institutions, 3 published in 1999, while drawing on other relevant disciplines, such as
fundamental credit risk management and market risk management. 4
CCR management techniques have evolved rapidly over the past decade along with the
complexity of derivatives and securities financing transaction (SFT) products, concurrent with the growth
in – and banks’ interlinkages with – NBFIs, including highly leveraged institutions. The guidelines aim to
take account of market developments in CCR management over the past decade, address recent CCR
management failings, and lay out sound practices for CCR management and robust supervisory
expectations.
2.
Scope, proportionality and risk-based application
The guidelines are intended to be applicable to a diverse range of banks and should be applied on a
proportionate basis depending on the size, complexity and materiality of the counterparty credit risk
profile of banks. While the guidelines are formulated with a view towards application to large
internationally active banks with material CCR exposures in BCBS member jurisdictions, the framework for
managing risk in the guidelines is broadly applicable to all banks with CCR exposures. In all jurisdictions,
2
Under the list of BCBS publication types at www.bis.org/bcbs/help/publ_types.htm, publications classified as “guidelines”
supplement standards in many areas, including risk management, corporate governance, anti-money laundering and
supervisory cooperation. BCBS members are encouraged to adopt guidelines, particularly with respect to internationally active
banks.
3
See BCBS, Sound practices for banks’ interactions with highly leveraged institutions, January 1999.
4
For example, see Financial Stability Board, The financial stability implications of leverage in non-bank financial intermediation,
September 2023.
2
Guidelines for counterparty credit risk management
smaller banks and banks with less material CCR exposures can benefit from the application of the
guidelines. Banks and supervisors are encouraged to use the guidelines to identify potential areas of
improvement in CCR management practices.
The guidelines should be used to manage banks’ CCR exposures to all types of counterparty.
Certain requirements are intended to be applied specifically to selected types of non-bank entity whose
leverage could potentially pose financial stability risks, including hedge funds and other leveraged
investments funds, insurance companies and pension funds.
The greatest potential benefits in terms of improvements in CCR management are expected to
be in cases where banks have high-risk exposures to NBFI counterparties. 5 Banks and supervisors are
encouraged to take a risk-based and proportional approach in the application of the guidelines, taking
into account the degree of CCR generated by banks’ lines of business and their trading and financing
activities, as well as the complexity of such CCR exposure. In the case of small and non-complex CCR
exposure, when adapting the guidelines, supervisors and banks should reflect the lower riskiness and
complexity of the respective CCR exposure. All provisions in these guidelines should be interpreted in this
way, including paragraphs where the principle of proportionality is not specifically mentioned.
3.
Due diligence and monitoring
Thorough counterparty credit risk due diligence is the starting point of a bank’s CCR relationship with its
clients and is therefore critical to risk management. Due diligence encompasses a wide range of processes
conducted by a bank as it collects information on its counterparty, assesses the level of risk that the
counterparty and its activities pose to the bank, and analyses information to make credit decisions.
Although aspects of due diligence will differ depending on whether the counterparty is being onboarded
for the first time or a review is taking place for the continuation of an existing relationship, a few key sound
practices are broadly applicable.
1.
Sound management of CCR requires both a strong initial assessment and an ongoing
understanding of the counterparty’s risk profile in both business-as-usual (BAU) and stressed
market conditions. The credit approval process should begin with a comprehensive collection
and review of financial and non-financial information, including legal, regulatory, reputational
and operational risks, as well as other relevant risks, leveraging available information from across
the bank to build a clear picture of a counterparty’s risk profile and risk management standards.
Additionally, banks should understand the rationale and economics of underlying exposures and
of the key drivers of the counterparty’s performance and growth. Banks should be particularly
wary of any mechanisms for conducting due diligence and managing material counterparties
purely on a portfolio basis, without due consideration of individual counterparties and the risks
they pose to the bank. Ongoing monitoring of counterparties requires updated information
about material developments such as changes in trading activities and leverage taken, profit and
loss developments and significant changes to how the counterparty measures and manages their
risks.
2.
Credit standards should clearly dictate initial and ongoing due diligence expectations for
different counterparty types and should conform to the bank’s stated risk appetite. Standards
should be appropriately informative, having regard to the product and industry, and be
commensurate with the bank’s risk profile and business model in that space. Due diligence
standards should discuss the frequency and intensity of credit reviews and be updated as
5
The BCBS has previously noted that supervisors consider exposures to highly leveraged counterparties via derivatives and SFTs
to be the riskiest. See BCBS, Newsletter on bank exposures to non-bank financial intermediaries, November 2022.
Guidelines for counterparty credit risk management
3
business strategy changes. In some cases, rating scorecards may, with appropriate guidance,
serve as a means of stratifying due diligence expectations by counterparty risk.
Information disclosure
3.
Effective due diligence processes rely upon sound information disclosures. To ensure a robust
process across the institution, banks should establish a risk-based disclosure framework that
includes minimum standards on counterparty disclosures, taking into account the counterparty
sector 6 and risk profile of the counterparty, as well as an exceptions management process.
4.
While defining minimum standards is important, banks with sound practices also directly
incorporate the quality of counterparties’ disclosures into the assessment of the internal risk
rating, setting the level of margin requested and setting limits on exposure to the counterparties.
In general, the more exposure and risk a bank has with regard to its counterparty, and the riskier
that counterparty is, the more visibility the bank should have into the counterparty. Ultimately,
a counterparty’s failure to provide information commensurate with their risk profile should lead
to a more conservative approach to risk rating, limit setting, margining and other forms of credit
risk mitigation, or even the rejection or offboarding of the client.
5.
Before onboarding and throughout the ongoing relationship with a client, banks should collect
sufficient information to understand the client’s overall risk profile. In some cases, the collection
of financial statements alone is insufficient to assess the riskiness of a counterparty. For example,
risky and complex counterparties such as hedge funds should provide additional disclosures and
risk metrics – such as value-at-risk or stress test results – so that banks have visibility into the
counterparty’s own assessment of their underlying leverage and risk profile. When counterparties
share internal risk reports produced on a regular basis, the bank should use these reports to
gauge the quality of the counterparty’s risk management capabilities and practices. Banks with
sound practices ensure that the frequency, granularity and quality of disclosure they receive
increase as their relationship with the counterparty grows in size, complexity and risk. Where
practicable and reasonable, banks may also benefit by obtaining additional information on key
metrics – such as unencumbered cash, cash equivalents and other unencumbered liquid assets
eligible as collateral under the CSA agreement – from their counterparties during times of stress.
6.
Banks with sound practices monitor the timeliness and quality of financial statements and risk
information provided by the client on an ongoing basis and track exceptions to established
standards at the counterparty level as well as at aggregated portfolio levels. As information from
the client is received, banks should also ensure that adequate proof, assurance or verification –
where relevant and practicable – is applied as part of their due diligence processes. This type of
practice helps ensure that credit risk decisions are not made based solely on unverified or verbal
information. In some cases, banks may benefit from engaging third-party information
verification services.
Onboarding
7.
In the onboarding process, banks should ensure that they have a holistic view of a
counterparty’s potential activities and risks throughout the banking organisation. This process
should ensure that onboarding and managing a counterparty’s risks across different trading and
lending products, and through multiple entities and jurisdictions, is transparent with clear lines
6
In establishing a disclosure framework, banks may also need to recognise that, in certain cases, there may be constraints on
publicly listed counterparties in terms of the information they can provide that is not publicly available.
4
Guidelines for counterparty credit risk management
of accountability. Economically equivalent risks should be onboarded similarly, regardless of
onboarding platform, business or legal entity. For example, central and remote booking should
follow the same due diligence process, with clear oversight and accountability.
8.
Before onboarding a counterparty, banks with sound practices inquire about its past and present
reputation and creditworthiness, for example by accessing credit registers, evaluating legal status,
considering the level of regulatory oversight and available regulatory reviews, and becoming
knowledgeable about the individuals responsible for managing the institution, including
considering any previous supervisory sanctions against the counterparty or the managers. Banks
should also assess qualitative factors such as strategy, quality of risk management practices, and
staff composition and turnover. However, a bank should not grant credit solely because the
counterparty or key members of its management are familiar to the bank or are perceived to be
highly reputable. Similarly, banks should not unduly rely on profitability considerations when
deciding on the onboarding of a new client.
9.
Banks with sound onboarding practices recognise that, although their initial onboarding decision
may be binary, their full credit risk decision-making process can be a spectrum of how much
credit and exposure the bank is willing to extend to the counterparty, including the terms of
margining used to control the amount of leverage in the trading relationship and transactions
with the counterparty. As a result, banks with sound practices demonstrate thoughtful and clear
linkages between information analysed during onboarding due diligence and their CCR decisions,
including but not limited to risk ratings, limits, contractual terms and risk mitigants (eg collateral
and guarantees).
10.
Banks should ensure, at the point of onboarding, that their processes consider and assess nonfinancial risks as part of the credit risk decision-making process. Banks should also establish an
escalation process and clear communication channels for the review of non-financial risks. For
instance, banks should appropriately characterise the intersection between CCR and geopolitical
or country risk. This is a process that may benefit from consultation with the legal department at
the point of onboarding. In some cases, risks such as reputational risk may not directly affect the
counterparty’s capacity to repay – ie probability of default – or immediate financial performance
but may introduce other non-quantifiable risks that could have a material impact on the overall
riskiness of the counterparty. These non-quantifiable risks can transform into CCR over the longer
term, even in cases where no direct impact on the probability of default can be seen.
11.
Banks may leverage upstream processes, such as those that may already exist in compliance and
operational risk management frameworks (eg know-your-customer), to inform and drive
assessments performed in the credit risk decision-making process, rather than replicate
capabilities across functions. Banks should ensure that the established processes are effective in
directing or channelling relevant and material considerations – including those regarding nonfinancial risks – to credit risk analysis and to the decision-making process. They should also ensure
that credit risk management processes adequately evidence analysis and outcomes in decisions.
12.
The credit process should identify the purpose and structure of the transactions for which
approval is requested and provide a forward-looking analysis of repayment capacity based on
the creditworthiness of the counterparty and available credit protections. Banks with sound
practices also consider idiosyncratic scenarios and circumstances that could present material risks
to the client’s creditworthiness. Banks should have a good understanding of key assumptions
made about a counterparty’s risk profile – such as their level and sources of liquidity and how the
orderly liquidation of underlying positions might occur – when establishing a relationship with
them in order to facilitate a deeper understanding of the inherent riskiness of the underlying
trades with the counterparty, including market directional risk, excessive concentration risk,
idiosyncratic risks and wrong-way risk (WWR) arising from the dependency between client default
and its underlying exposure.
Guidelines for counterparty credit risk management
5
13.
Banks are expected to review proposed trading positions or sample portfolios to assess the
underlying risks inherent in the activity that the bank will be financing. Banks with sound practices
apply this review when onboarding new clients or new funds or approving new types of trading
activity for existing clients. This analysis should span at least the main internal metrics used for
risk monitoring, including BAU and stressed exposures. In the case of new trading positions of
existing clients, the incremental impact of the new positions should be assessed against the
existing risk limits for the counterparty. Sound due diligence practices incorporate specialised
evaluation and technical knowledge of industries such as commodities, where terms vary
significantly depending on the type of product being traded and collateral obtained.
Ongoing credit assessment
14.
Banks with sound due diligence processes understand that due diligence obligations do not end
following the initial onboarding of a counterparty. Instead, they recognise the need to continually
receive and assess information that sheds light on a counterparty’s risk profile. For example,
banks should obtain information about material counterparty developments such as changes in
the direction of their trading activities and performance (eg net asset value (NAV)), profit and loss
developments, significant changes to leverage, alterations to their risk management procedures
or their risk measurement processes, and changes in key personnel. Banks with sound practices
rigorously explore whether high returns shown in a counterparty’s portfolio are associated with
higher risks that have not been properly considered or whether they represent unknowns and
cannot be substantiated without overreliance on the client’s representations.
15.
Following the characterisation of the counterparty’s risk profile at onboarding (such as through
proposed trading positions or sample portfolios noted earlier in this section), deviations from the
risk profile should be tracked and lead to adjustments in the ongoing monitoring process as
appropriate. Banks should also establish a frequency for ongoing monitoring and predefined
triggers for metrics such as performance, volatility, liquidity, management quality and
concentration, which should be commensurate with the risk presented by the client under normal
and stressed market conditions. The frequency of ongoing monitoring should also take into
account the assessment of a counterparty’s non-financial risks.
16.
An internal risk rating system used to assess and monitor quality both of individual counterparties
and across the portfolio should be suitable for and commensurate with the nature, size and
complexity of a bank’s activities. For counterparties with CCR exposures, due consideration
should be given to the dynamic nature of these relationships, as mark-to-market (MTM)
exposures can change materially over short time frames that may require updated credit risk
assessment and decisions. The frequency of internal risk rating reviews for counterparties should
account for their inherent risk as well as the dynamic nature of their positions. Ultimately, the risk
rating process should ensure that any material change in the counterparty’s risk profile triggers
a revised assessment. These revisions should include but are not limited to: the risk rating score,
products allowed for the relationship, margining terms, and exposures and concentration limits.
17.
As part of ongoing monitoring, banks should track non-standard contractual terms that are
outside their credit policy standards and assess the potential need for adjustments to terms,
where necessary, to further enhance their credit risk mitigation. Notwithstanding these practices,
banks should not rely solely on strong contractual terms and the ability to close out transactions
with a client to negate the need to conduct proper risk management. Similarly, covenants should
facilitate the timely monitoring of a counterparty’s risk profile so that banks are aware of adverse
financial events and take actions to adjust or mitigate the exposure before the need arises to
close out the client relationship.
6
Guidelines for counterparty credit risk management
4.
Credit risk mitigation
Credit risk mitigants are tools that are necessary for banks to effectively manage their CCR. Margin is the
primary component of risk mitigation for CCR exposures, and, in some cases, banks may also choose to
rely on other risk mitigants to support credit risk management decisions. These mitigants can range from
contractual terms to cross-collateralisation and written guarantees, all of which can provide additional risk
mitigation. In many cases, margin is necessary but may not be entirely sufficient to mitigate risk without
due consideration of other factors such as the creditworthiness of the counterparty, the frequency and
reliability of the disclosures, the level of transparency in the overall risk profile of the counterparty and the
riskiness of the counterparty’s positions relative to market depth and conditions.
Regardless of the credit risk mitigants, bank policies and procedures should determine the
necessary and allowable contractual provisions that govern counterparty relationships and help mitigate
CCR, including the circumstances under which these clauses may be reviewed. These legally binding and
enforceable contractual arrangements – coupled with the bank’s limit frameworks – determine the size of
the credit exposure assumed by the bank. It is therefore paramount that, in calibrating these contractual
terms, there be close consideration of their enforceability under various conditions, the nature and
creditworthiness of the counterparty, the riskiness of its underlying exposure to the bank, and the overall
transparency of the counterparty with respect to its positions and trading strategy. For example, banks
should request higher margin when faced with a lack of disclosure and should frequently monitor margin
sufficiency and shortfall vis-à-vis the underlying risks.
The next section discusses sound practices regarding margining and risk mitigation of CCR
exposure.
Margining
18.
Banks with sound practices develop and implement a transparent and robust margining
framework that is consistent across all trading products and onboarding platforms. Such practices
are reflective of underlying risks and the bank’s risk appetite. At a minimum, the margin
framework should adequately capture the risks associated with the counterparty’s underlying
exposure (including valuation risks), the quality of collateral received and the credit risk
associated with the counterparties.
19.
Margin levels should account for the market risk of the portfolio and be calibrated to ensure
adequacy of margin through various mechanisms including, charging upfront margin. It is best
practice that margin levels be sensitive to changes to the counterparty’s risk profile, underlying
risk characteristics and credit quality. For example, the preference is that margin for a
counterparty’s exposure be sensitive to the implementation of new trading strategies, as well as
changes in portfolio directionality, concentration, leverage, or other idiosyncratic risks. If margin
is not risk-sensitive or dynamic, such as independent amounts (IA) based on a per-trade notional
amount, banks should ensure margin sufficiency and rely on other risk mitigation tools, such as
limits or contractual terms, to manage exposure effectively. Other factors to consider include
market conditions affecting the underlying trading activity, such as increased volatility,
crowdedness, liquidation and market liquidity.
20.
The sophistication of margining frameworks should be commensurate with the complexity and
materiality of banks’ portfolios. The computed margins for a particular counterparty should be
reflective of its specific portfolio vulnerabilities and exposures and capture material risks at the
counterparty’s portfolio level. Banks should also require margin levels that reflect material risks
arising from other contractual terms such as early termination, margin lock-up and frequency of
margin resets, among others.
Guidelines for counterparty credit risk management
7
21.
The margining framework should be informed by and reflective of the bank’s assessment of the
overall risk profile of the counterparty based on available information, including financial
statements and, where appropriate, NAV trends and volatility. Banks could, for example, use
disclosed information such as NAV growth, volatility, etc to infer risk taken outside of their
portfolio.
22.
Banks should avoid opaque margining frameworks that lack effective oversight and fail to ensure
that adequate and sufficient margins are charged on trades or portfolios both at the inception of
the relationship and on an ongoing basis. Additionally, banks should preferably not engage in
margin customisation or deviate from approved margin policies to accommodate commercial or
competitive pressures. Where they do so, appropriate governance should be in place and support
should be provided by margin sufficiency benchmarking and analysis.
23.
Banks with sound practices have systems, policies and procedures to monitor the effectiveness
of their margining frameworks and methodologies, which should be periodically reported to
banks’ senior management. Margin frameworks should be subject to ongoing monitoring and
governance related to margin sufficiency, underlying assumptions, contractual terms, and limit
setting and risk appetite. Monitoring should be undertaken on both the counterparty level and
on an adequate portfolio aggregation level. House margin frameworks should undergo a level of
governance and scrutiny proportionate to their materiality. As part of this, margin frameworks
should be assessed for adequacy and sufficiency using benchmarking and quantitative testing.
For details on risk reporting, refer to the section titled “Management reporting” in Chapter 6 of
this document.
24.
Where applicable, banks should establish a formal risk framework for deviations from their
margin terms and monitor exposures against it. 7 This governance framework should include clear
escalation and approval requirements for material deviations.
25.
Initial margin (IM) requirements are a particularly important part of a margining framework. They
represent the amount of collateral necessary to absorb potential losses in relation to a particular
trade or portfolio of trades that may arise in the time between the last exchange of variation
margin and the liquidation or hedging of the positions. Such margin is either static or reevaluated and adjusted over time (ie dynamic) to reflect changes in a portfolio’s risk. When
adopted, static margin should be set appropriately and sufficiently so as to cover unexpected
changes in underlying exposure due to market value and riskiness.
26.
Variation margin (VM) is another important component of a margining framework and is
generally defined as the amount of collateral necessary to cover the current portfolio exposure,
accounting for changes in the MTM valuation of the positions on a contractually agreed
frequency. Banks with sound practices have rigorous and robust margin (IM and VM) dispute
resolution procedures in place with their counterparty and, to the extent possible, apply daily VM
to all material counterparties where thresholds and small minimum transfer amounts are set in
line with the banks’ risk tolerance.
27.
When banks agree to two-way collateral provisions, they should make sure that the resulting
additional exposure – of the posted collateral – is monitored and fully integrated into the overall
risk management and measurement processes. Banks should ensure that contractual terms
stipulating two-way VM do not exacerbate risk by increasing the counterparty’s leverage and
credit exposure. In granting two-way margining and rehypothecation rights, banks should give
due consideration to the credit quality of the counterparty and the riskiness of the underlying
7
For an example of related guidance, see Prudential Regulation Authority and Financial Conduct Authority, Supervisory review
of global equity finance businesses, December 2021.
8
Guidelines for counterparty credit risk management
exposure, including collateral. This guidance does not supersede any regulatory requirements to
enter into two-way margin agreements with certain counterparties.
28.
Banks should assess the need for margin based on the risks and vulnerabilities of the traded
positions. For example, banks should assess the margin sufficiency – ie the estimated margin
based on underlying risks versus the margin posted by a counterparty – of all traded products,
regardless of product type and whether the exposure is cleared or non-cleared, and should
consider the risk of potential delay in margin delivery as well as substitution of collateral, if
contractually permissible.
29.
In managing the risk of counterparties at low risk of default, banks cannot have a double benefit
from collateral in the measurement of both default and exposure risks. Regardless of the
likelihood of a counterparty’s default, banks should assess margin needs based on the riskiness
of the underlying exposure, including collateral being posted. Similarly, default risk should not
be assessed based solely on the lower risk of the underlying exposure to counterparties due, for
example, to perceived diversification or market neutrality in long/short types of exposure.
30.
Banks should establish policies and methodological frameworks that define eligible collateral and
quantify the collateral haircuts to be applied to SFT exposures. Banks should also ensure that
collateral haircuts and VM for SFTs reflect the underlying risks of the counterparty and riskiness
of the exposure and that IM is applied consistently across similar products. Banks with sound
practices make SFT collateral haircuts dependent on both the riskiness of the security and on the
riskiness of the counterparty.
31.
When acting as agents for derivatives transactions, banks should make their own assessment of
the adequate margin levels for their counterparties. Banks with sound practices do not simply
pass on the clearing house or regulatory margins to their counterparties, but rather determine
margin sufficiency based on their internal risk assessment. Banks with sound practices have
processes to determine if and when they may need to consider applying margin multipliers.
32.
Banks should pay particular attention to concentration and WWR in which margin and collateral
established to cover counterparty credit exposures may be significantly reduced if the probability
of the counterparty’s default is negatively correlated with the value of the collateral or positively
correlated with the market value of the contracts.
Guarantees and other risk mitigants
33.
Bank policies and procedures should determine the range of allowable credit risk mitigants where
possible. These policies should ensure that the usage of mitigants is controlled and monitored
appropriately across the bank’s portfolio. Furthermore, the assessment of such mitigants should
closely relate to the creditworthiness of the counterparty and the riskiness of the underlying
exposures.
34.
The contractual provisions that govern counterparty relationships are a particularly important
consideration. Banks with sound practices clearly define the types of allowable and necessary
contractual terms which affect CCR – including, for example, early termination rights, margin lockup agreements and default notification periods – and ensure that contractual terms are clearly
considered when setting limits and risk appetite for trading with a counterparty.
35.
Additionally, the contractual terms of specific trades have significant impact on their risk profile,
as certain trades can either generate additional risk or mitigate risk based on the features of the
trade. For example, banks should be aware of the use of derivatives such as a bullet swap, which,
if left thinly margined or unmargined, can present elevated risks when compared with a similar
resetting swap.
Guidelines for counterparty credit risk management
9
36.
Banks should assess the legal enforceability of all credit risk mitigants and incorporate potential
delays in accessing collateral when measuring exposure and margin. This review should consider
not just differences in relevant jurisdictions, but also differences across products and collateral
types. 8 For example, this practice should determine the criteria under which the protections
provided by the legal framework are enforceable to the benefit of the creditor.
37.
In situations in which a bank has CCR exposure to a counterparty that – as a standalone legal
entity – is not a creditworthy entity, the bank may seek a guarantee. Banks with sound practices
assess the credit quality of the guarantor in order to ensure that they can rely primarily on written
guarantees that contractually obligate a guarantor to support the obligations of the bank’s
counterparty.
38.
In other situations, there could be a support provider without an explicit written guarantee. In
such cases, banks should establish a robust framework for assessing the likelihood, willingness
and capacity of a support provider to step in and provide support. In all cases, banks should
ensure that implied support is not considered equivalent to written guarantees and appropriately
discount the strength of implied support when making decisions about other risk mitigants that
should be obtained. This is especially important when a bank has significant trading activity with
subsidiaries which rely on parental support to substantiate credit risk decisions.
39.
Banks may obtain written guarantees that are capped, limiting the amount of exposure
guaranteed by the guarantor. In the context of CCR exposures, which can increase rapidly as the
market environment changes, banks should ensure that they have processes in place for
assessing the use of capped guarantees, including guidelines for sizing and monitoring current
or potential exceeding of the cap.
5.
Exposure measurement
CCR default losses are often driven by tail events, such as large and sudden asset moves or the unforeseen
occurrence of unusual market scenarios, which can have a dramatic impact on the solvency and portfolio
performance of certain counterparties. Moreover, CCR is by nature multi-dimensional, involving up to
several thousand counterparties and a much higher number of underlying assets, combined in portfolios
of trades spanning all sorts of risk configurations: linear and non-linear, concentrated and diversified,
hedged and directional.
Dealing with this plethora of different risk profiles – and specifically with their tail behaviour –
requires banks, in managing CCR, to rely holistically on a variety of non-equivalent risk metrics that assess
all the material dimensions of CCR. Such metrics should provide a complementary and comprehensive
view of risk, covering for both BAU and stressed market conditions as well as for any material vulnerability
to specific idiosyncratic risks. The signal of these metrics should be calibrated with a sufficient level of
conservatism, aimed at compensating for the inherent model risk of the quantitative methods used.
Exposure metrics
40.
8
10
CCR exposure metrics for a given counterparty should be computed with appropriate
consideration for the level of aggregation embedded in the calculation. Exposure metrics should
be produced frequently and in a timely manner and include all trades giving rise to CCR, across
See Committee on Payment and Settlement Systems and the Euro-currency Standing Committee, OTC derivatives: settlement
procedures and counterparty risk management, September 1998. The report discusses legal risk associated with collateral.
Guidelines for counterparty credit risk management
product types (eg bilateral, centrally cleared and exchange-traded derivatives and SFTs), as well
as across business lines and legal entities. In addition, the risk monitoring process should be fully
informed of any additional credit exposure with the counterparty, such as loans outstanding or
unused credit commitments.
41.
CCR exposure metrics should be comprehensive in covering banks’ material risks at portfolio,
counterparty and a more granular level, as appropriate. For every counterparty, exposure metrics
should account for the contractual terms – and for their inherent risks, eg related to netting and
collateral enforceability – and be consolidated across product types, desks and books. Overall,
this suite of metrics should provide a holistic view of the characteristics of the entire distribution
of CCR exposures, including average, high quantiles and residual tail risks. Residual tail risks can
be very significant for counterparties such as highly leveraged institutions in which solvency,
liquidity or both closely depend on portfolio performance.
42.
Exposure metrics should be actionable and embedded in the different stages of the CCR
management process, including: (i) the pricing and setting of contractual margins (eg x-value
adjustment (XVA) and IM methodologies); (ii) risk monitoring (eg potential future exposure (PFE)
and stress testing); and (iii) capital assessment (eg standardised approach for counterparty credit
risk (SA-CCR), internal models method (IMM), when applicable, and stress testing). Such metrics
should supply the bank with an ongoing, timely and accurate view of the counterparty’s
exposures. When relevant changes occur either in the portfolio or the risk profile of a specific
counterparty, such changes should be promptly reflected in the exposure metrics.
43.
The metrics used to quantify risk at any stage of CCR management should undergo the
appropriate level of internal governance and independent review applicable to the models used,
irrespective of any perceived analytical simplicity. This should include the initial and ongoing
review by an independent validation unit. As part of the challenge process for the metrics, end
users – including senior risk officers – could be actively involved by reviewing parallel runs, impact
studies and concrete examples based on existing and/or historical portfolios. Stakeholders should
maintain a sound understanding of: (i) the risks captured by each of these risk metrics; and (ii) the
inherent limitations of these risk metrics.
44.
Related to the previous paragraph, end users and key stakeholders should be provided with a
clear and actionable taxonomy of the supported CCR metrics – including their range of
applicability and known limitations – across counterparty groups, product types and contractual
arrangements. Such taxonomy, given its central role within the CCR management process, should
be subject to appropriate senior management oversight and reviewed by an independent
validation function for the appropriateness and scope of usage of its main modelling
components.
45.
The exposure metrics should, collectively, provide complementary risk capture and give banks
visibility of material drivers of exposure under current and stressed market conditions. Such
drivers should account for the potential structural risks and vulnerabilities of the positions –
considering factors such as leverage, concentration, liquidity and WWR – even when they cannot
be fully characterised because of partial information regarding the true risk profile of the
counterparty. In a similar fashion, exposure metrics should account for the possibility that
perceived risk mitigants or diversification benefits may not work as intended. For example, PFE,
as well as IMM and CVA EE profiles, generally produce hardly any actionable signal for overcollateralised counterparties (such as hedge funds or other highly leveraged institutions) since
they are often computed ignoring (at least general) WWR and the possibility of margin-driven
Guidelines for counterparty credit risk management
11
defaults. 9 Therefore, such metrics should be complemented by additional metrics that better
capture the residual risks.
46.
In measuring exposure, banks should properly identify, evaluate and capture idiosyncratic risks
such as excessive concentration to a single name or single risk factor, material dispersion or basis
risk between long and short positions, lack of liquidity due to limited trading volume, the
presence of complex or bespoke positions in the portfolio, or simply the sheer position size. Banks
with sound practices directly consider how such idiosyncratic risks may affect portfolio
correlations and the accuracy of the valuations used to determine margins. They should also
consider how such risks may exacerbate WWR and ultimately magnify closeout losses. In this
context, the overall risk profile of the counterparty should be assessed conservatively, giving due
consideration to scenarios such as horizontal hoarding 10 or crowding that can materially skew
the exposures distribution.
47.
Beside PFE and stress-based exposures (see the next two sections), banks should monitor their
aggregated CCR position and the risk profiles of their counterparties using simple and intuitive
risk metrics that are model-free, ie based solely on the structural features of the portfolios. These
metrics should provide indicative CCR losses in extreme market scenarios, such as a sudden
breakdown in asset correlations, a major liquidity dry-up or other idiosyncratic events in specific
trade underlying, or country/regional turmoil directly affecting the solvency of local
counterparties.
48.
The metrics described in the previous paragraph and monitored by banks with sound practices –
either at the counterparty or bank’s portfolio level – include for example: (i) gross notional
amount or gross market value (a tool for identifying a vulnerability to the breakdown of specific
long/short hedges within a counterparty’s portfolio); (ii) gross trades’ delta exposure (a tool for
identifying, either at the counterparty or bank’s portfolio level, a potential exposure concentration
in specific risk factors); (iii) received and posted collateral composition (a tool for identifying, at
the bank’s portfolio level, a potential concentration in specific collateral assets); and (iv) country
or regional gross exposure (a tool for identifying, at the bank’s portfolio level, potential exposure
concentration with regard to countries or regions with significant geopolitical risk).
49.
Banks should have a dedicated WWR framework in place that is integrated into the general risk
assessment framework and gives due consideration to both general wrong-way risk (GWWR) and
specific wrong-way risk (SWWR). The WWR framework should be commensurate with the risk
appetite and be designed to effectively allow for the identification, measurement, monitoring,
regular reporting, limit setting and explicit treatment of exposures giving rise to WWR. Such a
framework should explicitly account for relevant risk factors, going beyond mere compliance with
regulatory requirements. This is specifically relevant for counterparties whose business strategy
is particularly vulnerable to certain market risk scenarios, including those with high leverage and
other specific structural features of their portfolio.
50.
To identify and monitor GWWR, banks should have clear definitions in place in terms of the risk
categories applicable to their portfolios, including industry, region, business areas, products and
any additional relevant dimension. The regular GWWR identification process should be supported
9
In the case of Archegos Capital Management, the default event was triggered by a massive VM margin call that was not met.
It was originated by large gap moves in a few correlated technology stocks. Whereas PFE and IMM/CVA EE profiles are generally
computed according to a smooth default paradigm, with closeout losses solely driven by stochastic fluctuations of trades and
collateral values over the MPOR horizon.
10
In this context, “horizontal hoarding” refers to the replication by a single counterparty of the same or similar position across
multiple broker-dealers.
12
Guidelines for counterparty credit risk management
by well defined stress testing, based on scenarios of credible severity, that are reported with
appropriate frequency to senior management.
51.
Banks’ processes and methodologies for SWWR assessment and monitoring should be well
defined and documented. They should enable the identification of relationships between a
counterparty’s creditworthiness and the CCR exposure to the counterparty. The SWWR
classification should be based on a clear definition of legal connection that considers legal
frameworks on ownership, including control or consolidation requirements. In addition, for CCR
management, banks should also consider applying the SWWR classification to cases with no strict
legal connection but where the counterparty is significantly economically dependent on its
underlying exposure. The results of the regular SWWR identification process should be reported
with adequate frequency and escalated to senior management where necessary.
52.
The exposure metrics should account for WWR (either directly or via suitable adjustments or
overlays). This is especially relevant for NBFIs, particularly institutions with high leverage and/or
concentrated exposures, whose solvency – because of the leverage and concentration – becomes
materially correlated with portfolio performance. In such cases, banks should ensure that at least
some of the risk metrics used to monitor CCR are calibrated to historical and idiosyncratic
scenarios commensurate, for instance, with those observed during the Archegos Capital
Management and Long-Term Capital Management defaults, when WWR drove large gap moves
for the underlying portfolio assets and ultimately magnified the closeout losses.
Potential future exposure
53.
Banks should quantify CCR exposure daily, using PFE or alternative metrics to measure the future
exposure against a given counterparty conditional upon its default. PFE is a risk metric calibrated
on current/recent market conditions that quantifies, over a defined future horizon and at a
specified confidence level, how sizeable the CCR exposure of a given counterparty’s portfolio may
become given the applicable contractual terms and credit risk mitigants. PFE is predominantly
computed based on scenarios generated with Monte Carlo simulations, 11 considering multiple
forecasting horizons (typically up to the life of the contract) and a high percentile (eg 95% or
99%) of the simulated portfolio exposures distribution (alternatively, expected shortfall measures
linked to such confidence levels are used). For risk monitoring, when calibrating PFE or alternative
metrics, banks should have due regard to the modelled risk factor dynamics (including, when
appropriate, the calibrated gap moves for the underlying assets), as well as the applicable margin
period of risk (MPOR) 12 and collateral haircuts.
54.
While using PFE to monitor risk limits at counterparty and product levels, banks should ensure
that the counterparties’ PFEs are: (i) reflective of the contractual terms, including trade attributes,
netting and collateral requirements; (ii) computed and monitored across all the applicable risk
horizons; (iii) based on risk scenarios that conservatively account for the stochastic behaviour of
the portfolio’s material risk factors and the collateral dynamics over the MPOR; and (iv) computed
with a sound modelling of correlations among risk factors and of any risk basis (eg long/short
positions with residual dispersion) that may materialise in ordinary or distressed markets. In
11
For products in scope of IMM, the PFE is based on the same scenarios and valuation framework used to compute the Pillar 1
EE profiles and effective expected positive exposures (EEPEs).
12
For the Basel Framework definition of MPOR, refer to “Calculation of risk-weighted assets (RWAs) for credit risk” (CRE) 50.19.
In the case of collateralised counterparties, the PFE should consistently account for both the trades’ MTM and the collateral,
and the forecasted loss materialises over the MPOR after the default event. Specifically, for a default horizon h, the PFE is
generally computed as the closeout loss (trades’ MTM minus collateral) accrued between h and h + MPOR.
Guidelines for counterparty credit risk management
13
general, banks should be conservative in their treatment and modelling of excess collateral
received from counterparties.
55.
When relying on PFE to manage CCR, stakeholders should maintain a sound understanding of
both the risks captured by the metric and its inherent limitations, such as the risks not captured
in the PFE. The limitations should be documented and reviewed on an ongoing basis and
compensated in the CCR management process by assessing exposures using complementary risk
metrics such as factor sensitivities, aggregation on a gross basis and stress testing. For example,
should the peculiar risk dynamics of over-collateralised and/or highly leveraged counterparties
not be fully captured within the PFE model, it is crucial to consider them within stress testing.
56.
Banks should adjust the MPOR to account for excessive risks driven from concentrated and/or
illiquid portfolios or collateral and give due consideration to related idiosyncratic risks that can
materialise upon the default of the counterparty, such as crowding during liquidation and a
consequent large drop in the value of the assets. Such risks should primarily be addressed
through: (i) a suitable framework capable of quantifying the closeout MPOR based on the
counterparty’s portfolio; and (ii) for potentially illiquid trades/underlyings, by simulating the
portfolio dynamics with stochastic models calibrated to a level of distress commensurate with
the market risk of liquidating highly concentrated positions. It is noteworthy that, in the case of
Archegos Capital Management (whose closeout period was not unusually long), the forecasted
PFE was less than a tenth of the realised closeout losses. As such, the PFE modelling framework
was severely understating the impact of liquidity and concentration on the closeout exposure.
57.
Banks should be mindful that plainly offsetting the scenarios trades exposures with the forecasted
level of IM (in addition to any applicable VM) may result in zero or negligible PFEs for
collateralised counterparties. 13 This perspective does not account for the material risk of margindriven defaults, where the available IM may not compensate for the large VM collateral shortfall
originated by a sudden gap move of the underlying portfolio assets (for instance, driven by the
leverage/WWR dynamics previously discussed). This scenario is especially relevant for highly
leveraged institutions, particularly those that take excessive leverage and have significant
concentrations.
58.
As part of the ongoing model governance, PFE should be backtested using either real or
hypothetical portfolios (or a combination of both) so as to extensively probe the modelling
assumptions versus the realised historical markets. In addition, banks should benchmark their PFE
models versus the realised dynamics of well publicised defaults such as Long-Term Capital
Management and Archegos Capital Management. They should assess whether: (i) their PFE model
is able to produce commensurate exposures at realistic quantiles; and/or (ii) the banks’ overall
CCR management framework has adequate compensating measures able to flag an excess of
CCR for similar portfolios.
CCR stress testing and scenarios analysis
59.
As a necessary and complementary metric to PFE, banks with sound practices have developed a
dedicated CCR stress testing framework for the assessment of counterparties’ exposures in a
stressed market environment, where the resulting stressed exposures are fully integrated into the
bank’s BAU risk management process and monitored against limits. This is especially relevant for
13
For standard PFE implementations, this is generally the case by construction for various reasons: (i) the VM at scenario level is
obtained by matching the current level of the trade exposure at default; (ii) the IM is calibrated to compensate for adverse
portfolio moves over the MPOR at a high level of confidence; and (iii) as a result of (i) and (ii), the scenarios with material
exposure at closeout are very few and much deeper in the tail compared with the quantiles at which the PFE is typically
calibrated.
14
Guidelines for counterparty credit risk management
exposures to NBFIs for whom stress testing may be the only systemic approach to identifying
and quantifying the main portfolio’s vulnerabilities.
60.
Banks should have clear, documented governance of their CCR stress testing framework in order
to ensure the appropriate identification of relevant scenarios, as well as their design and revision
when necessary. The framework should include a robust number of scenarios, exhaustive of the
multi-dimensional nature of the risks to which the bank’s portfolio is exposed. In addition, banks
should have the ability to perform ad hoc stress tests, reverse stress testing and scenarios analysis
in a reasonably short time. Based on the business model of the counterparty, a bank should be
able to characterise extreme but plausible scenarios that could result in significant adverse
outcomes.
61.
CCR stress testing should be consistent and have a broad scope of coverage across all business
lines and product types. Banks with sound practices apply market shocks simultaneously to both
the trades and collateral. The resulting counterparty’s exposures should be compared with risk
limits at the individual counterparty level as well as at aggregated portfolio risk levels. The CCR
stress testing framework should inform the bank’s day-to-day exposure and concentration risk
management and be able to identify extreme market conditions that could excessively strain the
financial resources of the bank.
As part of CCR stress testing, a comprehensive set of severe stress tests should be routinely
performed at the counterparty and portfolio levels, applying both macroeconomic scenarios and
relevant combinations of shocks to individual risk factors. These standard stress scenarios should
be designed to identify counterparties’ material vulnerabilities. To provide a realistic assessment
of exposures to counterparties under stress, these scenarios should be granular at the level of
material risk factors and be able to capture material idiosyncratic risks such as concentration in a
single name, sector, geography, tenor, risk rating etc, as well as dispersion, basis risks and liquidity
issues.
62.
In designing a suite of scenarios for CCR stress testing, due regard should be given to: (i) historical
events; (ii) the current macroeconomic and financial environment; and (iii) hypothetical future
events, including new information and idiosyncratic and emerging risks. 14 Regarding the latter,
an effective design process should, for example, consider specific hypothetical geopolitical or
natural disaster scenarios that for some counterparties – eg in the commodities or insurance
sectors – are more likely to be the ultimate drivers of the exposure conditional upon default. Risk
managers should contemplate different hypothetical scenarios that are conceivable regardless of
their level of severity. Overall, the design of CCR stress testing scenarios should be informed by
periodic vulnerabilities assessments at the level of both the whole book (eg in terms of risk factor
coverage) and the most material counterparties (in terms of scenarios’ appropriateness, see next
paragraph).
63.
To the extent that specific risk dynamics relevant to the portfolio structure of material
counterparties are not captured by the standard set of stress scenarios, banks should design
bespoke stress tests capable of accounting for them. Direct and reverse stress testing at the
counterparty level, as well as scenario analysis, should be used as active tools to identify the tail
risks to which material counterparties may be exposed.
64.
When conducting CCR stress testing, banks should test for situations in which risk mitigation
measures do not work as intended, especially under stress or counterparty default conditions.
This may entail challenging the strength of assumptions made about the legal enforceability of
14
Scenarios not based on historical events and empirically observed relationships may be warranted for some or all risks if new
or heightened vulnerabilities are identified or if historical data do not contain a severe crisis episode or idiosyncratic risks such
as excessive concentration, liquidation, WWR or the geopolitical and natural disaster events mentioned in the main text.
Guidelines for counterparty credit risk management
15
contracts (eg under specific geopolitical risk scenarios in certain jurisdictions), netting and
portfolio diversification, and the ability to collect and liquidate collateral or benefit from any other
risk mitigation measures. Stress testing the collateral should provide the bank with an alternative
view of its CCR that is not shown when relying solely on PFE. The importance of this is clearly
highlighted by the Archegos Capital Management case, in which the realised VM collateral
shortfall at default for one of the exposed broker-dealers was more than $1 billion, as compared
with no projected shortfall under the PFE metric.
65.
The stress testing scenarios should appropriately capture the impacts derived from the costs of
winding down portfolios or netting sets comprising less liquid collateral or transactions that are
hard to replace after default by the counterparty. In the absence of reliable information on
horizontal concentration in portfolios maintained with high-risk counterparties, the stress testing
framework should incorporate conservative assumptions with regard to the bank’s ability to wind
down the defaulted position under stressed market conditions, paying due consideration to
measurement of the potential market risk losses derived from unmatched hedging positions
upon the default of the counterparty.
66.
The CCR stress testing framework should pay particular attention to riskier counterparties, as well
as to the identification of counterparties for which certain market scenarios could lead to acute
stress on their solvency or liquidity positions and which are therefore particularly vulnerable to
exposure tail events. The resulting stressed exposures enable the bank’s risk management
function to: (i) identify particularly vulnerable counterparties under certain scenarios; and
(ii) identify the most relevant scenarios for the bank’s overall CCR portfolio. Senior management
should take a leading role in integrating CCR stress testing into the bank’s risk management
framework and risk culture.
67.
As part of the governance of the CCR stress testing framework, the scenarios – as well as any
other key modelling inputs used in computing stressed exposures – should be reviewed
periodically by end users and key stakeholders in order to ensure ongoing comprehensiveness,
granularity and relevance. 15 This periodic assessment should include some level of benchmarking
for the severity of the applied shocks, eg by comparing the resulting stressed exposures with
historically realised exposures for – at the least – the most material and/or vulnerable
counterparties.
Limits
68.
It is essential that banks develop comprehensive and effective limit frameworks that allow for
monitoring and control of the bank’s exposures to its counterparties at both the individual
counterparty level and the aggregate portfolio level. Banks with sound practices leverage their
suite of exposure metrics when designing a limit structure, recognising that any one metric and
limit has weaknesses. Broadly speaking, a bank’s limit structure should cover a range of both
exposure metrics calibrated on current/recent market conditions and exposure metrics calibrated
on stressed market conditions that can include, for example, PFE, gross notional amount or gross
market value, as well as other stress test-based measures.
69.
The risk limits framework should be informed by and provide visibility into the key risks – eg
concentration, liquidation, dispersion and maturity term structure – in the underlying exposure
to a counterparty. Risk limits should also capture all the credit exposures to the counterparty
15
For example, when designing stress scenarios, banks should not rely solely on parallel shocks, ignoring dispersion among
tenors, sectors, ratings, currencies, long/shorts etc. Instead, stress test metrics would also need to calculate the MTM of the
exposure under instantaneous market shocks.
16
Guidelines for counterparty credit risk management
across all products and financial relationships within the banking organisation. Banks should
ensure that risk aggregation practices, for the purpose of limit setting, are accurate and reliable.
70.
Effective limit frameworks should be calibrated with a level of severity consistent with a bank’s
risk appetite statement, with justifications on the severities used. Risk limits should not be set so
high such that they would lead to excessive build-up of risk and prevent a bank from taking the
necessary actions to effectively reduce the level of exposure in a timely manner. Additionally, risk
limits should not be set too low such that they do not serve as a credible reflection of the bank’s
risk tolerance.
71.
Banks should ensure that limit calibration processes are rigorous and subject to senior
management review and challenge. Limit frameworks should be reviewed and, when appropriate,
recalibrated with reasonable frequency and upon significant changes in overall risk appetite,
market conditions, business strategy, business organisation and risk measurement
methodologies. In addition, limits set against a single counterparty should be reflective of any
material change in the riskiness of the counterparty and/or of its underlying exposures.
6.
Governance
Solid governance for CCR relies on three pillars. The first pillar consists of competent people and the right
risk culture in the organisation. The second pillar is an adequate strategy for managing CCR, with clear
processes and effective limits in place. The third pillar is management reporting and its integration into
the decision-making process. This management reporting should enable swift analyses of key CCR in any
market situation.
As part of the principle of proportionality and risk-based application, solid governance should
account for the size and complexity of the organisation and its business model, as well as related
counterparties. Organisations with a more complex business model and higher-risk counterparties should
have an appropriate number of qualified staff and are expected to have a more elaborate governance
structure. This is not necessarily dependent on the size of the balance sheet. Complexity can arise, for
example, as a result of the organisation and management of the business in various cross-border locations
or through the trading of highly complex and/or illiquid transactions with a counterparty. Sound
governance has to take account of all potential sources of complexity.
People and risk culture
72.
Banks should foster a culture that ensures understanding of all risks, with accountability for taking
risk management actions when necessary. Banks with sound practices have clear lines that link
CCR management reporting and metrics to risk-taking or reducing decisions in a way that is
consistent across business lines.
73.
Banks should foster a culture that values the important role played by data and models in
managing CCR. A bank’s culture should encourage an appropriate degree of confidence in the
data and models underlying CCR management, balanced with an appropriate level of challenge
and an awareness of limitations.
74.
CCR contains elements of both market risk and credit risk, requiring CCR management to involve
strong collaboration between the market risk and credit risk functions at the bank. Banks with
sound practices have dedicated functions for CCR. At a minimum, the bank’s risk culture should
foster strong collaboration, including but not limited to knowledge and information transfer
between the market and credit risk departments. Therefore, banks should prevent siloed thinking
Guidelines for counterparty credit risk management
17
in their risk departments and strongly encourage the exchange of information gathered, in
particular on market or credit risk that may be relevant to assessing the credit risk of a
counterparty or potentially market-distorting events due to the deteriorating credit quality of a
counterparty.
75.
Banks with sound practices demonstrate that risk management oversight is conducted by risk
managers with clearly defined roles and responsibilities and appropriate levels of authority,
including exception approval and a clearly defined and actionable escalation framework.
76.
Banks’ CCR managers need to have sufficient experience, expertise and stature to understand
CCR and interact with counterparts in trading businesses and with the bank's most senior
managers, including the risk committees of the boards of directors. Banks should appoint
managers that have a reasonable level of understanding of CCR from both business and risk
perspectives, as well as an understanding of how data and models are used to assess and manage
CCR. Bank boards of directors should know that they are ultimately accountable for the quality
of senior management.
77.
Banks should foster a culture that enables adequate consideration of CCR arising from changes
or dysfunctionalities in the geopolitical landscape. They should be able to assess the impact of
potential wars and sanctions on their ongoing businesses. Furthermore, banks with an
international presence should be able to swiftly assess the impact of wars and sanctions on
intragroup transactions that involve their own legal entities, especially those located in potentially
sanctionable jurisdictions.
Risk framework
78.
Banks should establish a clear CCR strategy and an effective CCR management process approved
by the board of directors and implemented by senior management. The CCR strategy should
define the bank’s risk appetite, its desired risk-return trade-off and mix of products and markets.
Such a strategy should be supplemented by clear, robust and actionable policies and procedures
that establish the effective monitoring and control of CCR relationships. These policies and
procedures should drive the credit-setting process and govern banks’ relationships with
counterparties and should not be overridden by competitive pressures.
79.
Policies and procedures should be clear with regards to ownership, roles and responsibilities,
providing clear guidelines for credit approval authority, remediation and escalation processes.
Banks with sound practices strike a strong balance between ensuring individual ownership of
policies and ensuring that important changes to policy are approved by relevant oversight
committees. Additionally, regular policy reviews are conducted on a systematic basis to
adequately reflect the bank's risk and business model 16 and to ensure their continued relevance.
In all cases, authorship and ownership of policies and procedures should be clearly separated.
80.
Banks should ensure that CCR oversight – including second and third lines of defence – is
effective, with clear mandates, sufficient knowledge and stature, and the ability to operate in an
environment in which managers and staff throughout the organisation are incentivised to
identify, challenge, escalate and resolve risks.
81.
The long-term success of a bank’s credit relationships relies heavily on effective and sophisticated
risk management. Sound monitoring of a counterparty’s activities requires thorough knowledge
and understanding of the economics of the relevant exposures, including purpose, source of
16
18
Banks are encouraged to aim for a yearly policy review.
Guidelines for counterparty credit risk management
repayment, risks associated with collateral, risk concentrations and controls. Reliance on collateral
cannot be a substitute for day-to-day risk management and monitoring.
82.
Banks should establish and empower risk committees as governing bodies with authority over all
risk-taking aspects of trading businesses, including risk limits, permitted products, hedging
strategies, collateral eligibility, margins, risk measurement methodologies and overall risk
appetite. As governing bodies, risk committees should receive, on a timely basis, appropriate
information on the key risk drivers and risk trends of ongoing trading activities through risk
sensitivities, risk scenarios and stress tests.
83.
Banks’ governing bodies should have accountability for limit exceptions and approvals in line
with the bank’s established delegation of authority. Banks with sound practices embed approval
authority for policy changes in risk committees that oversee all trading activities for market and
CCR and give risk committees review authority for all approved exceptions. Risk committees are
encouraged to delegate their approval and review authority. Nevertheless, in case of delegation
of authority, senior management and risk committees retain ultimate accountability for limit
exceptions and approvals.
84.
Risk committees should include senior managers from trading and risk functions as well as from
compliance, finance, legal and operations groups. Furthermore, risk committees should report
regularly to the bank’s board risk committee. Risk committees should be of a size that is adequate
to promote the dissemination of decisions taken throughout the organisation, without reducing
the accountability of individual participants. Ideally, the chair of the committee is accountable for
the committee's decisions.
85.
Remote cross-border activities are more challenging for banks in terms of allocating adequate
responsibility for risk management. Banks with sound practices manage their counterparty
exposure by assigning clear accountabilities for risk management that align to the specificities of
their cross-border activities.
Management reporting
86.
Management is directly accountable for the implementation of a sufficiently detailed CCR
reporting framework. This reporting should allow management – as well as key risk committees –
to easily understand the CCR taken by the bank and to act based on the reported risks.
Furthermore, management reporting should empower managers to aggregate the data at an
adequate level across key risk dimensions and over time periods. It should also enable managers
to easily analyse data and conduct drilldowns on a timely basis.
87.
Banks with sound practices have CCR reporting that includes but is not limited to:
88.
a.
the key CCR exposure metrics used at both a single name and portfolio level of aggregation;
b.
the evolution of CCR exposure over time;
c.
top CCRs;
d.
relevant limits, breaches and other flagged risks (such as concerning or potentially distressed
counterparties or industries); and
e.
the degree of likelihood of a potential loss.
Management reporting should inform senior management about non-standard terms and
conditions in CCR contracts. Non-standard terms and conditions in such contracts should be
discussed by management on a regular basis.
Guidelines for counterparty credit risk management
19
89.
Managers are encouraged to continuously improve the quality of CCR reporting in their
institutions. Management reports should be comprehensive, accurate, consistent, actionable,
relevant and timely. Furthermore, a bank should be able to produce and analyse reports in both
normal and stressed market conditions. This applies both to the reports produced on a BAU basis,
and to the ad hoc reports that may be necessary due to the stressed market environment.
90.
Bank management is responsible for building a management information system (MIS) that does
not overwhelm users with data. Managers should use the bank's MIS for management reporting
and be able to perform on-request analysis without external help for counterparties with material
exposure or those on watch lists/close monitoring lists.
91.
Managers should foster a culture that stresses the importance of management reporting in
managing CCR. This includes but is not limited to valuing the important role played by data and
models in managing CCR.
92.
Banks with sound practices also promote a holistic view of market and CCR management,
enabling the assessment of the impact of a counterparty default on market risk and vice versa,
as well as a clear and actionable risk framework around these assessments.
Limit governance and exception management
93.
Banks should implement a transparent and actionable limit governance framework with clear
and proper oversight and review. The limit framework should include a remediation process for
limit breach, with distinct and accurate oversight, review and challenge stages commensurate
with the severity and materiality of limit breaches.
94.
Limits should be set and verified independently of the business function.
95.
Limit actions such as exceptions should require approval from an independent risk function. If
exceptions are sufficiently large, then delegation of authority should require approvals from
senior management. Banks should ensure an adequate audit trail of such approvals. Those with
sound practices record and document such approvals in their risk systems.
96.
Banks should not disregard limit exceptions that may be considered technical breaches without
proper review and escalation. Technical breaches – ie breaches caused by bad data, incorrect
mapping or similar issues – should be subject to exception approvals that are sized appropriately
to allow for meaningful limit monitoring while the root cause of the breach is remediated.
97.
Passive breaches of counterparty credit limits – ie breaches caused by changes in MTM, not
position changes – should require the same review and challenge as active breaches.
98.
Risk limits should be set based on the risk tolerance level established by the designated risk
committee within the bank. The risk committee should be represented by senior management,
including senior risk officers. Risk committees members should have the ability to mandate
decisive actions to reduce risk even when there are disagreements with the business units.
99.
At the counterparty level, risk limits should be set at levels consistent with the bank’s assessment
of the counterparty’s credit quality, the degree of transparency the bank has on the
counterparty’s overall financial condition and leverage, and the bank’s ability to effectively
unwind the counterparty’s portfolio in a timely manner in the event of counterparty default.
100.
Banks monitor exposures against established risk limits at least on a daily basis. In addition, banks
are encouraged to develop a framework for intraday exposure monitoring that can provide early
warning of material developments in counterparties' portfolios and mitigate the risk of a breach
of relevant risk limits. For transactions with material risk impact, banks should be able to estimate
20
Guidelines for counterparty credit risk management
in a timely fashion whether a new transaction could potentially lead to a breach of the applicable
limit and consider controls to mitigate the occurrence of a breach and the size of the breach.
101.
Banks with sound practices can estimate intraday the potential impact of large market moves on
limit utilisation, at least for clients with large portfolios in terms of potential adverse market
moves and for clients that are most prone to a downgrade in creditworthiness. Furthermore,
banks are encouraged to keep pace with technological developments and improve their exposure
monitoring framework such that an intraday exposure calculation is performed wherever
technically feasible and adequate for a better risk mitigation.
102.
Banks should have a clear and actionable strategy for de-risking exposure in case of limit
breaches. Furthermore, these procedures should also be actionable during phases of high
volatility and illiquidity.
103.
Banks may set early warning indicators when limit utilisations increase significantly or are elevated
but do not yet result in limit breaches. Early warning indicators can promote proactive
management of risk and help a bank take early actions when warranted to mitigate risk.
7.
Infrastructure, data and risk systems
Timely, accurate and reliable counterparty infrastructure, data and risk systems are necessary for sound
management of CCR, as outlined in and reinforced by Principles for effective risk data aggregation and risk
reporting. 17 All aspects of CCR are affected by the quality of the data, systems and aggregation capabilities
used by banks to manage their risks. This includes, for example, information collection that feeds into due
diligence, the digitisation of key contractual terms governing the adequacy of credit risk mitigants, the risk
metrics used to size counterparty exposure, and the information and reporting needs of not only senior
management but also traders and credit officers involved in the day-to-day risk management of CCR.
104.
Banks should ensure that the risk systems (eg front office, valuation and booking systems, and
risk engines) and data management capabilities underpinning CCR management – including risk
measurement and limit monitoring – are commensurate with the size and complexity of
counterparty exposures. Systems, models and data management capabilities should be sound
and sophisticated enough to support CCR measurement under current and stressed market
conditions, and they should be enhanced as the bank’s risk profile evolves and newer sound
practices are established.
105.
CCR measurement is a highly involved risk data aggregation process given the complexity of
calculations and processes. It is best exemplified by reliance on large internal and external data
sets, numerous upstream data systems and platforms, and interdependent models involved in
risk measurement. The complexity of these processes requires commensurate capabilities and
controls that ensure comprehensive, granular, accurate and timely risk metrics. The inability to
produce fit-for-purpose risk metrics that meet these critical data dimensions can have a negative
impact on a bank’s ability to effectively measure, monitor and control CCR given the highly
dynamic nature of trading book exposures.
106.
Banks should ensure that key risk systems have minimal frictions that would impede
comprehensive, accurate and timely risk data aggregation and measurement. Where necessary,
they should implement adequate compensating processes and controls, such as data staging
platforms to mitigate known shortcomings. Banks should aim to reduce the number of systems
17
See BCBS, Principles for effective risk data aggregation and risk reporting, January 2013.
Guidelines for counterparty credit risk management
21
involved in exposure measurement and management in order to reduce operational risk. They
should allocate adequate resources to implementing the required upgrades to capabilities where
deemed necessary, ie commensurate with the business model and risk profile. Banks with sound
practices maintain capabilities to aggregate and measure risk exposures seamlessly across
products, businesses, geographies and risk factors to support concentration monitoring at both
the counterparty and portfolio levels.
107.
Banks should ensure that the data management protocols, processes and controls underlying
counterparty risk data aggregation and measurement are aligned to enterprise/bank-wide data
management frameworks and standards in order to ensure comprehensive, accurate and timely
risk monitoring. Banks with sound practices have consistent data taxonomies across businesses
that align with enterprise classifications to ensure, for instance, that the risk metrics estimated by
different systems are aggregated accurately and conservatively. Further, stronger practices entail
data issue/incident remediation processes for counterparty risk measurement that are directly
linked to bank-wide processes in order to ensure strategic, long-term solutions for system and/or
data issues.
108.
Banks should ensure that reporting and oversight routines provide key stakeholders with
sufficient information about the overall effectiveness of counterparty risk data aggregation and
measurement processes. These insights ultimately ensure that end users of risk metrics and
reports – eg credit risk officers and front office traders – make informed risk appetite decisions
at the desk, counterparty and portfolio levels. Such decisions include the approval or restriction
of new trades and the implementation of risk mitigation or reduction strategies. The socialisation
of known and identified issues with stakeholders and/or end users of reports and metrics is critical
to maintaining and strengthening risk aggregation and measurement processes, including
receiving sufficient resources, ie “buy-in”, to remediate issues and implement system/capabilities
upgrades. Material issues and weaknesses should also be escalated to relevant bank-wide
technology and data management forums for awareness and effective resolution.
109.
Strong governance practices are grounded in sound preventative, detective and corrective
technology and data quality controls that facilitate the identification, monitoring, escalation and
remediation of system, data and model issues. Banks with sound practices maintain a suite of
controls to support counterparty risk data aggregation and measurement, including:
22
a.
robust preventative and detective controls to identify data anomalies for all key or material
counterparty risk metrics used to constrain risk-taking at the portfolio, desk and counterparty
levels, ie not limited to a select few metrics;
b.
key controls that include data reconciliation and variance analysis processes that efficiently
build on each other as opposed to creating control redundancies;
c.
a robust process to monitor data feed transfer from upstream systems to data staging
platforms and risk engines, underpinned by well documented service-level agreements that
are strictly enforced and monitored. Data feed management processes and other relevant
technology controls are not executed and managed in a silo by a technology and/or
operational team, but are instead integrated into counterparty risk measurement
governance and control frameworks;
d.
a robust process to manually adjust missing or incorrect data identified via technology, data
reconciliation and variance analysis, or other detective controls. Banks with sound practices
have a metrics adjustment process that is well documented and executed through
automated capabilities to minimise operational risk. An adjustment process also addresses
data issues identified and flagged by upstream data providers;
Guidelines for counterparty credit risk management
e.
a key performance indicator (KPI) or risk indicator (KRI) framework designed and monitored
against outcomes of technology (eg data feed) and data management controls (eg manual
adjustments). The framework synthesises control outcomes to facilitate reporting to end
users, ie a “scorecard” on the overall effectiveness of the counterparty risk data aggregation
and measurement process;
f.
material issues and/or critical KPIs, including KPIs tracking the level of manual intervention
(ie data adjustments) or data feed timeliness, which are further escalated to senior
governance forums with mandates to oversee CCR. Escalation and reporting to bank-wide
management risk committees and the chief risk officer in order to facilitate awareness of the
extent to which CCR exposure is a key contributor to the bank’s overall risk profile; and
g.
forums established for the sole purpose of overseeing the counterparty risk data aggregation
and measurement processes. These governance bodies serve as the first escalation point for
system, data or model issues affecting the production of portfolio, desk and counterparty
level risk metrics. KPI scorecards, issue logs, manual data adjustments etc are all key inputs
into ongoing discussions. Participants include system/application owners, model owners,
owners of reports/metrics, end users of reports and key upstream data providers.
Counterparty credit risk reporting
110.
Banks should embrace the risk reporting practices stated in Principles for effective risk data
aggregation and risk reporting 18 with respect to their CCR reporting. All principles below should
be seen as enhancing these generally formulated risk reporting practices.
111.
Banks should regularly assess the relevance, timeliness and quality of CCR reporting. This should
include, but not be limited to, an assessment of input data quality, analysis of comments on
potential data anomalies, assessment of the frequency of reporting and ensuring adequate
socialisation of reports within key business and oversight functions. Banks should discourage
fragmented reporting environments for CCR. If the reporting environment is deemed to be too
fragmented, banks should redesign the environment without delay.
112.
Banks should set up risk reporting through appropriate MIS in order to ensure an adequate level
of CCR analysis. Adequate reporting includes aggregating the data for each decision level,
allowing for aggregation across key risk dimensions and over time periods, and enabling easy
data analysis and drilldowns on a timely basis.
113.
Banks should build up MIS so that relevant CCR data are easily retrievable at the risk factor,
counterparty and aggregate levels. Banks’ MIS should avoid overwhelming users with data, while
allowing for detailed on-request analysis by decision-makers.
114.
Banks should build an MIS for CCR reporting that is user-friendly and intuitive. Each decisionmaker should have the ability to analyse data individually, ideally without using tools outside the
MIS. Furthermore, banks should consider enabling users to comment on the most relevant CCR
measures and store these comments in the MIS. There should be an audit trail of the analysis.
115.
Banks should train their personnel in the operation of the MIS. Each user of the MIS should be
able to understand and analyse the data to a level that enables consistent and effective risk
reporting.
18
See BCBS, Principles for effective risk data aggregation and risk reporting, January 2013.
Guidelines for counterparty credit risk management
23
8.
Closeout practices
Sound management of CCR includes banks recognising the need to act quickly based on their contractual
ability to close out a counterparty when necessary, with full knowledge of all of the steps needed to initiate,
execute and manage residual impacts, including, where applicable, collateral liquidation and risk
replacement.
Watch list practices and default management protocol
116.
Banks closing out counterparties should know that the potential costs of such actions can be
high. Closeout of counterparties involves business, legal and risk staff carrying out actions
properly, as banks serving notice on counterparties should not breach legal provisions in
agreements such as the International Swaps and Derivatives Association Master Agreement, 19
the related credit support annex (CSA), 20 the International Capital Market Association’s Global
Master Repurchase Agreement 21 or the Global Master Securities Lending Agreement. 22
Liquidation of trades invariably leads to the realisation of MTM losses and the need for new
replacement trades. The costs to the bank of carrying out a closeout are material and should be
known.
117.
Banks should ensure that seasoned professionals familiar with the legal processes for carrying
out a declaration of counterparty default are able to initiate closeouts as needed. Involvement
from the legal department is critical to carrying out all aspects of a counterparty closeout. The
process should have input from credit risk and risk management more broadly. As part of the
bank’s ongoing credit monitoring process, independent credit officers should be engaged in
regular oversight of counterparties and they should maintain a watch list of any names that
require restricted or risk-reducing activity only.
118.
Banks with sound practices maintain up-to-date closeout playbooks. They carry out mock
closeout exercises to uncover potential issues in advance of an actual closeout. The mock
closeout candidate should be a name that involves more than one legal jurisdiction and,
potentially, multiple business lines. The counterparty type should vary from year to year. In the
event of a closeout, the bank’s teams should complete a post-mortem exercise following such
incidents to compile lessons learned. Any lessons learned should then be used to enhance
existing playbooks for such events in the future. The exercise should include participants from
credit, finance, legal, operations, risk and trading teams, with the following minimum objectives:
a.
All involved parties are identified and have sufficient resources to execute the closeout in
parallel with ongoing BAU.
b.
Demonstrate that relevant reporting is shared with involved functions in due time and is
complete and correct.
19
The Master Agreement is published by the International Swaps and Derivatives Association. It outlines the terms to be applied
to a derivatives transaction between two parties.
20
A CSA may accompany the Master Agreement, allowing the two parties involved to mitigate credit risk by stipulating the terms
and conditions for posting collateral to each other.
21
See International Capital Market Association, Global Master Repurchase Agreement (GMRA), 2011.
22
For example, the master agreements by the International Securities Lending Association for securities lending transacted under
a title transfer arrangement available at www.islaemea.org/gmsla-title-transfer/.
24
Guidelines for counterparty credit risk management
119.
c.
Closeout governance allows for fast and consistent decision-making by involved
management functions, and all decisions taken are in line with internal policies and
procedures and are consistent with the legal framework for the affected financial contracts.
d.
Trading capabilities that enable the orderly unwinding of positions (including experienced
traders, access to capital markets and counterparty limits) are available, and mission-critical
payments and securities transfer protocols should be designed with kill switches for manual
operation only.
Banks with sound risk management will understand that contractual terms embedded in legal
agreements can limit a bank’s ability to reduce or discontinue activity with a counterparty.
Closeout provisions should be carefully calibrated based on the bank’s assessment of
counterparty credit quality, including control and ownership. Any concession to a counterparty
regarding such provisions should be made with awareness of the bank’s need to maintain
flexibility in order to avoid the need to declare a counterparty in default.
Guidelines for counterparty credit risk management
25
Glossary
BAU
Business as usual
CCR
Counterparty credit risk
CSA
Credit support annex
CVA
Credit valuation adjustment
EE
Expected exposure
EEPE
Effective expected positive exposure
GWWR
General wrong-way risk
IA
Independent amount
IM
Initial margin
IMM
Internal models method
MIS
Management information system
MPOR
Margin period of risk
MTM
Mark-to-market
NAV
Net asset value
NBFI
Non-bank financial intermediary
PFE
Potential future exposure
RWA
Risk-weighted asset
SA-CCR
Standardised approach for counterparty credit risk
SFT
Securities financing transaction
SWWR
Specific wrong-way risk
VM
Variation margin
WWR
Wrong-way risk
XVA
X-value adjustment
26
Guidelines for counterparty credit risk management
No. 599 / June 2018
Counterparty credit risk and the
effectiveness of banking regulation
Sînziana Kroon and Iman van Lelyveld
Counterparty credit risk and the effectiveness of
banking regulation*
Sînziana Kroona and Iman van Lelyvelda,b
a
b
De Nederlandsche Bank
VU University Amsterdam
June 2018
Abstract
We investigate how counterparty credit risk influences the prices of over-the-counter CDS
contracts using confidential transaction level data for practically all Dutch trades. We
confirm our prior of a significant negative relationship between the credit worthiness of
the CDS seller and the price of the CDS contract. We find that an increase of 100 basis
points in the credit spread of the seller, decreases the price of the CDS contract by 7.2
basis points. Also, the larger the size of the CDS contract the lower the price of the CDS
contract. Finally, we find that regulatory exemptions have a statistically significant but
economically negligible impact on CDS pricing: Transactions exempted from banking
capital requirements for Credit Valuation Adjustment risk – mostly banks transacting with
non-financial institutions, sovereigns and pension funds – trade 0.14 basis points lower,
all else equal.
Keywords: OTC market, counterparty credit risk, credit default swap.
JEL classifications: G10, G12, G14, G20, G23.
*
We thank Damiaan Chen, Michiel Marck, Hiroko Matsumoto and colleagues at De Nederlandsche Bank for
their input. All remaining errors are ours. The opinions expressed in this paper are the authors’ personal
opinions and do not necessarily represent those of De Nederlandsche Bank. Corresponding author:
s.kroon@dnb.nl
1.
Introduction
Counterparty credit risk emerged to be a key contributor and driver of a significant
portion of the losses during the global financial crisis. This type of risk is characteristic to over-the-counter derivative markets, which at that time were opaque and
difficult to monitor, encouraging the build up of concentrated positions.
When Lehman Brothers defaulted in 2008, the direct effect of counterparty
credit risk (CCR) on its counterparties became visible. Concerns about systemic
defaults increased the credit spread of large dealer banks up to extreme values, even
as high as 500 basis points. Since the default of a dealer bank became a conceivable
possibility, the value of credit protection sold by these banks dropped significantly
causing losses to buyers. These losses are the materialization of Credit Valuation
Adjustment (CVA) risk, and have caused a quarter of the trading book losses of
British banks (EBA (2015)).
The financial crisis gave rise to many discussions about the large impact of
OTC derivatives markets on financial stability and systemic risk and therefore several regulatory initiatives followed. In 2009, the G20 Leaders agreed to reforms
that increase transparency and market discipline. The Dodd-Frank Act and the
European Market Infrastructure Regulation framework (EMIR) followed in the US
and Europe, respectively. These reforms introduced requirements for mandatory
clearing of standardized OTC contracts and mandatory reporting of all OTC transactions to trade repositories. As a result of these reforms, all OTC transactions in
Europe started to be reported to trade repositories (TRs) in February 2014.1
As for the capitalisation of CCR by banks, the Basel Committee on Banking
Supervision (BCBS) strengthened the banking capital requirements for the default
of a counterparty (also known as the CCR charge) and introduced a new capital
charge for the Credit Value Adjustment to ensure higher capital requirements for
non-centrally cleared derivatives. These banking risks have become two of the
highest profile risks faced by banks active in the over-the-counter financial markets.
The European implementation of the Basel CVA rules diverges from the Basel
1 Currently six TRs are in operation, namely CME Trade Repository Ltd., DTCC Derivatives
Repository Ltd., ICE Trade Vault Europe Ltd., Krajowy Depozyt Papierów Wartościowych S.A.,
Regis-TR S.A., and UnaVista Limited.
2
rules in terms of coverage. From the various types of counterparties that are trading OTC derivatives, corporates, sovereigns and pension funds have been exempted
(CRR (2013)). At the time of drafting the regulation, one of the reasons to allow for
exemptions was to avoid an increase in the price paid by these entities for the derivatives they bought. The EU implementation of the Basel CVA standard is however
“not compliant” because its scope deviates significantly from the scope covered
in the Basel Accord. The BCBS Regulatory Consistency Assessment Programme
(RCAP) findings conclude as much (BCBS (2013)).
The exemptions are, however, not expected to last forever. The European Banking Authority, for instance, notes: "Overall, the EBA is of the opinion that EU exemptions on the application of CVA charges should be reconsidered or removed,
since they leave potential risks uncaptured" (EBA (2015)). Our analysis studies
the impact of the regulatory exemptions in the CDS market and this analysis can
be useful in the policy debate on the impact of the removal of the exemptions.
Research on how counterparty credit risk is priced is scarce, and none of it uses
European data. This is due to a lack of granular data available at transaction level.
The newly available derivatives data set gathered by trade repositories allows us
to study CCR. Our paper aims to understand whether and how markets price CCR
when selling CDS contracts bilaterally. In addition, we also take a close look at
the impact of regulation on pricing for transactions with counterparties that are
exempted by the EU regulation.
We use a data panel set containing banks active in the European market in 2016
to understand whether prices of single name CDS contracts sold are influenced by
the credit risk of their seller. This would be proof that the markets price in the
CCR risk. Our empirical approach is to estimate the transaction spread of the same
single-name CDS contracts, traded on the same day, bought by the same buyer, but
sold by different sellers which differ in term of credit worthiness.
In line with previous US studies, we find that CCR is priced in the value of
credit derivatives. In our study, however, CCR has a larger impact than in the
previous studies. Furthermore, the size of the contract influences pricing; the CDS
contract trades 2.65 basis points lower if the notional increases by e1 million.
What is truly novel, is that regulatory exemptions have a significant impact on the
price of CDS contracts which trade 0.14 basis points lower than those contracts
3
with counterparties that are not exempted.
Our paper is structured as follows. In Section 2 we explain how our research
relates to the existing literature followed by an overview of the post-crisis developments in the CDS market in Section 3. In Section 4 we present the data and
hypothesis we use. In Section 5 we present the methodology, followed by the results in Section 6, robustness tests in Section 7 and, finally, conclusions in Section 8.
2.
The CDS market and counterparty credit risk
2.1.
Existing literature
There is limited but growing literature studying the effects of counterparty credit
risk on derivative markets. An early study by Segoviano and Singh (2008) on
CCR in the over-the-counter derivatives market emphasises the importance of CCR
losses and is the first to discuss policy changes that should follow the global financial crisis. Specifically for the CDS market we are aware of three publications.
Arora et al. (2012) were the first to analyse CDS transaction data obtained from
an US asset manager. They find that counterparty credit risk is priced although the
magnitude of the effect is extremely small, almost negligible in size. The authors
point out that an increase of 100 basis points in the credit spread of dealer translates
to a 0.15 basis points decrease in the price of the credit protection. Our analysis on
a much more recent, European data set, reveal a 64 times larger larger effect: an
increase of 100 basis points in the seller’s credit spread would already translate to
7.2 basis point decrease in the price of the CDS.
Du et al. (2015) analyse a granular CDS data set with US transactions and
also find that counterparty risk has an effect on the pricing of CDS contracts: 100
basis points increase in the sellers credit worthiness results in a decrease of 0.6
basis points in the CDS price. The authors also study the effect of CCR on the
choice of counterparties. Du et al. (2015) conclude that counterparty credit risk
is managed mostly by choosing the right counterparty. Their evidence shows that
dealers search for counterparties with high credit worthiness and low correlation
to the underlying of the CDS contract. In other words, buyers of protection try to
avoid wrong-way risk. They also find that transaction spreads of centrally cleared
trades are significantly lower compared to the spreads of uncleared transactions.
4
Moreover, when controlling for past trading relations and the identity of the buyer
and seller, they find that relations do not have an effect on transaction spreads.
A recent contribution using OTC CDS data as well is Iercosan and Jiron (2017).
The authors show that the execution cost of a CDS transaction can partially be
explained by the trading relationships, counterparties’ trading activity level and
trading networks. Their paper uses CDS data from DTCC as well and focuses
on analyzing the effect of counterparties’ matching and negotiation abilities on
the terms of trade of CDS contracts, under incomplete information about market
liquidity and quotes.
Hau et al. (2017) investigate the OTC FX market and find out that less sophisticated clients pay higher spreads on FX contracts. The authors make a case for
moving FX OTC trading to multi-dealer request-for-quote platforms because they
eliminate discriminatory pricing and thus introduce competitive spreads regardless
of the sophistication of the clients.
2.2.
Assumptions and background on how CCR works
Counterparty credit risk is the risk that a counterparty in a financial derivative contract will default prior to the expiration of the contract and/or will fail to make
future payments. Counterparty risk concerns both parties in an over-the-counter
(OTC) derivatives contract for all asset classes. Financial institutions, whilst making use of risk mitigation factors such as collateralisation and netting, will still be
exposed to a significant amount of counterparty risk which needs to be managed
and priced appropriately. Since the financial crisis, financial institutions have built
up their capabilities for handling counterparty risk and active hedging has also
become more common, largely in the form of buying credit default swap (CDS)
protection. Nowadays, most banks have a dedicated counterparty risk management
unit which will charge a premium to each business line to bear the counterparty risk
of a new trade, taking advantage of portfolio level risk mitigation factors such as
netting and collateralisation (Gregory (2013)). Such risk management has several
important features detailed below.
First, we do not observe the contractual terms of the CDS contracts and – similar
to other studies – we cannot study the effect of (cross asset class) netting sets
and collateralisation. We therefore maintain the assumption that collateralisation
5
cannot mitigate counterparty credit risk completely. This is especially true in times
of stress when netting and collateral is not enough to cover potential losses from
counterparty credit risk that arise from sudden increases in derivatives negative
exposures.
Second, during the time period of our data sample, central clearing of CDS contracts was not mandatory and thus not yet a feasible option to mitigate counterparty
credit risk in Europe. In our sample, only a limited number of transactions are centrally cleared – i.e. only 1% of the 20,000 transactions in our sample. In Europe,
mandatory clearing of index CDS contracts is enforced only since February 2017
and only for certain types of counterparties that are already clearing members. 2
Third, Acharya et al. (2016) show that financial institutions tend to purchase
more protection on a dealer as reference entity when exposed to that dealer through
counterparty risk. Buying a CDS contract referencing the counterparty to which an
institution has a large derivative exposure to, is the most straightforward manner to
hedge CCR. These hedges are not perfect because they introduce risk by increasing the sensitivity of the profit and loss account to other risk factors (i.e. market
risk factors) and they are generally costly to put in place. This is why in practice
CCR hedging is executed mostly by large dealers banks. Our working assumptions regarding hedging is that most counterparties do not pursue hedging CCR on
a large scale. This assumption is in line with the findings of Oehmke and Zawadowski (2017) who investigated the motivations for trading in CDS markets and the
economic function these markets perform. They find that speculative trading concentrates in the CDS market, and hedging is motivated mostly by high volumes in
bonds and CDS markets.
Fourth, another method to reduce CCR is to actively choose counterparties that
have a low correlation with the underlying of the CDS contract. For example,
an institution could actively avoid buying a CDS contract on a Dutch underlying
from a Dutch counterparty. In this way, decreasing the correlation between the
counterparty and the underlying entity increases the odds that the insurance pays
off in case the underlying actually defaults.
Fifth, counterparty credit risk can be reflected in the price of the derivative via
2 See https://www.esma.europa.eu/regulation/post-trading/otc-derivatives-and-clearing-obligation
6
the credit risk adjustment. The CVA is the difference in the intrinsic value of the
derivative that is CCR free and the derivative value when counterparty credit risk
is present. This is why the CVA is also known as the price for bearing the CCR
– it does not address CCR. In that sense, it can be seen as a premium. Only additional capital held by the institution against CVA can absorb potential losses arising
from value changes caused by changes in the credit worthiness of the counterparty.
Logically it follows that CVA losses are smaller than CCR losses.
Sixth, to diversify counterparty credit risk and limit building up large concentrated positions to one counterparty, it is common market practice to split large tickets into smaller trades and execute them with several counterparties. This means
that a counterparty will purchase a CDS contract with the same features and underlying from several counterparties at the same time or trading day. Besides avoiding
concentration risk, this type of trading behavior is also encouraged by the European
Market Infrastructure Regulation (EMIR) that requires non-financial counterparties
to maintain their positions beneath a threshold of e15 million in order to avoid
clearing and daily margining.
And finally, a method to reduce exposure to CCR is the newly available tool of
portfolio compression. In a nutshell, portfolio compression is a post-trade operation that reduces market gross notional without affecting participants’ net market
risk positions. It accomplishes this by netting out opposing trades and replacing
them with a new contract. Multilateral compression can impact counterparty credit
risk since more than two counterparts are involved and the net exposure among
them can change (D’Errico and Roukny (2017)).
3.
3.1.
Post crisis developments in the CDS Market
Standardisation of CDS contracts
With the aim to standardise the market and increase liquidity, the International
Swaps and Derivatives Association (ISDA) adjusted the standardised documentation for single name CDS contracts in its Big Bang of April 2009. Both the regular
coupon payments made by single-name CDS and the default-contingent payments
became standardised, making CDS contracts easy to compare, price, and trade.
7
The standardisation of coupon payments was achieved by the introduction of a
limited set of standard coupon rates. In combination with standard contract sizes,
these fixed the size of coupon payments, which were already paid on standard dates
(the 20th of March, June, September and December). Counterparties now settle the
differences between the appropriate premium and the chosen standard coupon rate
through an upfront payment. The final goal of having standard coupon rates and
standard contract sizes is to equalise cash flow payments.
The Big Bang also standardised default-contingent payments, harmonising the
triggers of credit events and their consequences for all CDS contracts and reducing
the scope to disagree about whether credit events have occurred. This also helped
harmonise payments for different contracts on the same reference entity, which are
now established via an auction system. Overall the Big Bang protocol ensures that
all protection sellers transfer the same amounts to the protection buyers and that all
outstanding contracts are affected by the same credit events. For a comprehensive
overview of credit default swaps, including their regulatory development we refer
to a survey by Augustin et al. (2014).
3.2.
Market trends
The notional amount of outstanding credit default swaps grew rapidly to a peak of
almost $60 trillion at the end of 2007, but then declined sharply to just over $31
trillion in the middle of 2010. Vause (2010) argues that the decline did not occur
because the CDS market lost its appeal in light of continuing market unrest because
trading volumes have continued to rise. Instead, he argues that the sharp drop in
the volume of outstanding CDS reported in the BIS statistics is due to post trade
compression of CDS transactions. This results in the reduction of the notional and
therefore the reduction of banks’ exposure to counterparty credit risk (cf. Aldasoro
and Koch (2017)).
Since 2009, CCPs also contribute to the reduction of CDS gross nationals and
therefore the reduction in CCR exposure. The table below provides an overview of
the decreasing trend of outstanding OTC CDS exposures since the financial crisis
in terms of notional and market value from 2010 onwards, as reported by the BIS.
At the end of June 2016, the level of single-name CDS notional was close to $6.7
trillion.
8
Table 1: The global OTC CDS market
Source: BIS (2016)
3.3.
Regulatory Developments
The significant losses caused by derivative portfolios led the G20 and the Basel
Committee to propose several regulatory reforms. These reforms aimed to strengthen
the resilience of the banking system and to enhance the transparency of the OTC
markets.
Banking capital reforms
The Basel Committee has strengthened the capital framework for banking institutions to increase banks’ resilience. The financial crisis has revealed new risks
that banks were not capitalising for and the need to increase capital for some of
the risks that were already addressed by the Basel framework but for which the
existent capital levels were insufficient to cover trading losses in times of financial
turmoil. The Basel Committee has therefore amended the Market Risk and Counterparty Credit Risk frameworks to better capture tail risks and asset correlations
in turbulent times. For example, the Market Risk capital charge for trading assets
has been increased three fold.3
3 To be precise, it has increased by 223% according to the Analysis of the trading book quantitative
impact study conducted by the Basel Committee (See BCBS (2009)).
9
The Basel Committee has also introduced a new risk category to be addressed
by banks with additional capital buffers: the Credit Valuation Adjustment (CVA)
capital charge. This capital charge is meant to absorb losses from a bank’s derivative book that is traded bilaterally and the market value of these books is sensitive
to the volatility of the credit spread of the bank’s counterparties. This is the market
price of counterparty credit risk. In practice, if the credit spread of the counterparty
in a derivative transaction increases then the value of the derivative decreases and
the bank needs to take the equivalent loss through their P&L account. These losses
are deducted from the bank’s shareholders equity and therefore, if the loss is larger
than the bank’s equity position, the bank would be insolvent.
Losses from CVA risk can be partially mitigated if a bank receives collateral
from its counterparties, preferably margining their trades daily. When this is the
case, then the CVA capital charge becomes very small depending on the amount of
collateral available. Derivatives that are traded via an exchange or are cleared do
not pose CVA risk because the counterparty (i.e. the clearing counterparty) does
not pose default risk for the bank and therefore it does not have a volatile credit
spread that could impact the valuation of the derivative position. Such exposures
do no attract capital requirements for banks.
The European legislation implementing the CVA capital charges for banks also
includes additional exemptions from CVA capital requirements. Derivatives transactions between banks and specified types of counterparties are exempted from
CVA banking capital charges, and these are:
• Transactions with non-financial counterparties where the notional amount of
the transactions does not exceed the e1 billion clearing threshold for credit
derivatives under the European Market Infrastructure Regulation (EMIR);
• Intra-group transactions;
• Transactions with central or regional governments and public entities owned
by sovereign entities;
• Transactions with Pension Plans. Transitional exemptions from CVA charges
are in place until 16 August 2018 and an extension is currently under discussion.
10
OTC derivatives reforms
In addition to increasing the capital charges for banks, the G20 has recommended to increase the transparency of the OTC derivative markets to prevent market
abuse and decrease systemic risk by imposing mandatory clearing and reporting
standards. There is a mandatory reporting requirement to trade repositories for all
counterparties involved in the OTC market for all OTC transactions as they occur
starting 1 July 2013.
In Europe, a clearing obligation for most categories of OTC derivatives is also
in place via the European Markets Infrastructure Regulation (EMIR (2012)). However, there is no mandatory clearing obligation for OTC single-name CDS contracts
which are in the scope of this paper. For this reason most of the single-name OTC
CDS contracts are not centrally cleared as described in the next section.
Were all the problems with the OTC derivatives markets that surfaced during
the financial crisis tackled by the post crisis reforms? Roe (2011) argues that a
broader rethink of the OTC markets is still required. He identifies an issue that
weakens market discipline of parties involved in derivatives trading because they
are not subject to the normal sequencing in bankruptcy proceedings. This enables
banks to jump to the head of the bankruptcy repayment cue in ways that secured
creditors cannot. Derivative counterparties are less concerned with credit risk because they can quickly recover their losses by liquidating collateral while all other
creditors need to wait in line in bankruptcy courts. Roe (2011) considers this a
de facto subsidy in the form of bankruptcy benefits for parties involved in derivative transactions and pleads for its repeal in order to improve market discipline and
financial stability.
4.
Data
We use data on OTC CDS transaction from DTCC, one of the six active trade
repositories. The time range runs from 1 December 2015 until 31 December 2016.
The transactions provided to us by DTCC fulfill either of two criteria: first, at least
one of the counterparts is regulated by the Dutch Central Bank or, second, the
underlying of the derivative contract is based in the Netherlands. For cleaning the
data we follow Levels et al. (2018) who build on Abad et al. (2016).
11
4.1.
Data sample
After the initial cleaning, we start with approximately 20,000 CDS transactions.4
Further filtering of the data – detailed below – gets us down to a baseline data
sample of 5959 transactions. Following Arora et al. (2012), we keep only the 5
year CDS contracts because these are the most liquid contracts; this filtering step
removes 70% of transactions. We also eliminate centrally cleared contracts, which
are only 1% of the sample, as they inherently do not have CCR and CVA risk. We
also eliminate six transactions with negative spreads because they are difficult to
explain from an economic perspective and spreads above 1000 basis points because
these companies are obviously in distress (cf. Du et al. (2015)). In addition, we
also drop transactions with missing upfront payment, currency type and recovery
rate fields because these parameters are indispensable for correctly pricing a CDS.
4.2.
CDS pricing model
To obtain our dependent variable, CDS price, we compute the CDS par spreads
using the ISDA Standard Model. This is a pricing model that allows us to compute
the par spread of the CDS contract post-trade (implemented the R package creditr
(Kane et al. (2014))). From the creditr package we used the upfront to spread transformation, taking into account the standard coupon payment, the upfront payment,
the transaction date, the maturity, the recovery rate and the currency as parameters.
The outcome of the pricing model – the CDS par spread noted as the CDS price – is
used as dependent variable in our empirical model.
Without computing the CDS par spreads it is not possible to fully understand
and analyse CDS pricing from the raw data. The coupon reported by institutions
to the trade repositories does not reflect the actual spread of the CDS contract
anymore. After the financial crisis the market has pursued standardising the CDS
contracts in the so called "Big Bang" protocol and the coupons have been fixed at
certain levels.
To settle the net present value of the coupon payments, market parties have
started to exchange an upfront payment. If the spread of the CDS contract would
be the same as the coupon chosen by the seller, then an upfront payment would
4 The cleaning steps are detailed in Levels et al. (2018).
12
not be necessary. However if the coupon level is smaller than the spread of the
contract agreed by the parties than the buyer of the CDS contract would make an
upfront payment to the seller of the CDS contract. In this case the upfront payment
is reported as a positive number. If the upfront payment is reported as negative then
it means that the buyer of CDS protection receives from the seller of protection an
upfront payment.
4.3.
Variables
The dependent variable is the CDS price and it is the par spread equivalent of the
transacted CDS contract. Figure 1 plots the distribution of this variable which
shows some clustering around 25bp, 100bp, and 500bp. Note that the distribution
of the riskiness of the seller displays similar multi-modality (cf. Figure 2). This
can be the outcome of the standardisation of the coupon payments around these
values after the financial crisis which caused market segmentation.
0
.002
Density
.004
.006
.008
Figure 1: Distribution of the CDS Price (in basis points)
0
200
400
600
CDS Price
800
1000
We follow Arora et al. (2012) and use two main independent variables. First, we retrieve the CDS spread at the end of day before the transaction date from Bloomberg.
This is our measure of the Seller Riskiness which represents the counterparty credit
risk of the seller of the CDS contract. The distribution of Seller Riskiness is plotted
in Figure 2 below. The second independent variable is the notional of the contract,
13
retrieved from our data set, to test whether the size of the contract also impacts the
price of the CDS. These two independent variables are not correlated.
0
.002
.004
Density
.006
.008
.01
Figure 2: Distribution of the CDS Spread of the Seller or Seller Riskiness (in basis points)
0
200
Seller Riskiness
400
600
.
Figure 3 below shows, first, the concentration in trading and, second, the volatility
in pricing. The bar charts at the bottom show the number of trades per week. Here a
pattern of increased trading volumes towards the end of each quarter is visible. This
pattern is caused by the standardization of the CDS starting dates on four specific
dates each year: 20th of March, June, September and December corresponding with
weeks 8, 12, 24 and 51 of the year. The distribution of prices is shown by the range
plot with varying shades of blue. The white dotted line in the middle shows the
median while the increasingly lighter shades show the different percentiles. Given
the limited number of transactions (around 6000), the number of observations is in
many of the weeks insufficient to guarantee a smooth plot. Although there is some
variation, there is no clear trend or bunching.
Finally, we include a dummy variable Exempted to study the impact of regulatory
exemptions on CDS pricing. Banks are exempted from holding capital for CVA for
transactions with corporates, sovereigns and pension funds. In our sample 26% of
banks’ total number of transactions involve such exempted counterparts. In terms
of notional, 31% of transactions are exempted.
14
0
0
200
400
600
100 200 300
Number of transactions per week
800
1000
Figure 3: Evolution of the CDS prices and number of transactions per week
2016w1
2016w14
2016w27
2016w40
2017w1
The distribution of CDS prices is shown with increasingly darker shades of blue starting at the 10th and 90th
percentile. The dashed line shows the median value.
Table 2: Summary statistics
Variables
Obs
Mean
Median
Min
Max
CDS price
Seller riskiness
Notional
U p f ront
Exempted
5,959
5,959
5,959
5,959
5,959
275
153
5,305,619
190,626
.26
153
123
3,000,000
37,506
0
0
35.5
250
-2,568,197
0
996
618
250,000,000
37,400,000
1
Note: values are in euro. Data from 1 December 2015 to 30 December 2016. CDS price is the spread of the
CDS contract, computed with the ISDA Standard Model with parameters from our data sample provided by
DTCC. Seller riskiness is the end-of-day CDS spread of the seller of CDS, from Bloomberg, the day previous to
the CDS contract transaction. Notional is the face value of the CDS contract representing the amount of credit
exposure that is insured in case of a credit event. Upfront is the payment made on the day of the transaction
in order to set the market-value of the CDS to 0. Exempted is a dummy that separates the transactions that are
exempted from capital requirements from transactions that are in scope of capital requirements.
4.4.
Hypotheses
Our main question is whether transaction spreads decrease with the credit risk of
the seller. To answer this question we pose the following three hypotheses.
Hypothesis 1: CCR is not priced. The null hypothesis is that the counterparty credit
15
risk is not priced, implying that the slope coefficient β, in regression
eq. (1) below, is zero.
Hypothesis 2: Regulatory exemptions do not influence the CDS price. To test this
hypothesis we include a dummy Exempted to distinguish among
transactions with non-exempted and exempted counterparties. Under the null hypothesis its coefficient γ in regression eq. (2) should
be zero.
Hypothesis 3: The size of the CDS contract does not influence its price. To test
this hypothesis we introduce the Notional of the contract as a control variable in regression eq. (3). Under the null hypothesis the
coefficient η should be zero.
5.
Methodology
Similar to Arora et al. (2012), we have simultaneous committed prices from multiple CDS trading banking institutions in the sample for each 5-year index CDS
for each date t in the sample. Following their methodology we can test whether
counterparty credit risk is priced using a panel regression of the price of the singlename CDS sold on the price of protection of the dealer itself at the end of the
previous day (Seller riskiness j,t−1 ). The distributions of the CDSPrice and the the
Seller riskiness are skewed so we have to scale them using a natural logarithm
function. To be consistent and allow Notional to impact the spread, we also incorporate the log normal of Notional.
Our model is in line with Arora et al. (2012) and estimates the transaction
spreads (CDS price ) on the same contract, traded on the same day t, bought by the
same buyer i, but sold by different sellers j, which are different in terms of credit
worthiness. The most basic specification is as follows:
ln(CDS price i, j,t ) = αi,t + β ln(Seller riskiness j,t−1 ) + εi, j,t
(1)
We then adapt the basic model to capture the effect of the regulatory exemptions
on the price of the CDS transaction. As mentioned before, Exempted is a dummy
variable that identifies those transactions for which the selling bank is exempted
16
from CVA capital requirements, based on the type of buyer.
ln(CDS price i, j,t ) = αi,t + β ln(Seller riskiness j,t−1 ) + γExemptedi, j,t + εi, j,t
(2)
We also run the following model specification to ensure that the results are robust.
We add the size of the contract as a control variable.
ln(CDS price i, j,t ) = αi,t + β ln(Seller riskiness j,t−1 ) + γExemptedi, j,t + η ln(Notional) + εi, j,t (3)
We use 3,595 transactions in which the selling entity is a bank. This sample translates into 1,023 panels where the same counterparty trades a CDS contract with the
same underlying on the same day. The results are shown in Table 3 with each of
the columns showing a more complete model.
We execute the Hausman test to identify whether fixed or random effects are
appropriate. The p − value is higher than 0.05 and therefore we can reject the
null hypothesis of the test according to which both type of models are appropriate.
The alternative hypothesis is that the model with fixed effects is appropriate and
the model with random effects is not. This means that panel regressions with fixed
effects are appropriate (chisq = 0.17, p − value = 0.68). Further, after executing an
F test, we can conclude that time fixed effects are not appropriate (F = 0.13632, p−
value = 0.7123). After testing the model performance with other types of fixed
effects, we find that the best option is to run a panel regression with underlying
fixed effects. Table 3 tabulates the results.
17
Table 3: Benchmark regression results with log variables: sellers are banks only
(1)
(2)
(3)
−0.0871∗∗
(0.0424)
−0.0810∗
(0.0420)
−0.0538∗
(0.0291)
Constant
5.080∗∗∗
(0.207)
5.051∗∗∗
(0.205)
−0.0806∗
(0.0417)
−0.0602∗∗
(0.0294)
−0.0609∗∗∗
(0.0163)
5.817∗∗∗
(0.332)
Observations
Number of panels
Underlying FE
r2 within
r2 between
r2 overall
3,595
1,023
Yes
0.005
0.725
0.591
3,595
1,023
Yes
0.005
0.725
0.592
3,595
1,023
Yes
0.016
0.729
0.595
Seller_riskiness
Exempted
Notional
Robust standard errors in parentheses. *** p<0.01, ** p<0.05,
* p<0.1
6.
Results
Is counterparty credit risk priced?
Our first finding is that the counterparty credit worthiness of the bank selling the
derivative contract has a significant impact on the price of the CDS price. This is
in line with earlier findings for the US.
To calculate the magnitude of the impact, we note that the level of the median
transaction spread in our sample is 153 basis points and the median credit spread
of the seller is 123 basis points. In this case the increase of the credit spread of the
seller
by
points will
h 100 basis
i decrease the spread of the CDS by 7.2 basis points
(123+100) −0,0806
153X
−1 .
153
This effect, is thus 12 times higher than what Du et al. (2015) find using US data.
Arora et al. (2012) found a negligible effect using a limited data set from during
the financial crisis. By comparison, our results show that the market is currently
pricing in CCR which means that counterparties are basically charging a premium
18
to bear counterparty credit risk. Note that we are abstracting from collateral due to
data constraints.
How does the CVA regulatory capital exemption impact CDS pricing?
Our second finding is that having in place the European exemption on banking
capital requirements for OTC derivatives transacted with non-financials, sovereigns
and pension funds results in a significant and negative impact on the CDS price.
It seems therefore that the exemption functions like a subsidy, making the CDS
contract cheaper by 0.16 basis points compared to a similar contract that is not
transacted with an exempted counterparty (the coefficient can be interpreted as
follows: e−0.0602 ).
However the difference of 0.16 basis points between the same CDS contract
sold to an exempted counterparty and to a non-exempted counterpart is relatively
small. This shows that the markets price in and expect compensation (in the form of
risk premium) to bear the CCR regardless of whether they have to hold capital for
CVA or not. This is in line with the assumption that markets price in all available
information.
Does the size of the contract influence pricing?
We find that the size of the contract, in terms of notional, influences pricing. If we
consider that the mean notional of the contracts in our sample is e3 million and
that the mean CDS price is 153 basis points then our results can be interpreted as
follows: the CDS
trades 2.65 basis points i
lower if the notional increases
contract
h
by e1 million 153X (3.000.000+1.000.000)
3.000.000
7.
−0,0609
−1
.
Robustness
In our main specifications, discussed in the previous section, we focus on banks
as sellers. They are the central intermediaries in this market and face regulatory
charges in selling CDS to other banks. To examine whether our analysis is sensitive
to this sample selection, we repeat the analysis for the entire sample of 5-year
CDS contracts, including seller counterparties that are not banking institutions.
This enlarges the sample from 3,595 to 5,959 observations and it translates into
19
Table 4: Robustness test: results of regression with log variables, all types of sellers
(1)
(2)
(3)
−0.0802∗∗
(0.0367)
−0.0741∗∗
(0.0365)
−0.0396
(0.0279)
Constant
5.047∗∗∗
(0.179)
5.017∗∗∗
(0.178)
−0.0736∗∗
(0.0361)
−0.0437
(0.0278)
−0.0590∗∗∗
(0.0115)
5.759∗∗∗
(0.252)
Observations
Number of panelID
Underlying FE
r2 within
r2 between
r2 overall
5,959
2,138
Yes
0.003
0.589
0.517
5,959
2,138
Yes
0.003
0.589
0.517
5,959
2,138
Yes
0.006
0.597
0.521
Seller_riskiness
Exempted
Notional
Robust standard errors in parentheses, *** p<0.01, ** p<0.05,
* p<0.1
2,138 panels where the same counterparty trades a CDS contract with the same
underlying, repeatedly, during the same day.
In the robustness test the significance of the coefficient of Exempted disappears.
This could be explained by the fact that the sample is extended to sellers that are
not banks which are also not influenced by banking capital requirements for CVA
when trading among themselves. However the interpretation that the market prices
in CCR even when there is a regulatory capital exemption remains valid.
All other coefficients preserve their significance as in the benchmark specification. The relationship between the sellers’ credit worthiness and the CDS price
remains significant and has a similar effect in terms of magnitude. The size of the
contract continues to have an impact on the CDS price, similar in magnitude as in
our benchmark specifications.
20
8.
Conclusions
We have examined CDS pricing with a particular focus on whether the seller’s
credit worthiness is a relevant factor. For this analysis we have collected a unique
data set including almost all single name CDS trades of all Dutch entities. In
addition we have all trading of any European entity if the underlying reference
entity is domiciled in the Netherlands. Using the roughly 200,000 daily positions
we filter out those transactions where the buying party is transacting multiple times
on the same day with multiple sellers. Since the buyer, the underlying, and the time
are the same we can isolate the effect of the seller’s riskiness on the prices recorded.
We find that the counterparty credit risk of the seller is a significant factor in determining the price of credit derivatives contracts. Moreover, we find a markedly
larger impact compared to studies conducted on US data.
From a policy perspective, our research can inform our thinking on the benefits of mandating central clearing-houses for CDS contracts. In practice, central
clearing of credit derivatives reduces CCR risk, but it was uncertain whether CCR
was a large concern for the markets by looking at previous studies. We show that
CCR has a material impact on credit derivatives sold by banking institutions and
therefore the possibility to clear single-name CDS contracts could be considered
beneficial.
We also show that the regulatory CVA exemption in the EU has a significant
but very low impact on CDS pricing. This proves that the markets expect a risk
premium to bear CCR regardless of regulatory capital exemptions present in the
European regulation. From a policy perspective, is it then prudent to continue to
exempt banks from capital for CVA risk when markets already price it in the value
of CDS contracts? This can lead to unintended consequences of regulation in the
financial markets. Specifically, it can create preferential asset classes and increase
risk taking with counterparts that are exempted.
A third conclusion of our analysis is that the size of the CDS contract influences
pricing. We find a significant price discount for higher volume and potentially to
compensate the credit protection buyer for concentration risk. The larger the CDS
contract in terms of notional the smaller the price. In practice this means that the
CDS seller will give the buyer of credit protection a discount if he purchases a lar-
21
ger contract. This can be motivated by the fact that with a larger contract the buyer
would increase exposure to the seller and therefore increase their concentration
risk.
All in all, this entire analysis was possible due to the G20 reforms on OTC derivatives. These reforms have increased the transparency of this previously opaque
market and gave both market parties and regulators access to an impressive amount
of financial transaction data.
22
Perspective
27 Jun 2024
10 minute read
Strengthening banks’ Counterparty Credit Risk
(CCR) management practices to meet increasing
supervisory expectations
Authors: Margarita Streltses
David Strachan
 Print




David Cowen
At a glance
It is no secret that policymakers globally are increasingly concerned
about the growing financial risk outside the banking system. This has
resulted in a large number of global, regional and national regulatory
workstreams targeting the resilience of non-bank financial institutions
(NBFIs) which we analysed in a previous article.
Many of these workstreams remain work in progress. In the meantime,
supervisors continue to emphasise the key role that the robustness of
banks’ counterparty credit risk (CCR) management practices plays in
reducing the perceived risk stemming from NBFIs.
CCR has been singled out in the latest ECB  and PRA  supervisory
priorities, the FCA wholesale bank portfolio letter, and the PRA “Dear
CRO” letters on fixed income financing  and private equity related
financing activities .
The ECB  and the BCBS  have also published guidelines for CCR
management including on governance, due diligence, risk
measurement and stress testing which supervisors will benchmark
banks against.
Supervisors are concerned that banks have not acted quickly or
effectively enough to improve risk management and controls in
response to previously identified weaknesses in CCR management.
Time is now running short for banks to act before supervisors start to
intervene even more forcefully to address what they perceive in some
cases as ineffective remediation.
We have analysed the PRA, FCA, ECB and BCBS expectations on CCR
management and identified five priority areas which feature in many
of them, indicating that supervisors around the world are thinking
about the risk issues along similar lines.
Banks should be looking to improve their CCR arrangements not only
to contend with rising supervisory expectations, but to position
themselves to weather storms better in an environment of increased
funding costs, tighter financing conditions, and increased volatility.
The deficiencies identified by the supervisors may be more acute for
smaller banks with more limited risk management resources.
Identified leading practices are also relevant for firms outside the
banking sector which are exposed to CCR.
In the analysis we set out below we discuss the key weaknesses
identified by supervisors in banks’ CCR management practices and
what they expect banks to do to remediate them. Banks should
consider performing a gap analysis against supervisory expectations.
The PRA has already mandated a gap analysis in its “Dear CRO” letter
on private equity related financing activities. The analysis and
remediation plan for any identified gaps are due for submission to the
PRA by the end of August 2024. Where gaps are identified, supervisors
expect banks to do a read-across to other relevant business areas
where similar gaps may exist.
Introduction
After 15 years of substantial growth, NBFIs account for c50% of UK (and
1
global) financial sector assets, while the framework for identifying any
systemic risks that NBFIs may pose to financial stability and the toolkit that
regulators have for responding to them are much less developed than for
banks. Banks and NBFIs are deeply interconnected – through loans,
securitisations, derivatives, and funding relationships. According to ECB
2
estimates, around 20% of euro area banks’ funding is provided by NBFIs .
NBFIs are also an essential driver of profitability. Prime brokerage, for
instance, accounted for more than half of the revenues from banks’ equities
3
businesses in 2023 .
Whilst policymakers around the world are progressing various workstreams
targeting NBFI resilience, supervisors continue to emphasise the important
role that banks’ play in maintaining financial stability through ensuring the
robustness of their CCR management practices. Fundamentally, most banks
get the basics of CCR right, consistent with what is required by the Capital
Requirements Directive (CRD) and by the Capital Requirements Regulation
(CRR). However, as laid bare by various market shocks, supervisors expect
banks to develop their CCR frameworks and associated capabilities to build
additional resilience against market shocks and tail events.
We have taken stock of the key messages about the deficiencies identified by
the supervisors and their expectations for improvement. We have then
identified five areas common to the PRA, FCA, ECB and BCBS publications
where banks can expect increased supervisory scrutiny. These five priority
areas are:
Counterparty due diligence, including an ability to distinguish
between different types of exposure and understand correlations and
concentrations among clients.
Governance and risk management, where the Board should
consider CCR exposures in setting the business strategy and satisfy
itself that the scale of those exposures is consistent with the overall
risk profile of the bank.
Risk measurement and risk appetite, and how banks need to
overcome the challenges of capturing, combining and measuring all
aspects of CCR.
Stress testing, where banks need to incorporate a wider range of
stresses into their stress testing and evidence how they use the results
to inform their business and risk management decisions.
Data and reporting require banks to invest in capabilities which
enable them to identify and aggregate CCR exposures and overcome
the difficulties of often fragmented systems in different business lines
and legal entities.
Below we investigate these areas in greater detail.
Five areas for improvement
1. Counterparty due diligence
Supervisory expectations
Improve customer due diligence and understanding of client business
profiles and extend enhanced principles to all client types.
In an environment where banks’ exposure to a wide variety of NBFIs is
growing in complexity, the ECB, the PRA and the FCA have all noted that
banks should improve their customer due diligence and understanding of
client business profiles to distinguish better between different types of
exposures and understand correlations and risk concentrations between
clients. For example, following the LDI crisis in the UK, the PRA expects banks
to differentiate between mandated and pooled LDI funds, with distinct onboarding procedures for each.
In the past, in response to supervisory requirements, banks have been
improving due diligence processes for specific types of counterparties, such
as hedge funds in prime brokerage business. However, the PRA is very clear
that banks should extend enhanced due diligence principles, client
disclosure standards and CCR management controls to all client types in all
relevant trading businesses.
Consider non-financial risk factors.
In assessing the riskiness of a counterparty, supervisors expect banks to
look beyond financial metrics and consider non-financial risk and other
qualitative metrics such as the quality of clients’ disclosures and their
reliance on third parties for the provision of critical services. A more
conservative approach to risk management may be needed for
counterparties which underperform in these categories.
Ensure continuous due diligence.
The BCBS draft guidelines emphasise that due diligence obligations do not
end with onboarding a counterparty and should be continuous,
incorporating information about material counterparty developments. Any
material change in a counterparty’s leverage or risk profile should trigger a
revised assessment. Specifically, in the case of NBFIs, ongoing due diligence
should ensure that they have sufficient shock absorbing capacity and
appropriate risk policies, procedures, and controls.
Challenges and leading practice
Enhanced client on-boarding can be achieved through a deeper
understanding of the economics of the underlying exposures and of the key
drivers of counterparties’ performance. Banks can also improve the
granularity of on-boarding processes and analysis of the inherent riskiness
of underlying trades including directional market risk. To achieve this, banks
need to consider excessive leverage or concentration risk, and idiosyncratic
and wrong way risk (WWR). Most importantly, the information gathered
during due diligence should feed directly into CCR decisions, including risk
ratings, limits, contractual terms such as margin requirements and collateral
haircuts, as well as risk mitigants.
The BCBS consultation suggest that banks should request additional
disclosures from complex counterparties which could carry a higher risk,
such as details of portfolio compositions, use of leverage, value-at-risk
metrics, or stress test results. Obtaining such information could be
challenging if counterparties are not willing to disclose this data due to its
proprietary nature and equivalent data is not available through a third party.
If this information is not available, banks could consider the use of
additional risk mitigation measures.
Ensuring a common set of onboarding procedures for a particular type of
counterparty across all the business units and legal entities of a banking
group can also be complex and time-consuming. Similarly challenging is to
differentiate adequately between the on-boarding procedures for different
types of counterparties. To solve both of those challenges banks may need
to enhance the capacity and capability of front office and risk management
teams.
2. Governance and risk management
Supervisory expectations
Build a dedicated CCR strategy and management framework.
Supervisors expect banks to have a dedicated CCR strategy and
management framework across all three lines of defence (LoD) with welldefined responsibilities and reporting lines, approved by the Board. Most of
the deficiencies identified by the supervisors relate to a lack of collaboration
across the CCR management function, limited CCR coverage and siloed
thinking.
Challenges and leading practice
Even in some more sophisticated banks with dedicated CCR teams in the
1LoD, the ECB found insufficient capacity to ensure full coverage of all
relevant counterparties. In the 2LoD, dedicated CCR teams in more
advanced banks have specialist knowledge of both market and credit risk
while in less advanced institutions CCR risk managers rely on separate
market and credit risk teams.
CCR is also often embedded within the wider credit risk function and may
not be recognised as a distinct risk type.
In the 3LoD, internal audits often tackle CCR from the perspective of
individual business units, with only a few more sophisticated banks with
internal model permission or extensive derivatives businesses having
adopted a more holistic approach to CCR assurance work.
In assessing CCR governance, the ECB found only few banks had a specific
CCR governance committee or dedicated fora to discuss CCR topics across
business lines. In most banks CCR is generally discussed monthly or even
less frequently and often in conjunction with general credit risk topics. Only
a few banks have dedicated CCR MI, usually as part of credit risk reporting,
and the various elements of CCR can be scattered across several reports.
To satisfy increasing supervisory expectations, banks need to ensure
adequate coverage of all relevant counterparties across all business lines
and develop a holistic view of CCR. This view needs to be consistently
reflected in credit and market risk assessments to evaluate the overall risk to
the bank. Firms with material or complex CCR exposures should have a
dedicated CCR resource in both the 1LoD and 2LoD. The 3LoD should assess
CCR processes and governance across business lines, legal entities and
jurisdictions.
Banks should focus on breaking up siloes in CCR management and ensure
that all the relevant risks are factored in before taking risk management
actions. Boards should also play an active role in CCR governance by
considering CCR exposures in business strategy decisions and ensuring
aggregate exposures are in line with risk appetite. Boards should satisfy
themselves that the scale and composition of CCR exposures are
appropriate in the context of the overall risk profile of the bank.
3. Risk measurement and risk appetite
Supervisory expectations
Develop exposure metrics to capture all aspects of CCR.
The ECB has identified substantial room for improvement with regards to
risk measurement. Supervisors expect banks to develop exposure metrics
that will capture CCR across all products, business lines and legal entities,
thereby providing a holistic view of the totality of CCR exposures.
The BCBS draft guidelines note that CCR metrics, supported by a clear and
actionable taxonomy, should account for instances when perceived risk
mitigants, or diversification benefits, may not work as intended. Whilst
focusing on the holistic understanding of CCR, banks should also be able to
identify, evaluate and capture idiosyncratic risks properly and understand
their effect on portfolio correlations and risk concentrations.
Improve the measurement of CCR portfolio wind-down cost.
Banks are also expected to measure the costs of CCR portfolio wind-down
more accurately. While supervisors regard the use of the regulatory margin
period of risk (MPOR) as a useful tool, they do not see it as sufficient to
account for all such costs and expect banks to develop complementary
measures. These should take into account the impact of a netting set winddown on hedging positions with other counterparties and reflect potential
additional market risk losses from any unmatched hedging positions. This is
particularly relevant for less liquid collateral or hard-to-replace transactions.
Challenges and leading practice
One of the challenges for banks is developing tools for measuring CCR which
capture and combine all elements of the risk, including credit and market
risk, at the portfolio, counterparty, and individual risk factor level. Use of
Monte Carlo Simulation models to determine counterparty exposure profiles
is computationally intensive and often requires the use of simplifying
assumptions for modelling the underlying risk factors. Breaking down
portfolio or netting set level metrics to individual trade level for more
granular analysis can also require the use of approximations.
Another challenge is to consider risk appetite comprehensively for CCR at
counterparty and portfolio level. The ECB found that the level of detail for
risk appetite policies varies between banks. Some banks explicitly mention
CCR in their risk appetite statement (RAS) but only a few banks set global
limits for CCR, general wrong way risk (GWWR) or specific wrong way risk
(SWWR). CCR is often embedded within the risk appetite and metrics for
credit risk, which may not fully capture all the CCR specific risks.
GWWR can be particularly challenging to identify and quantify, especially if it
arises only in certain tail market scenarios. Banks may need to invest in highquality scenario analysis of credible severity to model it accurately. Sound
assessment of SWWR will likely require well-resourced and experienced
teams across both 1LoD and 2LoD making the correct assessments on a
case-by-case basis using their knowledge of the counterparty and its
business model gained through the onboarding process and ongoing due
diligence. Such practices need to be well-defined and documented with the
responsibilities across 1LoDs and 2LoDs clearly delineated.
Exposure metrics, such as potential future exposure (PFE), should be
complemented with additional metrics calibrated to periods of stress to
capture residual and tail risks better. This is particularly relevant in the case
of overcollateralised portfolios with highly leveraged counterparties, where
the PFE and regulatory exposure may point to low or non-existent exposure,
but where residual risk may be significant. Stress testing and scenario
analysis (see section 4) can provide important complementary insights into
the risk profiles of specific counterparties and can help identify GWWR.
4
In addition, the ECB has also noted that banks using the internal model
method (IMM) for calculating the CCR need to consider if their models are
sufficient to cover all aspects of CCR risk. The ECB expects banks to apply a
“risk not in effective expected positive exposure” (RNIEPE) add-on for the
risks that are not adequately captured as part of IMM exposure value.
Banks should set the risk appetite for CCR distinctly in policies and RAS,
differentiating by exposure and counterparty type, client rating and
potentially other terms of business. Risk management frameworks need to
be dynamic and able to absorb non-standard inputs, such as the outcome of
a non-financial risk assessment.
4. Stress testing
Supervisory expectations
Incorporate new and broader stresses into CCR stress testing
framework.
The CRR requires banks to incorporate CCR into their stress testing
frameworks. However, supervisors do not consider these practices to be
sufficiently developed, especially with regards to exposures to high-risk
counterparties vulnerable to tail risk events and potential close-out risk.
Supervisors expect banks to incorporate new and broader stresses into their
CCR stress testing framework. These stress scenarios should leverage
lessons learned from various market events and a better understanding of
client profiles, including their vulnerability to market shocks via WWR,
leverage and maturity mismatches, and their potential exposure to tail
events. Risk managers should challenge themselves to consider risks that
were previously deemed improbable including hypothetical geopolitical and
natural disaster scenarios and apply market shocks simultaneously to trades
and collateral. Stress tests should be granular enough to capture exposure
to material risk factors and idiosyncratic risk.
Ensure decisions take account of the outcomes of stress testing.
Supervisors also focus on the prominence of stress testing for risk
management processes and decision making. The ECB found that a few
banks do assess stress testing results, but none use this information as a
mandatory call for action. Supervisors expect banks to integrate stress test
results fully into their risk management processes and use them when
setting business terms and margin requirements. This is especially relevant
for exposures to NBFIs for which “stress testing may be the only systemic
5
approach to identify and quantify main portfolio vulnerabilities” .
Challenges and leading practice
The ECB highlighted establishing a comprehensive stress testing programme
for CCR as one of the key challenges for banks. Although the majority of
banks conduct regular stress testing at a portfolio and counterparty level,
only half of the reviewed banks regularly use risk factor-specific stress tests
to identify vulnerabilities in their CCR portfolio.
Performing regular stress tests at different levels of aggregation (portfolio,
counterparty, risk factor) requires high quality data and systems
infrastructure to provide timely and actionable insights into counterparties’
risk profiles. In the case of NBFI counterparties, there may be a lack of
historical loss data, as trading with these counterparties may be relatively
recent. A clear and documented stress testing framework should be
implemented consistently across business lines and the frequency of stress
testing should be continually revised to reflect material changes in the risk
environment.
Leading practice includes performing a number of separate CCR stress tests
at different frequencies (daily, monthly, quarterly, annually) and with
different stress scenarios and shocks. In the absence of historical data on
periods of stress and losses, banks should determine forward-looking
hypothetical stress scenarios. Some banks use daily stress testing to set CCR
limits for 1LoD trading desks at an individual counterparty level. The nature
of each stress test should complement the others, and the assumptions and
limitations of each stress test should be clearly communicated to senior
management.
5. Data and reporting
Supervisory expectations
Ensure a holistic approach to CCR reporting.
CCR reporting is subject to general risk reporting and risk data aggregation
standards, first outlined in the BCBS principles for effective risk data
aggregation and risk reporting (BCBS 239) and therefore should be timely,
accurate and of sufficient specificity. The BCBS draft guidelines are clear that
banks should avoid a fragmented reporting environment for CCR.
The PRA expects banks to flag all relevant transactions and exposure data
systematically, together with the respective collateral pledges, enabling risk
managers to identify and consolidate relevant CCR information. The
resulting CCR MI should provide a holistic view of CCR exposure, recognising
and measuring the presence of overlapping credit exposures, collateral
pledges, and financial claims where the performance and recovery values
are interlinked. Supervisors encourage additional focus on potentially
concentrated positions and illiquid collateral.
Challenges and leading practice
Building comprehensive data capabilities, overarching exposure measures,
and reporting to senior management are particularly challenging if
information is not easily transferable between different systems in various
business lines and legal entities. In many cases banks are using bespoke
technology and systems for particular business units or activities with no
alignment of data formats and metrics across the group as a whole,
resulting in a fractured CCR data landscape.
Banks should have capabilities to aggregate and measure risk exposure
seamlessly across products, businesses, legal entities, geographies and risk
factors to ensure effective monitoring of concentrations at counterparty and
portfolio level. It is important that data related controls, including over the
data feed process, are integrated into CCR governance and control
frameworks rather than being managed in silos by operational teams. A
central data warehouse with common data formats and definitions can
facilitate the aggregation of the data and the calculations required for the
different CCR metrics.
Conclusion
Policymakers are busy developing a globally consistent approach which will
consider both the idiosyncratic and systemic risks potentially posed by
NBFIs. However, until this work is complete and new rules are adopted
consistently by key supervisors around the world, banks should expect
increased supervisory scrutiny of their risk management frameworks,
particularly for more leveraged NBFI counterparties. Banks can prepare by
overhauling their CCR frameworks to improve counterparty due-diligence,
governance and risk management, risk measurement and risk appetite,
stress testing, data aggregation and reporting to address increasing
supervisory expectations.
As the growth of financial assets outside of the banking system continues, so
do banks’ exposures to a wide variety of complex, interconnected
counterparties. Banks must respond to this by investing in additional risk
management resources and infrastructure and by evolving with the
changing market environment to promote safe, sound, and sustainable
outcomes.
As we saw with collapse of Archegos, the downsides to getting CCR wrong
can verge of the catastrophic. However, getting it right has significant
upsides. A bank with sound risk management, a detailed understanding of
its counterparties and their risk profiles and a clear sense of its own
capabilities will service its clients better.
A Guide to Modelling
Counterparty Credit Risk
What are the steps involved in calculating credit exposure? What are the differences between counterparty
and contract-level exposure? How can margin agreements be used to reduce counterparty credit risk? What
is credit value adjustment and how can it be measured? Michael Pykhtin and Steven Zhu offer a
blueprint for modelling credit exposure and pricing counterparty risk.
ounterparty credit risk is the risk that the
counterparty to a financial contract will
default prior to the expiration of the contract and will not make all the payments
required by the contract. Only the contracts privately negotiated between counterparties — over-the-counter (OTC) derivatives and
security financing transactions (SFT) — are subject to
counterparty risk. Exchange-traded derivatives are not
affected by counterparty risk, because the exchange
guarantees the cash flows promised by the derivative to
the counterparties.1
Counterparty risk is similar to other forms of credit
risk in that the cause of economic loss is obligor’s
default. There are, however, two features that set counterparty risk apart from more traditional forms of credit risk: the uncertainty of exposure and bilateral nature
of credit risk. (Canabarro and Duffie [2003] provide an
excellent introduction to the subject.)
In this article, we will focus on two main issues:
modelling credit exposure and pricing counterparty
risk. In the part devoted to credit exposure, we will
define credit exposure at contract and counterparty
levels, introduce netting and margin agreements as risk
management tools for reducing counterparty-level
exposure and present a framework for modelling
credit exposure. In the part devoted to pricing, we will
define credit value adjustment (CVA) as the price of
counterparty credit risk and discuss approaches to its
calculation.
C
Contract-Level Exposure
If a counterparty in a derivative contract defaults, the
bank must close out its position with the defaulting
counterparty. To determine the loss arising from the
counterparty’s default, it is convenient to assume that
the bank enters into a similar contract with another
counterparty in order to maintain its market position.2 Since the bank’s market position is unchanged
after replacing the contract, the loss is determined by
the contract’s replacement cost at the time of default.
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If the contract value is negative for the bank at the time of
default, the bank
• closes out the position by paying the defaulting counterparty the market value of the contract;
• enters into a similar contract with another counterparty
and receives the market value of the contract; and
• has a net loss of zero.
If the contract value is positive for the bank at the time of
default, the bank
• closes out the position, but receives nothing from the
defaulting counterparty;
• enters into a similar contract with another counterparty
and pays the market value of the contract; and
• has a net loss equal to the contract’s market value.
Thus, the credit exposure of a bank that has a single derivative contract with a counterparty is the maximum of the contract’s market value and zero. Denoting the value of contract
i at time t as Vi (t), the contract-level exposure is given by
Since the contract value changes unpredictably over time as
the market moves, only the current exposure is known with
certainty, while the future exposure is uncertain. Moreover,
since the derivative contract can be either an asset or a liability to the bank, counterparty risk is bilateral between the
bank and its counterparty.
Counterparty-Level Exposure
In general, if there is more than one trade with a defaulted
counterparty and counterparty risk is not mitigated in any
way, the maximum loss for the bank is equal to the sum of
the contract-level credit exposures:
This exposure can be greatly reduced by the means of netting
agreements. A netting agreement is a legally binding contract
between two counterparties that, in the event of default,
allows aggregation of transactions between two counterparties – i.e., transactions with negative value can be used to offset the ones with positive value and only the net positive
value represents credit exposure at the time of default. Thus,
the total credit exposure created by all transactions in a netting set (i.e., those under the jurisdiction of the netting agreement) is reduced to the maximum of the net portfolio value
and zero:
More generally, there can be several netting agreements with
one counterparty. There may also be trades that are not covered by any netting agreement. Let us denote the k th netting
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agreement with a counterparty as NAk. Then, the counterparty-level exposure is given by
The inner sum in the first term sums values of all trades covered only by the k th netting agreement (hence, the i 僆 NAk
notation), while the outer one sums exposures over all netting agreements. The second term in Equation 4 is simply the
sum of contract-level exposures of all trades that do not
belong to any netting agreement (hence, the i 僆 {NA} notation).
Modelling Credit Exposure
In this section, we describe a general framework for calculating the potential future exposure on the OTC derivative
products. Such a framework is necessary for banks to compare exposure against limits, to price and hedge counterparty credit risk and to calculate economic and regulatory
capital.3 These calculations may lead to different characteristics of the exposure distribution — such as expectation,
standard deviation and percentile statistics. The exposure
framework outlined herein is universal because it allows
one to calculate the entire exposure distribution at any
future date. (For more details, see De Prisco and Rosen
[2005] and Pykhtin and Zhu [2006].)
There are three main components in calculating the distribution of counterparty-level credit exposure:
1. Scenario Generation. Future market scenarios are simulated for a fixed set of simulation dates using evolution
models of the risk factors.
2. Instrument Valuation. For each simulation date and for
each realization of the underlying market risk factors,
instrument valuation is performed for each trade in the
counterparty portfolio.
3. Portfolio Aggregation. For each simulation date and for
each realization of the underlying market risk factors,
counterparty-level exposure is obtained according to
Equation 4 by applying necessary netting rules.
The outcome of this process is a set of realizations of
counterparty-level exposure (each realization corresponds
to one market scenario) at each simulation date, as
schematically illustrated in Figure 1, next page.
Because of the computational intensity required to calculate counterparty exposures — especially for a bank with a
large portfolio — compromises are usually made with
regard to the number of simulation dates and/or the number of market scenarios. For example, the number of market scenarios is limited to a few thousand and the simulation dates (also called “time buckets”) used by most banks
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to calculate credit exposure usually comprise daily or
weekly intervals up to a month, then monthly up to a year
and yearly up to five years, etc.
SDE, we can construct either the PDS model:
or the DJS model:
Figure 1: Simulation Framework for
Credit Exposure
where is a standard normal variable and
Scenario Generation
The first step in calculating credit exposure is to generate
potential market scenarios at a fixed set of simulation
N
dates {tk} k=1
in the future. Each market scenario is a realization of a set of price factors that affect the values of
the trades in the portfolio. Examples of price factors
include foreign exchange (FX) rates, interest rates, equity
prices, commodity prices and credit spreads.
There are two ways that we can generate possible
future values of the price factors. The first is to generate
a “path” of the market factors through time, so that each
simulation describes a possible trajectory from time t=0
to the longest simulation date, t=T. The other method is
to simulate directly from time t=0 to the relevant simulation date t.
We will refer to the first method as “Path-Dependent
Simulation (PDS)” and to the second method as “Direct
Jump to Simulation Date (DJS).” Figure 2A (across, top)
illustrates a sample path for X(ti), while Figure 2B
(across, bottom) illustrates a direct jump to a simulation
date.
The price factor distribution at a given simulation date
obtained using either PDS or DJS is identical. However, a
PDS method may be more suitable for path-dependent,
American/Bermudan and asset-settled derivatives.
Scenarios can be generated either under the real probability measure or under the risk-neutral probability measure.
Under the real measure, both drifts and volatilities are calibrated to the historical data of price factors. Under the riskneutral measure, drifts must be calibrated to ensure there is
no arbitrage of traded securities on the price factors.
Additionally, volatilities must be calibrated to match marketimplied volatilities of options on the price factors.
For example, the risk-neutral drift of an FX spot rate is
simply given by the interest rate difference between domestic
and foreign currencies, and the volatility should be equal to
Figure 2 (A and B): Two Ways of
Generating Market Scenarios >>
The scenarios are usually specified via stochastic differential
equations (SDE). Typically, these SDEs describe Markovian
processes and are solvable in closed form. For example, a
popular choice for modelling FX rates and stock indices is
the generalized geometric Brownian motion given by
where ␮(t) is time-dependent drift and ␴(t) is time-dependent
deterministic volatility. From the known solution of this
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the FX option implied volatility. Traditionally, the real measure has been used in risk management modelling of future
events. However, such applications as pricing counterparty
risk may require modelling scenarios under the risk-neutral
measure.
Instrument Valuation
The second step in credit exposure calculation is to value the
instrument at different future times using the simulated scenarios. The valuation models used to calculate exposure
could be very different from the front-office pricing models.
Typically, analytical approximations or simplified valuation
models are used.
While the front office can afford to spend several minutes
or even hours for a trade valuation, valuations in the credit
exposure framework must be done much faster, because each
instrument in the portfolio must be valued at many simulation dates for a few thousand market risk scenarios.
Therefore, valuation models such as those that involve
Monte Carlo simulations or numerical solutions of partial
differential equations do not satisfy the requirements on
computation time.
Path-dependent, American/Bermudan and asset-settled
derivatives present additional difficulty for valuation that
precludes direct application of front-office models. The value
of these instruments may depend on either some event that
happened at an earlier time (e.g., exercising an option) or on
the entire path leading to the valuation date (e.g., barrier or
Asian options). This does not present a problem for frontoffice valuation, which is always done at the present time
when the entire path prior to the valuation date is known.
For example, front-office systems always know at the valuation time whether an option has been exercised or a barrier
has been hit.
In contrast, risk management valuation is done at a discrete set of future simulation dates, while the value of an
instrument may depend on the full continuous path prior to
the simulation date or on a discrete set of dates different
from the given set of simulation dates. For example, at a
future simulation date, it is often not known with certainty
whether a barrier option is alive or dead or whether a
Bermudan swaption has been exercised.
This problem presents an even greater challenge for the
DJS approach, where scenarios at previous simulation dates
are completely unrelated to scenarios at the current simulation date. As a solution to this problem, Lomibao and Zhu
(2005) proposed the notion of “conditional valuation,”
which is a probabilistic technique that “adjusts” the markto-market valuation model to account for the events that
could happen between the simulation dates.
Let us assume that we know how to price a derivative when
all information about the past is known. We will denote this
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mark-to-market (MTM) value at simulation date tk by VMTM
(tk ,{X(t)}tⱕtk), where X(t) is the market price factor that affects
the value of the derivative contract. However, the complete
path of the price factor is not known at tk. Under a PDS
approach, the risk factor is only known at a discrete set of simulation dates, while under a DJS approach, the risk factor is not
known at all between today (t=0) and the simulation date (t=tk).
The idea behind conditional valuation is to average future
MTM values over all continuous paths of price factors consistent with a given simulation scenario. Mathematically, we
set the value of a derivative contract at a future simulation
date equal to the expectation of the MTM value, conditional
on all the information available between today and the simulation date. Under the PDS approach, the scenario is given by
the set of price factor values xj at all simulation dates tj, such
that jⱕk. The conditional valuation is given by
Under the DJS approach, the scenario is given by a single
price factor value xk at the current simulation date tk. The
conditional valuation is given by
Lomibao and Zhu (2005) have shown that these conditional
expectations can be computed in closed form for such instruments as barrier options, average options and physically settled swaptions. The conditional valuation approach described
by Equations 9 and 10 provides a consistent framework within which the transactions of various types can be aggregated
to recognize the benefits of the netting rule across multiple
price factors.
Exposure Profiles
Uncertain future exposure can be visualized by means of
exposure profiles. These profiles are obtained by calculating
certain statistics of the exposure distribution at each simulation date. For example, the expected exposure profile is
obtained by computing the expectation of exposure at each
simulation date, while a potential future exposure profile
(such profiles are popular for measuring exposure against
credit limits) is obtained by computing a high-level (e.g.,
95%) percentile of exposure at each simulation date.
Though profiles obtained from different exposure measures
have different magnitude, they normally have similar shapes.
There are two main effects that determine the credit
exposure over time for a single transaction or for a portfolio
of transactions with the same counterparty: diffusion and
amortization. As time passes, the “diffusion effect” tends to
increase the exposure, since there is greater variability and,
hence, greater potential for market price factors (such as the
FX or interest rates) to move significantly away from current
levels; the “amortization effect,” in contrast, tends to
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decrease the exposure over time, because it reduces the
remaining cash flows that are exposed to default.
These two effects act in opposite directions — the diffusion effect increases the credit exposure and the amortization
effect decreases it over time. For single cash flow products,
such as FX forwards, the potential exposure peaks at the
maturity of the transaction, because it is driven purely by diffusion effect.4 On the other hand, for products with multiple
cash flows, such as interest-rate swaps, the potential exposure usually peaks at one-third to one-half of the way into
the life of the transaction, as shown in the following exhibit:
Figure 3: Exposure Profile of
Interest-Rate Swap
Different types of instruments can generate very different
credit exposure profiles, and the exposure profile of the
same instruments may also vary under different market
conditions. When the yield curve is upward sloping, the
exposure is greater for a payer swap than the same receiver
swap, because the fixed payments in early periods are
greater than the floating payments, resulting in positive forward values on the payer swap. The opposite is true if the
yield curve is downward sloping.
However, for a humped yield curve, it is not clear which
swap carries more risk, because the forward value on a payer
swap is initially positive and then becomes negative (and vice
versa for a receiver swap). The overall effect implies that
both are almost “equally risky” — i.e., the exposure is
roughly the same between a payer swap and a receiver swap.
Counterparty-level exposure profiles usually have a less intuitive shape than simple trade-level profiles. These profiles are
very useful in comparing credit exposure against credit limits
and calculating economic and regulatory capital, as well as
in pricing and hedging counterparty risk.
Collateral Modelling for Margined Portfolios
Banks that are active in OTC derivative markets are increasingly using margin agreements to reduce counterparty credit
risk. A margin agreement is a legally binding contract that
requires one or both counterparties to post collateral when
the uncollateralized exposure exceeds a threshold and to
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GLOBAL ASSOCIATION OF RISK PROFESSIONALS
post additional collateral if this excess grows larger. If this
excess of uncollateralized exposure over the threshold
declines, part of the posted collateral (if there is any) is
returned to bring the difference back to the threshold. To
reduce the frequency of collateral exchanges, a minimum
transfer amount (MTA) is specified; this ensures that no
transfer of collateral occurs unless the required transfer
amount exceeds the MTA.
The following time periods are essential for margin
agreements:
• Call Period. The period that defines the frequency at
which collateral is monitored and called for (typically,
one day).
• Cure Period. The time interval necessary to close out the
counterparty and re-hedge the resulting market risk.
• Margin Period of Risk. The time interval from the last
exchange of collateral until the defaulting counterparty
is closed out and the resulting market risk is re-hedged;
it is usually assumed to be the sum of call period and
cure period.
While margin agreements can reduce the counterparty exposure, they pose a challenge in modelling collateralized exposure. Below, we briefly outline a common procedure that has
been used by many banks to model the effect of margin call
and collateral requirements.
First, the collateral amount C(t) at a given simulation date
t is determined by comparing the uncollateralized exposure
at time t – s against the threshold value H
where s is the margin period of risk, and collateral is set to
zero if it is less than the MTA. Subsequently, the collateralized
exposure at the simulation date t is calculated by subtracting
the collateral C(t) from the uncollateralized exposure
To compute exposure at time t – s, additional simulation
dates (secondary time buckets) are placed prior to the main
simulation dates. Since the margin period of risk can be different for different margin agreements, secondary time
buckets are not fixed. This process is schematically illustrated in Figure 4, next page.
Collateral calculation requires the knowledge of exposure
at the secondary time bucket. The obvious approach is calculating this exposure by the Monte-Carlo simulation. This,
however, would result in doubling the computation time for
margined counterparties. In 2006 (see references), we proposed a simplified approach to modelling the collateral. We
used the concept of the conditional valuation approach of
Lomibao and Zhu (2005) and calculated the exposure value
J U LY / A U G U S T 0 7 I S S U E 3 7
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G L O B A L A S S O C I AT I O N O F R I S K P R O F E S S I O N A L S
C O V E R S TO R Y : C O U N T E R PA R T Y R I S K
at the secondary time bucket t – s for each scenario as the
expectation conditional on simulated exposure value at the
primary simulation date(s).
Figure 4: Treatment of Collateral at
Secondary Time Bucket
Credit Value Adjustment
For years, the standard practice in the industry was to mark
derivatives portfolios to market without taking the counterparty credit quality into account. All cash flows were discounted by the LIBOR curve, and the resulting values were
often referred to as risk-free values.5 However, the true portfolio value must incorporate the possibility of losses due to
counterparty default. Credit value adjustment (CVA) is by
definition the difference between the risk-free portfolio value
and the true portfolio value that takes into account the possibility of a counterparty’s default. In other words, CVA is the
market value of counterparty credit risk.
How do we calculate CVA? Let us assume that a bank has
a portfolio of derivative contracts with a counterparty. We
will denote the bank’s exposure to the counterparty at any
future time t by E(t). This exposure takes into account all
netting and margin agreements between the bank and the
counterparty. If the counterparty defaults, the bank will be
able to recover a constant fraction of exposure that we will
denote by R. Denoting the time of counterparty default by ␶,
we can write the discounted loss as
where T is the maturity of the longest transaction in the portfolio, Bt is the future value of one unit of the base currency
invested today at the prevailing interest rate for maturity t.
and 1{.} is the indicator function that takes value one if the
argument is true (and zero otherwise).
Unilateral CVA is given by the risk-neutral expectation of
the discounted loss. The risk-neutral expectation of of
Equation 13 can be written as
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where PD(s,t) is the risk neutral probability of counterparty
default between times s and t. These probabilities can be
obtained from the term structure of credit-default swap
(CDS) spreads.
We would like to emphasize that the expectation of the discounted exposure at time t in Equation 14 is conditional on
counterparty default occurring at time t. This conditioning is
material when there is a significant dependence between the
exposure and counterparty credit quality. This dependence is
known as right/wrong-way risk.
The risk is wrong way if exposure tends to increase when
counterparty credit quality worsens. Typical examples of
wrong-way risk include (1) a bank that enters a swap with
an oil producer where the bank receives fixed and pays the
floating crude oil price (lower oil prices simultaneously
worsen credit quality of an oil producer and increase the
value of the swap to the bank); and (2) a bank that buys
credit protection on an underlying reference entity whose
credit quality is positively correlated with that of the counterparty to the trade. As the credit quality of the counterparty worsens, it is likely that the credit quality of the reference
name will also worsen, which leads to an increase in value of
the credit protection purchased by the bank.
The risk is right way if exposure tends to decrease when
counterparty credit quality worsens. Typical examples of
right-way risk include (1) a bank that enters a swap with an
oil producer where the bank pays fixed and receives the floating crude oil price; and (2) a bank that sells credit protection
on an underlying reference entity whose credit quality is positively correlated with that of the counterparty to the trade.
While right/wrong-way risk may be important for commodity, credit and equity derivatives, it is less significant for
FX and interest rate contracts. Since the bulk of banks’ counterparty credit risk has originated from interest-rate derivative transactions, most banks are comfortable to assume independence between exposure and counterparty credit quality.
Exposure, Independent of Counterparty Default
Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this
assumption, Equation 14 simplifies to
where EE*(t) is the risk-neutral discounted expected exposure (EE) given by
which is now independent of counterparty default event.
Discounted EE can be computed analytically only at the
contract level for several simple cases. For example, expo-
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C O V E R S TO R Y : C O U N T E R PA R T Y R I S K
sure of a single European option is E(t)=VEO(t), because
European option value VEO(t) is always positive. Since there
are no cash flows between today and option maturity, substitution of this exposure into Equation 16 yields a flat discounted EE profile at the current option value:
EE*EO(t)=VEO(0).
However, calculating discounted EE at the counterparty
level requires simulations. These simulations can be performed according to the exposure modelling framework
described in the previous section. According to this framework, exposure is simulated at a fixed set of simulation dates
N
{tk} k=1
. Therefore, the integral in Equation 15 has to be
approximated by the sum:
Since expectation in Equation 16 is risk neutral, scenario
models for all price factors should be arbitrage free. This is
achieved by appropriate calibration of drifts and volatilities
specified in the price-factor evolution model. Drift calibration depends on the choice of numeraire and probability
measure, while volatilities should be calibrated to the available prices of options on the price factor.
For PDS scenarios, the same probability measure should be
used across all simulation dates (i.e., the use of spot risk-neutral measure is appropriate). In contrast, the DJS approach
does not require the same probability measure, because sce-
narios at different simulation dates are not directly connected.
A very convenient choice of measure under the DJS approach
is to model exposure under the forward to simulation date
probability measure Pt , which makes it possible to use today’s
zero coupon bond prices B(0,t) for discounting exposure:
In principle, Equation 18 is equivalent to Equation 16 and,
if properly calibrated, they should generate the same result.
Parting Thoughts
Any firm participating in the OTC derivatives market is
exposed to counterparty credit risk. This risk is especially
important for banks that have large derivatives portfolios. Banks manage counterparty credit risk by setting
credit limits at counterparty level, by pricing and hedging
counterparty risk and by calculating and allocating economic capital.
Modelling counterparty risk is more difficult than
modelling lending risk, because of the uncertainty of
future credit exposure. In this article, we have discussed
two modelling issues: modelling credit exposure and calculating CVA. Modelling credit exposure is vital for any
risk management application, while modelling CVA is a
necessary step for pricing and hedging counterparty
credit risk. ■
FOOTNOTES
1. There is a much more remote risk of loss if the exchange itself fails with insufficient collateral in hand to cover all its obligations.
2. In reality, the bank may or may not replace the contract, but the loss can always be determined under the replacement assumption.The loss is, of
course, independent of the strategy the bank chooses after the counterparty’s default.
3. Economic and regulatory capital are out of scope of this article because of space limitation. Economic capital for counterparty risk is covered in
Picoult (2004). For regulatory capital, see Fleck and Schmidt (2005).
4. Currency swaps are also an exception to this amortization effect since most (although not all) of the potential value arises from exchange-rate
movements that affect the value of the final payment.
5. This description is not entirely accurate, because LIBOR rates roughly correspond to AA risk rating and incorporate typical credit risk of large banks.
REFERENCES:
Arvanitis,A. and J. Gregory, 2001. Credit. Risk Books, London.
Canabarro, E. and D. Duffie, 2003. “Measuring and Marking Counterparty Risk. In Asset/Liability Management for Financial Institutions,edited by L.
Tilman. Institutional Investor Books.
De Prisco, B. and D. Rosen, 2005. “Modeling Stochastic Counterparty Credit Exposures for Derivatives Portfolios.” In Counterparty Credit Risk
Modeling, edited by M. Pykhtin, Risk Books, London.
Fleck, M. and A. Schmidt, 2005. “Analysis of Basel II Treatment of Counterparty Credit Risk.” In Counterparty Credit Risk Modeling, edited by M.
Pykhtin, Risk Books, London.
Gibson, M., 2005. “Measuring Counterparty Credit Exposure to a Margined Counterparty.” In Counterparty Credit Risk Modeling, edited by M.
Pykhtin, Risk Books, London.
Lomibao, D. and S. Zhu, 2005. “A Conditional Valuation Approach for Path-Dependent Instruments.” In Counterparty Credit Risk Modeling, edited
by M. Pykhtin, Risk Books, London.
Picout, E., March 2004.“Economic Capital for Counterparty Credit Risk.” RMA Journal.
Pykhtin M. and S. Zhu, 2006.“Measuring Counterparty Credit Risk for Trading Products under Basel II.” In The Basel Handbook (2nd edition), edited
by M. K. Ong, Risk Books, London.
✎ MICHAEL PYKHTIN and STEVEN ZHU are responsible for credit risk methodology in the risk architecture group of the global markets risk management department at Bank of America. Pykhtin can be reached at michael.pykhtin@bankofamerica.com and Zhu can be
reached at steven.zhu@bofasecurities.com.The opinions expressed here are those of the authors and do not necessarily reflect the views or
policies of Bank of America, N.A.
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J U LY / A U G U S T 0 7 I S S U E 3 7
Electronic copy available at: https://ssrn.com/abstract=1032522
Counterparty credit risk in OTC derivatives\ast \mathrm{F}\mathrm{L}\mathrm{O}\mathrm{R}\mathrm{I}\mathrm{A}\mathrm{N} \mathrm{B}\mathrm{A}\mathrm{L}\mathrm{K}\mathrm{E}, \mathrm{A}\mathrm{N}\mathrm{D}\mathrm{R}\mathrm{E}\mathrm{A}\mathrm{S} \mathrm{B}\mathrm{A}\mathrm{R}\mathrm{T}\mathrm{H}, \mathrm{A}\mathrm{R}\mathrm{N}\mathrm{E} \mathrm{R}\mathrm{E}\mathrm{I}\mathrm{C}\mathrm{H}\mathrm{E}\mathrm{L}, \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{M}\mathrm{A}\mathrm{R}\mathrm{K} \mathrm{W}\mathrm{A}\mathrm{H}\mathrm{R}\mathrm{E}\mathrm{N}\mathrm{B}\mathrm{U}\mathrm{R}\mathrm{G}\dagger \mathrm{D}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r} 1, 2019
ABSTRACT
We document how counterparty credit risk is priced in FX OTC derivatives. We employ a novel
dataset of dealer-specific bid-ask quotes to analyze risk pricing using the decoupling of Swiss franc
from the euro as an exogenous shock. First, the removal of the peg increased both the level of
volatility and dealers' sensitivity to volatility for the FX spot prices of all currency pairs including
the Swiss franc. Second, the exaggerations in Swiss francs induced dealers to price jump risks
in currencies similarly pegged to the euro, e.g. the Danish krone. Finally, both effects are significantly more pronounced for riskier customers, suggesting that dealers price counterparty credit
risk. Results indicate that there was a central bank-induced risk discount through credible currency
pegs.
JEL Classification: F33, G14, G15, G2
Keywords: counterparty credit risk, fixed exchange rate regime, FX swaps, Swiss franc decoupling
event, international banks
\ast For helpful comments and suggestions, we thank Hans Gersbach, Nora Laurinaityte, Steven Ongena, Jos\'e-Luis
Peydr\'
o, Christian Schlag, Maik Schmeling, Guillaume Vuillemey, Christian Wagner, Christian Westheide, and Fabian
Woebbeking, participants at the 9\mathrm{t}\mathrm{h} Workshop Banks and Financial Markets, and seminar participants in Frankfurt
and Eltville.
\dagger Goethe University Frankfurt, House of Finance, Theodor-W.-Adorno-Platz 3, 60323 Frankfurt/Main,
Germany,
B:
florian.balke@finance.uni-frankfurt.de;
andreas.barth@finance.uni-frankfurt.de;
reichel@finance.uni-frankfurt.de; wahrenburg@finance.uni-frankfurt.de
Electronic copy available at: https://ssrn.com/abstract=3498958
1
Introduction
The recent financial crisis has shown that counterparty credit risk (CCR) is one important
factor affecting the functioning of over-the-counter (OTC) markets. While there is some evidence
that counterparty credit risk is priced in the CDS market (Arora, Gandhi and Longstaff, 2012; Du,
Gadgil, Gordy and Vega, 2016), little is known about the pricing of counterparty risk in other OTC
markets.
We use a granular dataset of two-way quotes for a large number of foreign exchange (FX)
swap auctions from one of the leading electronic FX trading platforms in Europe, and exploit the
removal of the CHF-EUR currency peg on January 15, 2015 as an exogenous shock. We provide
evidence for three channels that affect the risk pricing in FX swaps. First, the peg removal led to an
exogenous increase in the volatility of spot rates for currency pairs including the Swiss franc (CHF),
which translates into wider bid-ask spreads of FX swaps for the respective currency pairs through
an increase in both inventory holding costs and costs related to CCR. Second, the decoupling of
CHF made market participants aware of a potential jump risk for pegged currencies that emerges
whenever a fixed exchange rate regime is terminated. This second channel suggests that the Swiss
National Bank's (SNB) action spilled over to the FX risk of other pegged currencies, such as the
Danish krone (DKK), and thus served as a wake-up call for repricing risks in such currencies.
Third, additional risk premiums for currency pairs including CHF or DKK are significantly larger
for riskier customers, i.e. customers with higher exposure to FX markets. The last channel provides
evidence that dealers price individual counterparty credit risk in their bid-ask spreads.
On September 6, 2011, the SNB introduced a minimum exchange rate of the Swiss franc against
the euro at 1.20 CHF. The fixed peg was removed on January 15, 2015, when the SNB Governing
Board announced the discontinuation of the minimum exchange rate, and came as a complete surprise to the market. This announcement, although in absence of any other monetary interventions,
led to a strong appreciation of the Swiss franc. As counterparties of FX contracts face margin calls
after exchange rate movements, the tremendous market adjustment on CHF strongly deteriorated
counterparties' creditworthiness, leading to defaults of many small-scale investors and brokerages
and to large losses at some major banks.1
A typical feature of derivative transactions is the regular exchange of liquid collateral to minimize counterparty risk. In fact, counterparty risk can be mitigated by the presence of collateral
as long as the collateral is kept in line with the mark-to-market value of the underlying with the
counterparty. Thus, in an OTC transaction between two the counterparties A and B, A has to post
collateral to B if the price of the underlying moves in an adverse direction. However, once the markto-market of the position changes dramatically due to a systemic event, counterparty risk might
not be fully offset. The risk of mark-to-market losses due to the deterioration of a counterparty's
creditworthiness in derivative contracts, i.e. the default risk induced by the derivative position,
or costs to mitigate such risks, such as the funding costs of collateral, are described by different
1
For example, the UK retail broker Alpari filed for insolvency just one day after the decoupling announcement
and the UK bank Barclay's lost ``tens of millions of dollars"" due to the peg removal of the SNB, see Reuters (2015).
2
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derivative valuation adjustments (XVAs).2 The decoupling of a currency from its fixed currency
regime therefore affects a counterparties' XVAs in two ways: first, a floating currency can have a
larger variance of spot prices compared to a pegged currency, which results in a higher probability
of (large) margin calls; second, the decoupling leads to a severe market movement, for example, the
CHF exchange rate temporarily appreciated by over 40\%.3 Both aspects should translate into the
pricing of FX swaps and thus, into wider bid-ask spreads of FX swaps on CHF after the decoupling.
Using the unique dataset of two-way quotes of FX swaps from a leading trading platform in Europe, we find a significant increase in bid-ask spreads of similar relative size across major maturities
for currency pairs involving CHF after the decoupling of the Swiss franc from the euro, which is
not observable for other free-floating currency pairs. The increase is economically significant with a
permanent relative spread increase of 170-350\% in the long-term, i.e. after the market turbulences
due to the event had calmed down. This spread increase is equivalent to a substantial increase in
loan margins by 5.0-7.5\%. The increase in bid-ask spreads for FX swaps on CHF can be explained
by the event impact on two cost components for which the swap dealer demands compensation.
The decoupling resulted in a larger possible range of CHF spot rates, which translated into higher
realized volatility. First, higher volatility increased the dealer's inventory holding costs, i.e. cost
form taking a non-optimal position in terms of the dealer's risk preference or risk diversification.
Second, costs related to CCR, i.e. XVAs, increased due to the higher risks of mark-to-market losses
related to the deterioration of customer's creditworthiness from the derivative position.
We provide evidence for a channel based on changes in realized volatility as one of the major
drivers behind the increase in both inventory holding costs and XVAs in CHF currency pairs.
Introducing the realized volatility interacted with a dummy variable structure similar to the applied
difference-in-differences setup into our regression model reveals the impact of volatility on the bidask spreads. Dealers became more sensitive to realized volatility and attribute a higher unit price
to volatility observed for CHF currency pairs after the decoupling event. Together with an overall
higher volatility level, dealers' increased sensitivity to volatility can explain a significant share of
the widening of the bid-ask spreads for CHF currency pairs in the permanent effect. Subsequent
to the turbulences following the CHF-EUR decoupling event, the market seems to have reached a
``new normal"", with a combination of both significantly higher prices per unit volatility along with
higher levels of volatility, and significantly increased other risk components of the bid-ask spread
for currency pairs including the Swiss franc. In order to disentangle the impact on inventory
holding costs from the impact on XVAs, we estimate the differential impact on different customer
segments using a difference-in-differences-in-differences approach. We find that customers with an
above average exposure to FX markets who should be perceived riskier by dealers in FX derivative
transactions pay substantially higher risk premiums, especially for longer maturities. Moreover,
dealers acknowledge the beneficial position of Swiss customers after the appreciation of the Swiss
franc and grant a risk discount relative to non-Swiss customers during the temporary market
2
XVAs encompass credit valuation adjustments, debt valuation adjustments, funding valuation adjustments,
margin value adjustments, and capital value adjustments. See Section 3.1 for details.
3
See, e.g., Cielinska, Joseph, Shreyas, Tanner and Vasios (2017) for a detailed description of the decoupling day.
3
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excess. Dealers are less sensitive to CRR in overnight maturities, which is in line with the common
perception of being the last risk-free domain; however, for longer maturities, XVAs explain a
significant share of the bid-ask spread increase of riskier customers.
We further find that, due to the realization of the jump risk, the SNB action had implications
over and above the foreign exchange market on CHF. In particular, the decoupling demonstrated
to market participants that any currency with a fixed exchange rate might suffer from a discrete
jump in the spot price as soon as the central bank removes the peg and induced them to reevaluate
the credibility of other currency pegs, along with their risk pricing. We demonstrate this spillover
by looking at the example of the Danish krone -- a currency that has been pegged initially to the
D-mark and then to the euro since the early 1980s and has a sufficiently liquid market in our
trading platform. We observe a gradual widening of bid-ask spreads after the Swiss decoupling
event -- reaching an even higher magnitude than for CHF currency pairs in the permanent effect.
However, the volatility channel identified for CHF currency pairs cannot explain the spread markup of DKK currency pairs confirming an adjusted pricing of jump risks connected to a potential
decoupling from the euro. We document a counterparty risk channel similar to CHF currency pairs
with significantly higher premiums for customers with high FX exposure relative to customers with
low FX exposure. In the temporary effect, CCR seems to be even the major driver behind wider
bid-ask spreads of DKK currency pairs.
The CHF decoupling event apparently served as a wake-up call for market participants reevaluating the credibility of fixed interest rate regimes. Consequently, our results suggest that currency
pegs can result in a central bank induced risk discount in FX markets as long as market participants
perceive them as being credible.
Related literature Our paper contributes to the literature in several ways. First, we build on
various papers that describe the FX markets around the date of the CHF decoupling, with the
most notable works by Hagstoemer and Menkveld (2019), Cielinska et al. (2017) and Breedon,
Chen, Ranaldo and Vause (2018). Hagstoemer and Menkveld (2019) use the ``EUR/CHF crash""
as a natural experiment for the emergence of a market structure as dealer banks were exogenously
transitioned from not learning to learning the EUR/CHF exchange rate. Using quote streams of
eight major FX dealers, the analysis focuses on how information is revealed in decentralized markets. As a main result, Hagstoemer and Menkveld (2019) find that central dealers respond to the
full shock more quickly and their price-quote innovations are more revealing of an informational
shock contemporaneously, which is interpreted as central dealers being more informed. Cielinska et
al. (2017) use trade repository data following the EMIR regulation to analyze the trading pattern
around the CHF decoupling. The study shows that trading in the Swiss franc options market was
practically halted and that the removal of the floor introduced extreme price fluctuations in the
forward market, similar to those in the spot market. Moreover, Cielinska et al. (2017) explain that
poor underlying market liquidity conditions led to the rapid intraday price fluctuation, particularly
the limited provision of dealer liquidity in the first hour after the event. They further document a
4
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reduced level of liquidity in the longer-term, associated with an increased level of market fragmentation, higher market volatility and a higher level of collateral in the weeks following the event.
The paper by Breedon et al. (2018) focuses on the question of how algorithmic trading responds
during times of extreme events. Using data on FX transactions that allow to identify algorithmic trading, it is shown that algorithmic traders withdrew liquidity and generated uninformative
volatility in Swiss franc currency pairs in the trading hours immediately after the announcement
of the decoupling, particularly in the 30 minutes following the SNB announcement, while human
traders did the opposite. Funke, Loermann and Moessner (2015) study option-implied densities for
EUR-CHF FX options around the Swiss decoupling event and conclude that the credibility of the
Swiss currency peg somewhat decreased when the spot rate approached the minimum exchange rate
or 1.20 CHF per EUR, especially for longer maturities. However, the derived break probabilities
never significantly exceeded 50\%, and they explain that option-implied densities are not able to
predict the entire range of exchange rate realizations.
Second, we build on the literature of asset pricing in OTC markets. Duffie, Garleanu and
Pedersen (2005) and Duffie, Garleanu and Pedersen (2007), for example, provide a theoretical
model describing search-and-bargaining frictions on prices in OTC markets. These models rely on
the assumption that investors bargain sequentially with market makers and receive a lower bid-ask
spread by market makers if they have better outside options. Within this strand of literature, we
focus particularly on the theoretical pricing of counterparty credit risk. Jarrow and Yu (2001), for
example, model counterparty risk pricing of defaultable securities in a reduced form model where
a variety of shapes for the term structure of credit spreads is generated by an interaction between
market-wide risk factors and firm-specific counterparty risks. The pricing of FX swaps follows a
similar logic to the pricing of vulnerable options, as the payoff of an FX swap is equivalent to the
payoff of an FX forward. Johnson and Stulz (1987) provide a model on how vulnerable options are
impacted by the assets of the option writer and thus by CCR. We build our conceptual framework
of FX swaps subject to CCR largely on this model, as described in more detail in Section 3.2.
Third, we contribute to the empirical literature analyzing whether and to what extent counterparty credit risk is priced in OTC derivative markets. This literature so far focuses mainly on CDS
pricing, such as, for example Arora et al. (2012), who use the proprietary data of CDS transaction
prices set by 14 different CDS dealers that sell credit protection on the same underlying firm to
identify the pricing of counterparty risk. The study shows that a dealer's credit risk affects the
transaction price they receive for providing the CDS on the underlying. The magnitude of the
effect, however, is found to be very small as the swap transaction asked counterparties to provide
collateral. In addition, Du et al. (2016) use confidential trade repository data on single-name CDS
transactions to investigate whether counterparty risk is priced in the OTC market. Similar to Arora
et al. (2012), they find that the impact of counterparty risk on transaction prices is in place, but
only to a modest degree. In addition, counterparty risk is shown to have a large impact on the
choice of counterparties: protection buyers avoid making transactions with protection sellers that
have a highly correlated credit risk to the reference entities. Counterparty credit risk in FX swap
5
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derivatives has been briefly discussed in Levich (2012). This paper argues that counterparty risk
has grown among many traditional FX market participants after the 2009 financial crisis, which
has arguably resulted in an increase in the trading volume of currency futures, which standardize
counterparty risks, and a decrease in the market share of interbank currency forward contracts.
Fourth, we add to the literature on FX swap pricing that discusses a systematic pattern of covered interest rate parity (CIP) violation (Sushko, Borio, McCauley and McGuire, 2016; Du, Tepper
and Verdelhan, 2018; Cenedese, Della Corte and Wang, 2019). Du et al. (2018) and Cenedese et al.
(2019) relate this deviation to post-crisis regulatory reforms on CIP arbitrage, in particular constraints on financial intermediaries and persistent international imbalances in investment demand
and funding supply across currencies. Similarly, Borio, McCauley, McGuire and Sushko (2016)
observe that imbalances in the demand for and the supply of FX hedges are the most important
driver of CIP deviations, as banks charge a premium for offering FX hedge arising from the costly
provision of collateral. The work by Abbassi and Br\"
auning (2018) shows that FX hedging costs vary
with bank-specific characteristics. In particular, they show that banks face lower costs of dollar
hedging if they have deeper internal dollar capital markets, and a lower shadow cost of capital.
Our paper adds to this literature by exploiting the CHF decoupling as an exogenous shock
that affected the Swiss franc market as a whole rather than only individual counterparties. If
counterparty risk was priced in FX markets, we would observe an increase in average bid-askspreads across all counterparties, since the market as a whole is carrying more risk due to higher
volatility. Moreover, instead of using only transaction prices, i.e. executed quotes, we use bid-ask
spreads on the dealer-level of all quotes provided in a request-for-quote procedure. Thus, we are able
to study heterogeneous treatment effects for different customer segments in terms of exposure to
FX markets, reflecting the riskiness of a counterparty, that should result in a counterparty-specific
risk pricing of FX swaps.
2
Institutional background and data
In the empirical setup, we use the SNB announcement to decouple the Swiss franc from the
euro for identification of how counterparty credit risk is priced in FX swaps. This section describes
some institutional details of the events relevant to the CHF-EUR decoupling announcement. We
further briefly discuss the background of FX swaps and provide some descriptive statistics on our
main data of dealer-individual two-way quotes for FX swaps in various currencies on an auction-like
requester market.
2.1
SNB policy and the decoupling event
The Swiss National Bank decided to introduce a minimum exchange rate of CHF 1.20 per EUR
on September 6, 2011. The introduction of a lower bound was motivated by an acute threat to
the Swiss economy with the deflationary risk due to the over-valuation of the Swiss franc. In the
press release to this announcement, the SNB stated explicitly to buy foreign currency in unlimited
6
Electronic copy available at: https://ssrn.com/abstract=3498958
Figure 1
CHF-EUR currency peg
(\bfa ) SNB foreign currency reserves
(\bfb ) CHF/EUR exchange rate
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{v}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{r}\mathrm{e}\mathrm{d} \mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{s} \mathrm{m}\mathrm{a}\mathrm{r}\mathrm{k} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p} \mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{C}\mathrm{H}\mathrm{F}-\mathrm{E}\mathrm{U}\mathrm{R} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p} \mathrm{e}\mathrm{g} \mathrm{b}\mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n} \mathrm{S}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{b} \mathrm{e}\mathrm{r} 6, 2011 \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{J}\mathrm{a}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 15, 2015.
\mathrm{T}\mathrm{h}\mathrm{e} \mathrm{h}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{z}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{b}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{k} \mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{m} \mathrm{e}\mathrm{x}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{C}\mathrm{H}\mathrm{F} 1.20 \mathrm{p} \mathrm{e}\mathrm{r} \mathrm{E}\mathrm{U}\mathrm{R} \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p} \mathrm{e}\mathrm{g} \mathrm{i}\mathrm{n} \mathrm{P}\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{l}
(\mathrm{b}). \mathrm{F}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{n} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{s} (\mathrm{i}\mathrm{n} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{n} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s}) \mathrm{i}\mathrm{n} \mathrm{P}\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{l} (\mathrm{a}) \mathrm{d}\mathrm{o} \mathrm{n}\mathrm{o}\mathrm{t} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e} \mathrm{I}\mathrm{M}\mathrm{F} \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e} \mathrm{p}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}, \mathrm{s}\mathrm{p} \mathrm{e}\mathrm{c}\mathrm{i}\mathrm{a}\mathrm{l}
\mathrm{d}\mathrm{r}\mathrm{a}\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{s}, \mathrm{g}\mathrm{o}\mathrm{l}\mathrm{d}, \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{n} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{a}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{s}, \mathrm{s}\mathrm{u}\mathrm{c}\mathrm{h} \mathrm{a}\mathrm{s}, \mathrm{d}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{v}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} fi\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{i}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s}.
\mathrm{S}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{s}: \mathrm{S}\mathrm{N}\mathrm{B} \mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a} \mathrm{P}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{a}\mathrm{l}, \mathrm{E}\mathrm{C}\mathrm{B} \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a} \mathrm{W}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{s}\mathrm{e}
quantity in order to weaken the Swiss franc both substantially and sustainably (Swiss National
Bank, 2011b). The announcement to enforce the minimum exchange rate was confirmed by a
monetary policy assessment on September 15, 2011, stating that the SNB will maintain its total
sight deposit level at significantly above CHF 200 billion, increased from well below CHF 100 billion
in earlier 2011 (Swiss National Bank, 2011a). As a result, foreign currency reserves of the SNB
soar to a new high during September 2011 (Panel (a) in Figure 1). While this first intervention
provided enough credibility to bring back the EUR-CHF exchange rate above the minimum rate
of CHF 1.20 per EUR, an unfavorable international environment and increasing economic pressure
from the accelerating debt crisis in the euro area forced the SNB to increase their foreign currency
investments further to prevent a repeated appreciation of the Swiss franc. A level of foreign currency
reserves somewhat above CHF 400 billion kept the Swiss franc from falling below the minimum
exchange rate until late 2014, but weaknesses in the euro area economy and a weakening of the
euro against the US dollar increased the appreciation pressure on the Swiss franc again despite
a further expansion of its foreign currency investments by the SNB (Panel (b) in Figure 1). On
January 15, 2015, the SNB issued a press release, stating that the SNB discontinues the minimum
exchange rate of CHF 1.20 per euro. At the same time, it is lowering the interest rate on sight
deposit account balances that exceed a given exemption threshold by 0.5 percentage points to
-0.75\% (Swiss National Bank, 2015). The removal of the minimum exchange rate was a complete
surprise to the market, especially due to the fact that the SNB Governor and a member of the
SNB Governing Board confirmed the currency peg in mid December 2014 and three days before
7
Electronic copy available at: https://ssrn.com/abstract=3498958
the discontinuation event, respectively.4
2.2
FX swaps
FX swaps are OTC-traded instruments that combine an FX spot and an FX forward transaction
to insure the FX swap buyer against unfavorable movements in the swapped currency. At the
beginning of the swap contract, the counterparties exchange two currencies at spot prices and
simultaneously enter into forward agreements to reverse the trade at the agreed forward price on
the maturity date. As the initial exchange of notional amounts sums up to a payoff of zero, the
payoff profile of an FX swap contract is identical to an FX forward contract.
Figure 2
Foreign exchange market size
(\bfb ) Daily turnover
(\bfa ) Notional amount outstanding
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{F}\mathrm{i}\mathrm{g}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{m}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{e}\mathrm{s}. \mathrm{N}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l} \mathrm{a}\mathrm{m}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{t} \mathrm{o}\mathrm{u}\mathrm{t}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{i}\mathrm{n} \mathrm{P}\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{l} (\mathrm{a}) \mathrm{r}\mathrm{e}\mathrm{f}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{t}\mathrm{o} \mathrm{t}\mathrm{h}\mathrm{e}
\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s} \mathrm{n}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{l} \mathrm{o}\mathrm{r} \mathrm{n}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{d}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{v}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{n}\mathrm{o}\mathrm{t} \mathrm{y}\mathrm{e}\mathrm{t} \mathrm{s}\mathrm{e}\mathrm{t}\mathrm{t}\mathrm{l}\mathrm{e}\mathrm{d} \mathrm{o}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{r}\mathrm{e}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e}. \mathrm{P}\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{l} (\mathrm{b})
\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{w}\mathrm{s} \mathrm{a}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e} \mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{a}\mathrm{m}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{d}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{v}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{s} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{a} \mathrm{d}\mathrm{a}\mathrm{y} \mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{o}\mathrm{n} ``\mathrm{n}\mathrm{e}\mathrm{t}-\mathrm{n}\mathrm{e}\mathrm{t}"" \mathrm{b}\mathrm{a}\mathrm{s}\mathrm{i}\mathrm{s}, \mathrm{i}.\mathrm{e}. \mathrm{e}\mathrm{l}\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{l}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{a}\mathrm{n}\mathrm{d}
\mathrm{c}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}-\mathrm{b}\mathrm{o}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{r} \mathrm{d}\mathrm{o}\mathrm{u}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g} (\mathrm{K}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{M}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{o}, 2010).
\mathrm{S}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{s}: \mathrm{B}\mathrm{I}\mathrm{S} \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{s} \mathrm{W}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{s}\mathrm{e}, \mathrm{B}\mathrm{I}\mathrm{S} \mathrm{O}\mathrm{T}\mathrm{C} \mathrm{d}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{v}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{s} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{s} (\mathrm{L}\mathrm{H}\mathrm{S}), \mathrm{T}\mathrm{r}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{n}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{C}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{l} \mathrm{B}\mathrm{a}\mathrm{n}\mathrm{k} \mathrm{S}\mathrm{u}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{y} \mathrm{o}\mathrm{f} \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{n} \mathrm{e}\mathrm{x}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}
\mathrm{m}\mathrm{a}\mathrm{r}\mathrm{k}\mathrm{e}\mathrm{t} \mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{t}\mathrm{y} (\mathrm{R}\mathrm{H}\mathrm{S})
As managing currency risks is essential for all industries that conduct business in different
currency markets, it comes as no surprise that foreign exchange markets are globally the second
largest OTC derivatives market in terms of notional amount outstanding.5 Only interest rate
derivatives are larger in terms of notional amount outstanding accounting for about 80\% of the
OTC derivative market. However, the daily turnover of traded foreign exchange contracts is, with
around \$5 trillion, almost double as large as the daily turnover of interest rate derivatives, which,
on average, have a longer maturity.6 . Panel (a) in Figure 2 shows that shortly before the CHF-EUR
decoupling event in Q4 2014, the total notional amount of outstanding FX derivative contracts was
4
See Breedon et al. (2018) for more details about the chronology of events during the CHF decoupling.
Around 90\% of global derivatives trading takes place OTC, see, e.g., Deutsche B\"
orse Group (2019).
6
See, e.g., Bank for International Settlements (2019), Bank for International Settlements (2016a), or Bank for
International Settlements (2016b) for a detailed description of global OTC derivative markets.
5
8
Electronic copy available at: https://ssrn.com/abstract=3498958
around \$82 trillion with about 50\% coming from FX forwards and FX swaps.7 Looking at Panel
(b) in Figure 2 underlines the importance of FX swaps, as it has the largest average daily turnover
of all FX instruments followed by FX spot transactions and more than three times the volume than
FX forwards as the second largest FX derivative instrument.
The theoretical fair forward rate (or fair mid-price) of an FX forward is determined by the
no-arbitrage condition stated in the covered interest rate parity (CIP). According to the CIP,
the interest rate differential between two currencies in the cash money market should equal the
differential between the forward and spot exchange rates, as stated in the following equation (Borio
et al., 2016):
1 + rswap
F
=
S0
1 + rbase
(1)
S0 denotes the spot price on the transaction day (t = 0), expressed in units of the swap currency
per one unit of the base currency, and F denotes the forward rate corresponding to the transaction
maturity. rbase is the interest rate of the base currency and rswap is the respective interest rate of
the swap currency for the transaction maturity. Re-arranging Equation 1 yields the fair forward
rate for exchanging the base currency against the swap currency at maturity:
F = S0 \cdot 1 + rswap
1 + rbase
(2)
Two counterparties concluding an FX swap contract exchange currencies at spot rate S0 and
agree to exchange currencies back at agreed forward rate F on the maturity date. Swaps are usually
quoted as the difference between F and S0 , which is equal to the implicit rate of return of an FX
swap, i.e. F - S (Borio et al., 2016).
\biggl( SwapQuote = F - S0 = S0 \cdot 1 + rswap
- 1
1 + rbase
\biggr) (3)
Having this equation in mind, we can apply the SNB action on January 15, 2015 to swap quotes
to hypothesize the theoretical movement of the EUR/CHF FX swap quote, i.e. EUR being the base
and CHF the swap currency. First, the SNB announced a cut in interest rates on sight deposits by
0.5 percentage points to -0.75\%. This policy change usually transmits immediately to the market
rate rCHF and should therefore result in a decrease in the forward rate. Second, the discontinuation
of the minimum exchange rate of CHF 1.20 per EUR resulted in a strong appreciation of the Swiss
franc, decreasing the spot rate S0 , as indicated in Panel (b) of Figure 1. Consequently, as the
CHF
actions taken by SNB on January 15, 2015 lower 1+r
1+rEU R as well as S0 in Equation 3, we should
observe a decrease in the EUR-CHF FX swap quotes, which is similar for bid and ask quotes.8
7
The BIS Statistic Warehouse only provides aggregate figures for the notional amount outstanding, combining
FX forwards and FX swaps.
8
Apprendix A.1 describes the swap bid and ask price movements around the decoupling event in detail and
confirm this expectation.
9
Electronic copy available at: https://ssrn.com/abstract=3498958
2.3
Data
The core of our analysis builds on a unique and comprehensive dataset of FX swap auctionlike transactions from one of the largest electronic trading platforms by volume in Europe. The
auction-like process is structured as a request for quotation (RfQ) offer: the customer, i.e. the
quote requester (either a financial or a non-financial corporation), specifies the deal characteristics
including the notional amount, the swap currency pair, as well as the start and maturity date, and
then invites dealer banks, i.e. the quote providers with which they have an existing trading framework agreement, to provide a quote for the specific request. Quotes are provided in ``percentage
in points"" (pips) as two-way quotes, i.e. bid and ask quotes.9 Dealers do not know the intended
action of the customer, i.e. whether they aim to buy or sell the swap. In addition, pricing of the
swap is private information as dealers cannot see the quotes of other dealers participating in the
auction, which is similar to a sealed-bid auction. After the bidding period, customers choose the
winning quote out of the received quotes of all bidding dealers at their own discretion, i.e. there
are no rules on how to select the winning quote. Note that the quotes on the platform, whether
executed or not, reflect the true market and risk evaluation of quote providing dealer banks, as their
price offers are not influenced by the behavior and risk evaluation of other bidders or directionally
distorted by the intended action of the customer. We observe in our dataset all quotes provided by
different dealers during the auctions and can identify different dealers and customers with a unique
ID, which allows us to track them over time.
We focus our analyses on currency pairs including the Group of Seven (G7) currencies and
Australian Dollars (AUD) as another major currency by volume traded on the platform.10 These
currency pairs are complemented by their respective currency pairs involving the Swiss franc and, for
identifying spillovers to other pegged currencies, the Danish krone (DKK). Within the time period
of one year before and after the CHF-EUR decoupling event, transactions in all these currency pairs
account for 83.6\% in terms of transaction volume on the platform with an average daily turnover
of ¤15 billion, which aggregates to an annual notional amount of ¤3.66 trillion in 118 thousand
transactions between 87 quote-providing dealer banks and 236 customers, of which 67\% are banks
too. The average maturity of transacted FX swaps on the platform is 27 days. Table 1 provides an
overview of the transaction volume for our sample currencies. Not surprisingly, the largest segment
is made up of currency pairs including USD and EUR, with 70.1\% of all traded swaps including
USD as a currency and 37.4\% including EUR.11
We additionally separate different FX-swap maturities and focus only on the four most relevant
maturities based on aggregate notional, overnight (48.9\%), one month (8.6\%), one week (7.0\%),
and three months (4.6\%), thereby capturing approximately 70\% of the requests for the selected
9
One-way quotes can be requested too, but due to regulatory reporting requirements, the number of one-way
quotes is negligible and not part of the sample.
10
The G7 currencies encompass EUR, USD, GBP, JPY, and CAD. Together with AUD, these currencies are
referred to as ``major currencies"" in the trading platform.
11
Note that the platform share relates to all currency pairs on the platform and is not restricted to the G7, AUD,
CHF and DKK sample. By definition, the sum of platform shares exceed 100\% due to double counts, as for example
a EUR-USD swap counts for the USD as well as for the EUR segment.
10
Electronic copy available at: https://ssrn.com/abstract=3498958
Table 1
Currency pair segment size
Segment
USD
EUR
GBP
JPY
CHF
AUD
CAD
DKK
Total
Aggregate notional
(EUR billion)
Platform share
(\%)
3,070
1,640
975
574
442
321
244
45
3,660
70.1
37.4
22.3
13.1
10.1
7.3
5.6
1.0
83.6
\mathrm{S}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}: \mathrm{F}\mathrm{X} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}.
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{A} \mathrm{s}\mathrm{e}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{i}\mathrm{s} \mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d}
\mathrm{b}\mathrm{y} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{d} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{l}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e}
\mathrm{t}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}. \mathrm{A}\mathrm{g}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{n}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m} \mathrm{s}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{e} \mathrm{r}\mathrm{e}\mathrm{f}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{o} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{o}\mathrm{n}\mathrm{e} \mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r} \mathrm{p}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{r} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{p} \mathrm{o}\mathrm{s}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{C}\mathrm{H}\mathrm{F}-\mathrm{E}\mathrm{U}\mathrm{R} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}
\mathrm{o}\mathrm{n} \mathrm{J}\mathrm{a}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 15, 2015. \mathrm{F}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}
\mathrm{s}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{e}, \mathrm{w}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{o}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}.
\mathrm{T}\mathrm{h}\mathrm{e} `\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}' \mathrm{s}\mathrm{e}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{s} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y}
\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{l}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}. \mathrm{B}\mathrm{y} \mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}, \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{s}\mathrm{e}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{d}\mathrm{o}\mathrm{u}\mathrm{b}\mathrm{l}\mathrm{e}-\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{s}\mathrm{o} \mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{u}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{s}\mathrm{e}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{s}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{s} \mathrm{e}\mathrm{x}\mathrm{c}\mathrm{e}\mathrm{e}\mathrm{d}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} `\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}' \mathrm{s}\mathrm{e}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}.
currency pairs. The remaining requests are distributed over maturities ranging from two days to
multiple years, but not considered in the analysis.
It is important to note that even though the platform at hand is large by itself, it constitutes a
relatively small share of the entire FX swap market due to the nature of the predominantly bilateral
agreement of FX trades. The platform, however, is by no means special in terms of counterparties,
so that their pricing behavior on the platform should be representative of their FX swap pricing in
other markets and thus, our results allow for broader inference of FX derivative pricing.
3
Conceptual framework and hypotheses
Dealers are an essential element of OTC derivative markets. In a non-frictionless world, they
incur costs from trading a volatile instrument with risky counterparties, so they ask for compensation for carrying these costs by selling at a price above the fair mid-price (ask price) and buying
at a price below the fair mid-price (bid price). Following Stoll (1978) and Klein and Inglis (2001),
these costs comprise inventory holding costs, as well as costs related to counterparty credit risk
(CCR), e.g., in the form of derivative valuation adjustments (XVAs).12
Inventory holding costs are costs that the dealer incurs from taking a non-optimal position
regarding his risk-return preferences or regarding his risk diversification. According to Stoll (1978),
the dealers' holding costs depend on dealer characteristics, such as risk aversion and capitalization,
12
In addition, dealers might face order costs, i.e. physical costs incurred by processing an order, and costs due to
asymmetric information between dealers and trades resulting from an information advantage of the customer. These
two costs have a negligible role in the decoupling event we are analyzing and thus, are not further investigated.
11
Electronic copy available at: https://ssrn.com/abstract=3498958
the transaction volume, and characteristics of the underlying asset, such as volatility and holding
period. He shows that inventory holding costs, and thus the bid-ask spreads, are increasing in
volatility of the underlying asset. In addition, Jankowitsch, Nashikkar and Subrahmanyam (2011)
interpret liquidity effects as being included in inventory risk.13
CCR Costs encompass expected losses due to the counterparty's or the own default, as well
as costs incurred from mitigating CCR. In complete markets, all trades are perfectly replicable so
that there is no distinction between price-makers and price-takers.14 However, market participants
realized after the financial crisis that derivative valuation adjustment costs due to market incompleteness (XVAs) are substantial (Albanese, Caenazzo and Crepey, 2016). Thus, price-makers have
started to add XVAs to their prices both voluntary as well as in response to regulatory reforms and
capital surcharges on CCR risks.
In the following, we will describe a model that shows how various market components affect bidask quotes through an increase in counterparty credit risk. Based on this theoretical motivation, we
subsequently derive hypotheses on how the decoupling event has affected bid-ask spreads through
an increase in counterparty credit risk that we will investigate in the empirical analysis.
3.1
Derivative valuation adjustments (XVAs)
Counterparty credit risk in terms of derivative valuation adjustments (XVAs) comprise different
cost components: First, there are credit valuation adjustments (CVAs). On the settlement date of
a derivative contract (at maturity or at a margin call), a counterparty for whom the swap is an
asset is exposed to the risk of the default of the other counterparty for whom the swap is a liability
(Duffie and Huang, 1996).15 Such claims can have a material impact on the creditworthiness of
both dealer and customer if faced with a particularly large market movement (Klein and Inglis,
2001). The dealer's risk of losses from the customer's payment obligation as a consequence of the
customer's default, i.e. the expected losses due to the customer's default, are captured by CVAs.
Second, there might be losses from the dealer's default, described by debt valuation adjustments
(DVA). Third, there are CCR mitigation costs, which encompass of initial margin requirements and
variation margins that track the mark-to-market value of a derivative contract. The discounted
expected cost of funding cash collateral for margin calls is known as funding valuation adjustments
(FVA), and the cost of funding segregated collateral posted as an initial margin is known as the
margin valuation adjustment (MVA). Banks are required to hold a capital reserve to cover losses
resulting from different XVAs.16 The cost incurred to remunerate such capital reserves are an
13
This interpretation is in line with papers arguing that the bid-ask spread of OTC derivatives reflects the liquidity
of the market of the underlying instrument (e.g., Baba, Packer and Nagano, 2008), as well as with Brunnermeier and
Pedersen (2009), who conclude that liquidity and the market volatility are correlated.
14
The complete market hypothesis is assumed in many seminal asset pricing papers, such as Black and Scholes
(1973) or Merton (1973).
15
The swap becomes an asset for one party if the market price development since the last settlement date is in
favor of that party.
16
Basel Committee on Banking Supervision (2011) has introduced a regulatory capital charge to cover the risk of
expected mark-to-market losses, i.e. CVA risk, to OTC derivatives.
12
Electronic copy available at: https://ssrn.com/abstract=3498958
additional capital valuation adjustment (KVA) itself that customers are ask to pay.17 The total
valuation adjustment (TVA) of a fair derivative price is the sum of the different XVAs. The TVA
accounts for dealers' counterparty and funding risk (Cr\'epey and Song, 2016).
Albanese et al. (2016) assume that market risks are perfectly hedged by means of back-toback trades in order to focus on CCR and XVAs. In this way, the FVA and the MVA reduce
to incremental funding cost increases caused by a deterioration of dealers creditworthiness from
entering the derivative position. Moreover, as described in Albanese et al. (2016), DVAs do not
affect the determination of entry prices of derivatives as they increase the recovery rate and thus
only benefit the creditors of the dealer in the case of its default.18 Following this reasoning, the
customer's default risk, which is the basis for calculating KVAs, is the major XVA relevant for FX
swap pricing. We will next provide a theoretical motivation regarding how CVAs impact bid and
ask prices in FX swap transactions.
3.2
FX swaps subject to default risk
The payment structure of an FX swap is, after the exchange of notional amounts, similar to an
FX forward. Counterparties settle differences between the spot rate and the agreed forward rate
on a regular basis. However, in the absence of a central counterparty, the dealer bears the risk that
the customer cannot fulfill the payment obligations due to default, i.e. if the assets of the customer
are worth less than the value of the liabilities on the settlement date (Klein and Inglis, 2001). This
risk is priced by widening the bid-ask spread.
Assume in the following the simplest case of an FX swap contract where counterparties have
no intermediate settlements until maturity. Thus, after the initial exchange of notional amounts,
both counterparties hold a forward contract with a terminal settlement payment of ST - F on the
long position of the forward, with ST being the FX spot rate on maturity date T and F the agreed
default risk-free forward rate. Following the model of Johnson and Stulz (1987), if the customer
(in the case of a payment obligation) cannot make the promised payment, the dealer receives the
remaining assets of the customer with a total value of VT at time T .19 Thus, the terminal payment
of a dealer's long forward position PTlong subject to default risk is ST - F if ST - F \leq VT , i.e. if the
customer is not in default, and VT if ST - F > VT , i.e. if the customer is in default.20 The resulting
payoff profile of a long FX forward subject to a customer's default risk is shown in Panel (a) of
Figure 3, and its terminal payment of a short forward position PTshort is shown in Panel (b) of
Figure 3.
17
See Albanese et al. (2016) for a detailed discussion of the different XVA components.
Effects from a dealer's own default risk would reduce overall capital charges and are therefore explicitly excluded
by the regulator (Basel Committee on Banking Supervision, 2017).
19
Johnson and Stulz (1987) look at vulnerable options, i.e. options subject to default risk, instead of forwards.
The deterministic forward price that we are interested in can be seen as a simplification to their option pricing model.
20
The approach by Johnson and Stulz (1987) does not explicitly model liabilities other than the claim of the
considered derivative contract, which is extended by Klein and Inglis (2001). We resort to the model by Johnson and
Stulz (1987) as it is the simplest, suitable model to motivate our hypotheses. Note further that we normalize the
notional value of the forward to 1.
18
13
Electronic copy available at: https://ssrn.com/abstract=3498958
Figure 3
Payoff profile FX forward subject to counterparty default risk
(\bfa ) Long position
(\bfb ) Short position
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: PT \mathrm{d}\mathrm{e}\mathrm{n}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{a}\mathrm{y}\mathrm{o}ff, ST \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{F}\mathrm{X} \mathrm{s}\mathrm{p} \mathrm{o}\mathrm{t} \mathrm{p}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{e}, \mathrm{a}\mathrm{n}\mathrm{d} VT \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}'\mathrm{s} \mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{a}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{s} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e} T . F \mathrm{i}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{w}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{p}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{e}
\mathrm{a}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{d} \mathrm{b} \mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t} \mathrm{i}\mathrm{s} \mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d} \mathrm{t}\mathrm{o} 1.
This terminal payments of a long forward position PTlong and of a short forward position PTshort
can be written as
PTlong = ST - F + min \{ F + VT - ST , 0\} = ST - F - max \{ ST - F - VT , 0\} PTshort = F - ST + min \{ ST - F + VT \} (4)
= F - ST - max \{ F - ST - VT , 0\} = - (ST - F + max \{ F - ST - VT , 0\} )
Thus, the dealer's terminal payoff of a forward contract subject to default risk can be described
as the default risk-free forward payoff and a component conditional on the default of the customer.
We assuming, similar to Klein (1996), that asset value of the counterparty V is ans exogenous
and non-stochastic default threshold. The default risk component for the long forward position
then becomes a short position in a standard European call option on the underlying asset (S - F )
with strike price V . Analogously, the default risk component for a short forward position becomes
a short position in a standard European put option on the underlying asset (F - S) with strike
price V . F denotes the agreed (deterministic) default risk-free forward price and S denotes the
stochastic spot price. Taking this default risk of the customer into account, the risk-neutral forward
price including the default risk component CVA, F CV A , can be expressed as
14
Electronic copy available at: https://ssrn.com/abstract=3498958
F CV A = F + CV A
with
\Biggl\{ CV A
=
(5)
\^ [max \{ ST - F - V, 0\} ] if delaer long
- E
\^ [max \{ F - ST - V, 0\} ] if dealer short
+E
\^ denotes the risk-neutral expectation. All other variables are the same as above. Inwhere E
corporating the CV A results in a lower forward rate for the dealer's long positions and a higher
forward rate for the dealer's short position. As the CV A component is either equal to the price of
a short call or a short put option, and both of these prices are increasing in volatility of the FX
spot rate \sigma S , the difference between the prices for long and short positions in a forward subject to
default risk, i.e. the bid-ask spread, increases in volatility, too.21
Transferring these findings from FX forward contracts to FX swap contracts explains the bidask spread component that is related to customer's default risk and its widening when volatility
increases. When entering into an FX swap, the dealer takes both a position in the spot market
and in the forward market, which depend on the intended action of the customer, i.e. to buy or
sell, as summarized in Table 2. By buying a swap at the ask price, the customer buys the base
currency. At the same time, the dealer enters into the opposite position, which results in a long
spot and a short forward position in the swap currency. For example, if the customer wants to buy
EUR (base currency) in exchange for CHF (swap currency), the dealer takes a long CHF spot and
a short CHF forward position. Vice versa, if the customer sells a swap at the bid price, the dealer
enters into a long position in the FX swap and consequently takes a short spot and a long forward
position in the swap currency. Applying the forward prices subject to default risk in Equation 5 of
the respective position by the dealer to the swap pricing formula in Equation 3 shows why the the
ask price should deviate upwards and the bid price downwards from the mid-price when accounting
for customer's default risk.
Table 2
Dealer's positions in an FX swap contract
Customer's action
Price
Dealer's swap position
Dealer's spot position
Dealer's forward position
buy
sell
ask price
bid price
short
long
long
short
short
long
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{C}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}'\mathrm{s} \mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{d}\mathrm{e}\mathrm{s}\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{b}\mathrm{e}\mathrm{s} \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{h}\mathrm{e} \mathrm{w}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{s} \mathrm{t}\mathrm{o} \mathrm{b}\mathrm{u}\mathrm{y} \mathrm{o}\mathrm{r} \mathrm{s}\mathrm{e}\mathrm{l}\mathrm{l} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r}'\mathrm{s}
\mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{p}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{d}\mathrm{e}\mathrm{s}\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{b} \mathrm{e}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{o}\mathrm{p}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{e} \mathrm{p}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{t}\mathrm{o} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{e}'\mathrm{s} \mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}. \mathrm{D}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r}'\mathrm{s} \mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{w}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{p}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{r}\mathrm{e}\mathrm{f}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{o}
\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r}'\mathrm{s} \mathrm{p} \mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{i}\mathrm{n} \mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e} \mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{F}\mathrm{X} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}
\mathrm{p}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{n}\mathrm{e} \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t} \mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}. \mathrm{F}\mathrm{o}\mathrm{r} \mathrm{e}\mathrm{x}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}, \mathrm{i}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} \mathrm{b}\mathrm{u}\mathrm{y}\mathrm{s} \mathrm{E}\mathrm{U}\mathrm{R}, \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{r}\mathrm{e}\mathrm{c}\mathrm{e}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{s} \mathrm{a} \mathrm{p}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{e}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t} \mathrm{i}\mathrm{s} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n}
\mathrm{C}\mathrm{H}\mathrm{F} \mathrm{p} \mathrm{e}\mathrm{r} \mathrm{o}\mathrm{n}\mathrm{e} \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t} \mathrm{E}\mathrm{U}\mathrm{R} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{g}\mathrm{o} \mathrm{e}\mathrm{s} \mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g} \mathrm{i}\mathrm{n} \mathrm{C}\mathrm{H}\mathrm{F} \mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}.
Default risk might arise both exogenously and endogenously in the FX swap contract. The
presented default risk model does not explicitly differentiate between different sources of default
risk, but focus on the endogenous part resulting from the price movements on the underlying. The
21
The partial derivative of the price of a European call or put option in a standard Black-Scholes-Merton model
with respect to volatility, i.e. Vega of a long option position, is always positive. See, e.g., John C.Hull (2015, Chapter
19) for details on Vega and other ``Greeks"" of option positions.
15
Electronic copy available at: https://ssrn.com/abstract=3498958
exogenous part of CCR stems from the idiosyncratic riskiness of a firm's business and its inherent
risk to default. Such exogenous default risks could be incorporated into Equation 5 by modeling V
as the stochastic process of a customer's asset values and including other liabilities into the default
threshold, similar to Johnson and Stulz (1987) or Klein and Inglis (2001). Even though our focus is
on market induced changes in default probabilities, additional sources of a customer's default risk
would probably further increase the bid-ask spread, especially if V and S were negatively correlated
as shown by Johnson and Stulz (1987).
Besides, the default risk model above assumes that all payments occur at maturity date T only,
and that there are no intermediate payments. Since OTC FX swaps normally follow a regular,
often daily, margin call convention, the model would need to be extended to cover mark-to-market
changes. In order to incorporate regular margin calls, the CVA introduced to the FX forward price
needs to be extended to multiple exercise times. This extension changes neither the directional
results nor the relationship between prices and volatility and therefore, does not add to the motivation of our empirical approach. Moreover, the model only considers CVA, while other XVAs might
be relevant for the FX swap bid-ask spread as well. For example, KVAs are directly connected
to CVA through capital charges. Moreover, if a perfect back-to-back hedge of market risk is not
possible, funding costs for margin requirements reflected by FVAs can be substantial, too. These
two components, however, are both increasing in the expected volatility of spot prices, too, leading
to a higher risk that dealers face from expected losses related to CCR.
3.3
Development of hypotheses
The decoupling of the Swiss franc from the euro increased the potential value range of the FX
spot rate, as visualized in Figure 4. During the currency peg, a spot price below CHF 1.20 per EUR
was effectively prevented by the peg, as shown in Panel (b) of Figure 1. After the discontinuation
of the minimum exchange rate, the potential range of values that the FX spot rate can take in
the future increased, enabling a higher volatility. Based on the theoretical motivation above, this
risk of higher prospective volatility should increase inventory holding costs and XVAs of FX swaps
involving CHF after the CHF-EUR decoupling. Therefore, bid-ask spreads of respective swaps
should widen, as postulated in the following hypothesis:
Hypothesis 1 (Bid-ask spreads): The redemption of the CHF currency peg increased bid-ask
spreads of FX swaps involving the Swiss franc.
There are two potential sorts of volatility that can drive the bid-ask spread: realized volatility
from past spot rate movements and forward looking volatility (Funke et al., 2015). Dealers' expectations on the spot rate are influenced by various aspects; one important factor certainly is the
observed, i.e. realized, volatility. This observation together with other market information influences the dealer's expectation on both the direction and the intensity of future price movements,
which eventually will be priced in FX swap quotes. If the CHF-EUR decoupling increased the risk
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Figure 4
FX rate value range with and without currency peg
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{o}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{s}\mathrm{o}\mathrm{l}\mathrm{i}\mathrm{d} \mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{s} \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{h}\mathrm{y}\mathrm{p}\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e} \mathrm{r}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e} \mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t} \mathrm{a}\mathrm{n} \mathrm{F}\mathrm{X} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{c}\mathrm{a}\mathrm{n} \mathrm{a}\mathrm{t}\mathrm{t}\mathrm{a}\mathrm{i}\mathrm{n} \mathrm{a}\mathrm{t} \mathrm{a} \mathrm{f}\mathrm{u}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}
\mathrm{p} \mathrm{o}\mathrm{i}\mathrm{n}\mathrm{t} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}. \mathrm{A} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{e}\mathrm{g} \mathrm{c}\mathrm{u}\mathrm{t}\mathrm{s} \mathrm{o}ff \mathrm{a} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{i}\mathrm{s} \mathrm{r}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}, \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e} \mathrm{r}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e} \mathrm{f}\mathrm{o}\mathrm{r}
\mathrm{p} \mathrm{o}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{f}\mathrm{u}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e} \mathrm{F}\mathrm{X} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s}.
awareness of dealers for currency pairs including CHF, they should have become more sensitive to
higher realized volatility for their risk pricing. Therefore, if bid-ask spreads widen, some parts of
this widening should be explained by a higher impact of realized volatility on bid and ask quotes
in combination with a higher level of volatility itself, as postulated in the following hypothesis:
Hypothesis 2 (Volatility risk channel): The decoupling event was a wake-up call to FX swap
dealers who subsequently increase their sensitivity to spot rate volatility for currency pairs including CHF. The increase in the sensitivity to volatility in combination with higher volatility levels
translates into larger bid-ask spreads.
The volatility \sigma S of the FX spot rate S drives both inventory holding costs and XVAs, but the
volatility channel does not disentangle these two components. Following the theoretical motivation
of bid-ask spread components in Section 3, the inventory holding cost component depends on market
and dealer characteristics, while XVAs mainly depend on expected costs from a customer's default
risk or its mitigation. If a dealer considers a customer's CCR in bid-ask spreads, we will expect
some heterogeneity between different types of customers. As the decoupling event has caused severe
uncertainty in the market about the future development of the Swiss franc and potential contagion
of the panic across currencies, the default risk of customers with a higher exposure to FX markets
increased relatively more and should result in higher TVA for such customers. As there was strong
appreciation of the Swiss franc (see Panel (b) of Figure 1), especially short exposures in CHF have
increased CCR after the decoupling. Customers with the Swiss franc as their home currency have
a naturally long exposure in CHF and should therefore face less severe consequences of the event.
Vice versa, customers with a home currency other than the Swiss franc can be assumed as having
17
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a natural short exposure in CHF and are more adversely affected by a Swiss franc appreciation.
While customers' identification are anonymized in our dataset, we observe a home country flag
for each counterparty. We therefore proxy CCR-relevant characteristics from their activity on the
platform, as well as their home country flag, and test the following hypothesis.
Hypothesis 3 (Counterparty risk channel): Customers with a higher FX exposure are perceived to be riskier after the decoupling event and are charged a higher TVA for currency pairs
including CHF. This is particularly true for non-Swiss customers in CHF, i.e. not being domiciled
in Switzerland, but trading currency pairs including CHF, since they are more adversely affected by
the Swiss franc appreciation.
The CHF-EUR decoupling has demonstrated that fixed exchange rate regimes can be abolished
on very short notice and bear the risk of substantial price changes. Market participants could
have started to doubt the credibility of similar fixed exchange rate regimes. The Danish krone is
a currencies that is similarly pegged to the euro at a fixed exchange rate. If dealers start to price
the risk of huge jumps after depegging the Danish krone from the euro, we should also observe
a bid-ask spread increase for currency pairs including DKK that cannot be explained by realized
volatility or dealers' sensitivity to realized volatility.
Hypothesis 4 (Jump risk channel): The Swiss franc decoupling has reminded dealers of the
possibility of larger jumps on FX spot markets after terminating a fixed exchange rate regime.
After the event, dealers start to price such jump risk into the bid-ask spreads of currency pairs
including DKK.
The risk of large spot rate jumps should be part of the expected volatility driving both inventory
holding costs and XVAs. Therefore, the magnitude of the bid-ask spread increase should depend
on the overall FX exposure of the customer. However, it is unclear as to whether the favorable
situation of being a Swiss customer during the CHF-EUR decoupling event also spills over to the
dealers' CCR evaluation in DKK markets. We therefore test a modified counterparty risk channel
for DKK, as postulated in the following hypothesis:
Hypothesis 5 (Counterparty risk channel (DKK)): Customers with a higher FX exposure
are perceived to be riskier after the CHF-EUR decoupling event and are charged a higher TVA for
currency pairs including DKK.
4
Counterparty credit risk in FX derivatives
This section empirically analyzes counterparty credit risk pricing using the decoupling of CHF
from EUR as an exogenous shock. After identifying an overall bid-ask spread impact, we show that
most of the spread increase is attributed to an increase in volatility. In order to make sure that the
spread increase from volatility is indeed due to counterparty credit risk, we use the cross-sectional
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variation of customers in terms of FX exposure and CHF endowment to show that in particular
customers with a large FX exposure and a small CHF endowment were charged a wider bid-ask
spread
4.1
Identifying risk premiums
The theoretical motivation above claims that dealers should widen bid-ask spreads for swaps
involving CHF but not for swaps on non-CHF currency pairs after the SNB decoupling decision.22
We therefore define for our analysis a treatment group encompassing all currency pairs composed
of CHF with major currencies in the trading platform, and the respective control group consisting
of all major currency pairs excluding CHF, as illustrated in Table 3.
Table 3
Treatment and control group currency pairs
\bfT \bfr \bfe \bfa \bft \bfm \bfe \bfn \bft \bfG \bfr \bfo \bfu \bfp X-CHF
EUR-X
GBP-X
\bfC \bfo \bfn \bft \bfr \bfo \bfl \bfG \bfr \bfo \bfu \bfp AUD-X
USD-X
CAD-X
JPY-X
\bfE \bfU \bfR \bfC \bfH \bfF GBPCHF
AUDCHF
USDCHF
CADCHF
JPYCHF
\ast EURGBP
EURAUD
EURUSD
EURCAD
EURJPY
\cdot \ast GBPAUD
GBPUSD
GBPCAD
GBPJPY
\cdot \cdot \ast AUDUSD
AUDCAD
AUDJPY
\cdot \cdot \cdot \cdot \ast CADJPY
\cdot \cdot \cdot \cdot \cdot \ast \cdot \cdot \cdot \ast USDCAD
USDJPY
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{M}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m} \mathrm{e}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{a}\mathrm{s}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{G}7 \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s}, \mathrm{i}.\mathrm{e}. \mathrm{C}\mathrm{A}\mathrm{D}, \mathrm{E}\mathrm{U}\mathrm{R}, \mathrm{G}\mathrm{B}\mathrm{P}, \mathrm{J}\mathrm{P}\mathrm{Y},
\mathrm{a}\mathrm{n}\mathrm{d} \mathrm{U}\mathrm{S}\mathrm{D} \mathrm{a}\mathrm{s} \mathrm{w}\mathrm{e}\mathrm{l}\mathrm{l} \mathrm{a}\mathrm{s} \mathrm{A}\mathrm{U}\mathrm{D}.
Figure 5 depicts the development of average dealer-specific bid-ask spreads for CHF and nonCHF currency pairs for the four most frequently traded maturities on the trading platform. The
line plot visually indicates that control and treatment currency pairs move parallel before the
decoupling event.23 After the decoupling, there is, on average, no effect on bid-ask spreads for
control currency pairs, but treatment currency pairs diverge sharply and remain at a higher level.
In order to test this observation more formally and to quantify the impact of the decoupling on
CHF-involving FX swap spreads, we estimate a difference-in-differences model. Consistent with the
time frames in Figure 5, the following equation is estimated for an observation period of 1.5 months
prior to and after the decoupling event on January 15, 2015, excluding the event day itself:24
ln(Spreadijtca ) = \alpha it + \alpha j t + (\alpha ij + \alpha ijt + \alpha c +)\beta 1 \cdot treatedc + \beta 2 \cdot postt
+ \beta 3 \cdot treatedc \cdot postt + \gamma \cdot volumea + \delta \cdot \bfitY c + \epsilon ijtca
(6)
The dependent variable ln(Spreadijtca ) is the natural logarithm of the dealer-specific bid-ask
22
See Appendix A.1 for descriptive evidence of the effects following the decoupling of the Swiss franc from the
euro.
23
See Appendix B.1 for a formal test of the parallel trend assumption.
24
There was a large overreaction on the day of the decoupling with spreads of CHF swaps being much larger than
in the following days. In order to rule out that our results were not only driven by this overreaction, we exclude the
event day from all analysis.
19
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Figure 5
FX swap spreads -- CHF currency pairs vs. major non-CHF currency pairs
(\bfa ) Bid-ask spreads (log) -- Overnight maturity
(\bfb ) Bid-ask spreads (log) -- 1 week maturity
(\bfc ) Bid-ask spreads (log) -- 1 month maturity
(\bfd ) Bid-ask spreads (log) -- 3 months maturity
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{o}\mathrm{f} \mathrm{C}\mathrm{H}\mathrm{F} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} (\mathrm{b}\mathrm{l}\mathrm{u}\mathrm{e} \mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}) \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{s}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{C}\mathrm{H}\mathrm{F} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{A}\mathrm{U}\mathrm{D}, \mathrm{C}\mathrm{A}\mathrm{D}, \mathrm{E}\mathrm{U}\mathrm{R},
\mathrm{G}\mathrm{B}\mathrm{P}, \mathrm{J}\mathrm{P}\mathrm{Y}, \mathrm{o}\mathrm{r} \mathrm{U}\mathrm{S}\mathrm{D}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{o}\mathrm{f} \mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{C}\mathrm{H}\mathrm{F} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} (\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}) \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{s}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{A}\mathrm{U}\mathrm{D}, \mathrm{C}\mathrm{A}\mathrm{D}, \mathrm{E}\mathrm{U}\mathrm{R},
\mathrm{G}\mathrm{B}\mathrm{P}, \mathrm{J}\mathrm{P}\mathrm{Y}, \mathrm{o}\mathrm{r} \mathrm{U}\mathrm{S}\mathrm{D}. \mathrm{O}\mathrm{n}\mathrm{l}\mathrm{y} \mathrm{m}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{u}\mathrm{b}-\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}. \mathrm{A}\mathrm{l}\mathrm{l} fi\mathrm{g}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{s} \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{a}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m}
\mathrm{o}\mathrm{f} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{s} \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}, \mathrm{i}.\mathrm{e}. \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{n} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{b}\mathrm{y} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{a}\mathrm{m}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{d}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{a}
\mathrm{d}\mathrm{a}\mathrm{y}, \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{p} \mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}.
\mathrm{S}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}: \mathrm{F}\mathrm{X} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}
spread, i.e. the difference between ask and bid quotes provided by quote-providing dealer bank i
to customer j on day t for currency pair c in auction a. treatedc is a dummy variable equal to 1
if currency pair c includes CHF, i.e. is part of the currency pair treatment group. The dummy
variable postt is equal to 1 if day t is after the decoupling event and 0 otherwise. We further control
for the swap transaction volume to ensure that differences in bid-as spreads were not due to a
structural change in the notional amount traded on CHF swaps after the decoupling and include
volumea in our regressions, defined as the logarithm of the swap transaction volume quoted for an
auction a. The vector \bfitY c contains year-end dummy variables per currency pair to control for yearend effects on the spread driven by abnormal supply and demand effects and liquidity situation per
currency pair at the end of the year that shall not distort the overall results. We build up the result
table (Table 4) with different combinations of fixed effects. In all specifications, we include currency
20
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pair fixed effects to make currency pairs fundamentally comparable. In column (1), we start with
a specification including dealer \times month and customer \times month fixed effects and thus absorb
all time varying dealer-specific and customer-specific characteristics. The latter also controls for
demand effects over time. To additionally account for relationship-driven behavior between certain
dealer-customer pairs, we add dealer \cdot customer fixed effects in column (3). To further absorb
confounding factors out of time-varying dealer-customer pair specific characteristics, we include
dealer \times customer \times month fixed effects in columns (3) to (7). The granularity of our dataset even
enables us to control for dealer-specific behavior on a daily basis, which we do by adding dealer\times day
fixed effects in the most saturated specifications in columns (4) to (7). The main variable of interest
is the difference-in-differences (diff-in-diff) variable treatedc \cdot postt , which describes the change in
FX swap bid-ask spreads of CHF involving currency pairs (treatment) relative to non-CHF currency
pairs (control) from the pre-decoupling to the post-decoupling period.
Results are shown in Table 4. We find a statistically and economically significant relative
increase in bid-ask spreads for currency pairs including CHF after the decoupling of the Swiss
franc from the euro, in line with 1. The point estimate of the log-spread regression depict a fairly
homogeneous relative increase of bid-ask spreads across the four major maturities by a log-factor
of 1.5 to 1.8, which translates into a massive relative spread increase by 350-500\%.25
Table 4
Regression on log(spreads) -- CHF currency pairs vs. major non-CHF currency pairs
(1)
overnight
(6)
1 month
(7)
3 months
treatedc \cdot postt
1.5378*** 1.5438*** 1.5363*** 1.4891*** 1.8478*** 1.4999***
(0.0761)
(0.0721)
(0.0775)
(0.0632)
(0.0838)
(0.0872)
1.6213***
(0.0839)
N
R2
121608
0.3140
121475
0.5893
121125
0.6261
120642
0.6860
11633
0.8788
22203
0.8762
12127
0.9008
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark Maturity:
Volume \& year-end controls
Dealer-day FE
Customer-month FE
Dealer-customer FE
Dealer-customer-month FE
Currency-pair FE
(2)
overnight
(3)
overnight
\checkmark \checkmark (4)
overnight
(5)
1 week
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{O}\mathrm{L}\mathrm{S} \mathrm{r}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 6. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p} \mathrm{e}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s} ln(Spreadijtca ) \mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{l} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f}
\mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}, \mathrm{i}.\mathrm{e}. \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{b} \mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} i \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} j \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{f}\mathrm{o}\mathrm{r}
\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} a. treatedc \mathrm{i}\mathrm{s} \mathrm{a} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{s} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}.
\mathrm{T}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{C}\mathrm{H}\mathrm{F} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{n}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l}
\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{s}\mathrm{u}\mathrm{c}\mathrm{h} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s}. postt \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r}
\mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{a}\mathrm{n}\mathrm{d} 0 \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}-\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{p} \mathrm{e}\mathrm{r}
\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}. \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{s}.
***, **, * \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} 1\%, 5\% \mathrm{a}\mathrm{n}\mathrm{d} 10\% \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{s}.
This finding is robust against different specifications of fixed effects. Moreover, we rule out that
the spread increase is predominantly driven by the very short-term turbulences in the CHF FX
25
The results are also robust to using bid-ask spreads in absolute terms, showing an absolute spread mark-up of
1-10 pips depending on the considered maturity. See Table B.1 in Appendix B.2 for regression results on absolute
bid-ask spreads in pips.
21
Electronic copy available at: https://ssrn.com/abstract=3498958
market and differentiate the post-period into a ``short-term"" window until the end of January and
a ``long-term"" window starting at the beginning of February. While the temporary effect in the
short-term on spreads is probably more driven by market turbulences, the permanent effect in the
long-term should reflect the ``new normal"" pricing behavior, adjusted for increased counterparty risk
and inventory holding costs. Thus, the long-term effect should economically reflect the permanent
increase in FX funding costs for foreign market participants operating in Swiss franc or vice versa.
We split the dummy variable postt in Equation 6 into two mutually exclusive dummy variables:
shortT ermt is equal to 1 from the day after the decoupling until the end of January 2015, and
longT ermt is equal to 1 in February 2015. We estimate Equation 7 for the most saturated fixed
effects specification in columns (3) to (7) in Table 4. The coefficient of the interaction treatedc \cdot shortT ermt reflects the temporary impact and the coefficient of the interaction treatedc \cdot longT ermt
the permanent impact on bid-ask spreads of CHF currency pairs after the decoupling event.
ln(Spreadijtca ) = \alpha it + \alpha ijt + \alpha c + \beta 1 \cdot treatedc + \beta 2 \cdot shortT ermt + \beta 3 \cdot longT ermt
+ \beta 4 \cdot treatedc \cdot shortT ermt + \beta 5 \cdot treatedc \cdot longT ermt
+ \gamma \cdot volumea + \delta \cdot \bfitY c + \epsilon ijtca
Table 5
Regression on log(spreads) -- CHF currency pairs vs. major non-CHF currency pairs:
Short-term and longer-term effect
(1)
overnight
(2)
1 week
(3)
1 month
(4)
3 months
2.1811***
(0.0818)
1.0365***
(0.0782)
2.1043***
(0.0822)
1.5242***
(0.1004)
1.9083***
(0.0859)
1.1082***
(0.1010)
1.8027***
(0.0850)
1.3684***
(0.1183)
120642
0.6938
11633
0.8807
22203
0.8819
12127
0.9017
Volume \& year-end controls
\checkmark \checkmark \checkmark \checkmark Dealer-day FE
Dealer-customer-month FE
Currency-pair FE
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark Maturity:
treatedc \cdot shortT ermt
treatedc \cdot longT ermt
N
R2
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{O}\mathrm{L}\mathrm{S} \mathrm{r}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 7. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p} \mathrm{e}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s} ln(Spreadijtca )
\mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{l} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}, \mathrm{i}.\mathrm{e}. \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{b} \mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n}
\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} i \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} j \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{n}
\mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} a. treatedc \mathrm{i}\mathrm{s} \mathrm{a} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{s} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e}
\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}. \mathrm{T}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{C}\mathrm{H}\mathrm{F} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{n}\mathrm{e}
\mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e}
\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{s}\mathrm{u}\mathrm{c}\mathrm{h} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s}. shortT ermt \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o}
1, \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}, \mathrm{b}\mathrm{u}\mathrm{t} \mathrm{b} \mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e} \mathrm{F}\mathrm{e}\mathrm{b}\mathrm{r}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 1, 2015 \mathrm{t}\mathrm{o} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{t}\mathrm{h}\mathrm{e}
\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} longT ermt \mathrm{w}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{h} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1
\mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{J}\mathrm{a}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 2015. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}. \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d}
\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{s}. ***, **, * \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e}
\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} 1\%, 5\% \mathrm{a}\mathrm{n}\mathrm{d} 10\% \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{s}.
22
Electronic copy available at: https://ssrn.com/abstract=3498958
(7)
The results are shown in Table 5. We find both in the short run as well as in the long run a
significant widening of bid-ask spreads of CHF FX swaps relative to non-CHF FX swaps, irrespective
of the swap maturity. However, the effect varies strongly in magnitude and indicates that the market
turmoil immediately after the decoupling led to a tremendous increase in bid-ask spreads, while the
spread increase in the longer-term time frame, i.e. treatedc \cdot longT ermt , indicates a ``new normal""
above the pre-decoupling level. Further focusing on this permanent effect, the results again depict
a fairly homogeneous relative increase of bid-ask spreads across the four major maturities by a
log-factor of 1.0 to 1.5, which still translates into a massive relative spread increase of 170-350\%.26
These results suggest a persistent bid-ask spread increase for FX swaps on CHF currency pairs,
lending full support to Hypothesis 1.
In order to emphasize the economic significance of the increase in bid-ask spreads, we consider
a loan with a notional amount of CHF 100m and a duration of 10 years originated by a non-Swiss
bank. According to our estimates of the permanent effect in Table B.2, the cost of using FX
swaps to obtain the CHF notional amount and to hedge the FX rate risk increases -- depending
on the swap roll-over period -- by CHF 1.3m (quarterly roll-over) to CHF 1.9m (monthly roll-over)
on average after the decoupling of the Swiss franc from the euro. Assuming these costs are fully
incorporated into the loan pricing, they lead to a loan margin increase of approximately 5.0-7.5\%
based on an average loan margin of 250 basis points per anno.27 Irrespective of whether and to
what extent the loan originator is transmitting the costs to its borrowers, the market as a whole is
facing a massive cost increase that was effectively prevented by the currency peg suggesting that
the Swiss central bank induced a risk discount prior to the peg redemption.
4.2
Volatility risk channel
After having confirmed a massive bid-ask spread widening of CHF currency pairs following the
decoupling event, we now investigate to what extent this widening is explained by a higher impact
of realized volatility on bid and ask quotes in combination with a higher level of volatility itself.
As hypothesized in Section 3.3, the historical volatility is assumed to be one of the major drivers
of a dealer's expectation on the future volatility. Therefore, dealers should become more sensitive
to changes in observed volatility in the market. Figure 6 depicts the realized volatility of major
CHF and corresponding EUR currency pairs. It clearly shows the main developments of FX rate
volatilities: before the decoupling event, the volatility of the EUR-CHF pair is very low, and the
volatility of CHF currency pairs moves parallel to the volatility of the corresponding EUR currency
pairs. The decoupling event, however, led to a huge jump in the volatility of CHF currency pairs, in
26
The results are again robust to using bid-ask spreads in absolute terms without taking the logarithm showing an
absolute spread mark-up of up to over 6 pips depending on the considered maturity. See Table B.2 in Appendix B.2
for regression results on absolute bid-ask spreads in pips.
27
Considering only executed quotes instead of all provided bid-ask spreads and thereby estimating the very lowest
bound of swap price increases, the effect is still economically large with an approximate cost increase equivalent to
around 1\% of the loan margin. However, as all quotes provided on the platform are, by platform design, marketcompliant and potentially executed in another FX market segment, this very lowest bound most likely underestimates
the actual market impact.
23
Electronic copy available at: https://ssrn.com/abstract=3498958
particular CHF-EUR, and discontinues the co-movement of CHF-X and EUR-X currency pairs. In
the very short run after the de-pegging until approximately the end of January 2015, CHF currency
pairs exhibit substantially higher realized volatility than the corresponding EUR currency pairs,
which seems to converge into a similar, but overall higher volatility level in February 2015 compared
to the volatility of currency peg times. For non-CHF and non-EUR currency pairs, there seems to
be no systematic impact besides a very short-term spillover of the decoupling turbulence.28
Figure 6
Realized volatility of FX spot rates -- CHF and corresponding EUR currency pairs
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{D}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{r}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y} \mathrm{r}\mathrm{e}\mathrm{f}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{t}\mathrm{o} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d} \mathrm{F}\mathrm{X} \mathrm{s}\mathrm{p} \mathrm{o}\mathrm{t} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}
\mathrm{d}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{h}\mathrm{e} 24 \mathrm{h}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{o} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} \mathrm{a}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{o}ff-\mathrm{t}\mathrm{h}\mathrm{e}-\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{l}\mathrm{f} \mathrm{b}\mathrm{y} \mathrm{B}\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{m}\mathrm{b} \mathrm{e}\mathrm{r}\mathrm{g} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}
\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{y}-\mathrm{a}\mathrm{x}\mathrm{i}\mathrm{s} \mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s} \mathrm{c}\mathrm{u}\mathrm{t} \mathrm{a}\mathrm{b}\mathrm{o}\mathrm{v}\mathrm{e} 40 \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{v}\mathrm{i}\mathrm{s}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{r}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{o}\mathrm{n}\mathrm{s}, \mathrm{s}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{r}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d} \mathrm{p}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{r} 24\mathrm{h}
\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{C}\mathrm{H}\mathrm{R}-\mathrm{E}\mathrm{U}\mathrm{R} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{s}\mathrm{p}\mathrm{i}\mathrm{k}\mathrm{e}\mathrm{s} \mathrm{t}\mathrm{o} \mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r} 270 \mathrm{o}\mathrm{n} \mathrm{J}\mathrm{a}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 16, 2015.
\mathrm{S}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}: \mathrm{B}\mathrm{l}\mathrm{o} \mathrm{o}\mathrm{m}\mathrm{b} \mathrm{e}\mathrm{r}\mathrm{g}
Following this observation, we analyze the impact of realized volatility as a transmission channel
to increasing bid-ask spreads more formally. We extend the regression framework in Equation 7
by a volatility component interacted with the diff-in-diff variables to investigate whether there was
a structural break in volatility pricing after the decoupling event. Note that we consider in this
exercise only the CHF-X and EUR-X currency pairs that were shown in Figure 6 as they follow, by
design of the currency peg, a parallel trend prior to the decoupling. We further exclude the EURCHF pair, as its volatility was almost zero in the pre-period but skyrocketed after the decoupling
event.29 We define the observation period as before and estimate the following extended equation:
28
See Figure B.2 in Appendix B.2 for details on the realized volatility of non-CHF and non-EUR currency pairs.
Including non-CHF and non-EUR currency pairs to the control group or the CHF-EUR pair to the treatment
group provides consistent regression results.
29
24
Electronic copy available at: https://ssrn.com/abstract=3498958
ln(Spreadijtca ) = RHS of Equation 7
+ \beta 6 \cdot volatc + \beta 7 \cdot volatc \cdot treatedc
(8)
+ \beta 8 \cdot volatc \cdot shortT ermt + \beta 9 \cdot volatc \cdot longT ermt
+ \beta 10 \cdot volatc \cdot treatedc \cdot shortT ermt + \beta 11 \cdot volatc \cdot treatedc \cdot longT ermt
The volatility proxy volatc is the logarithm of the annualized FX spot rate volatility during the
24 hours prior to the observation day t for currency pair c as provided off-the-shelf by Bloomberg.
We employ the most saturated specification in terms of fixed effects and control variables from the
base regression in Table 4 so that all other variables remain identical to the previous regression
model.
Table 6
Regression on log(spreads) -- CHF currency pairs vs. corresponding EUR currency pairs:
Volatility effect
(1)
overnight
(2)
overnight
(3)
1 month
(4)
1 month
1.2084***
(0.0945)
0.5541***
(0.1337)
0.0484***
(0.0092)
1.2481***
(0.1217)
0.4167
(0.2745)
0.0698***
(0.0176)
52416
0.7821
52416
0.7839
11385
0.9095
11385
0.9115
Volume \& year-end controls
\checkmark \checkmark \checkmark \checkmark Dealer-day FE
Dealer-customer-month FE
Currency-pair FE
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark Maturity:
treatedc \cdot longT ermt
volatc \cdot treatedc \cdot longT ermt
N
R2
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{O}\mathrm{L}\mathrm{S} \mathrm{r}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 7 \mathrm{i}\mathrm{n} \mathrm{c}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n}\mathrm{s} (1) \mathrm{a}\mathrm{n}\mathrm{d} (2) \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 8 \mathrm{i}\mathrm{n}
\mathrm{c}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n}\mathrm{s} (2) \mathrm{a}\mathrm{n}\mathrm{d} (4). \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p} \mathrm{e}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s} ln(Spreadijtca ) \mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{l}
\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}, \mathrm{i}.\mathrm{e}. \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{b} \mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}
\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} i \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} j \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} a. treatedc \mathrm{i}\mathrm{s} \mathrm{a}
\mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{s} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}. \mathrm{T}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}
\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{C}\mathrm{H}\mathrm{F} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{n}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e}
\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m} \mathrm{e}\mathrm{x}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{E}\mathrm{U}\mathrm{R} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{i}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{E}\mathrm{U}\mathrm{R} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}
\mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s}. shortT ermt \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}, \mathrm{b}\mathrm{u}\mathrm{t} \mathrm{b}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e} \mathrm{F}\mathrm{e}\mathrm{b}\mathrm{r}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y}
1, 2015 \mathrm{t}\mathrm{o} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} longT ermt
\mathrm{w}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{h} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1 \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{J}\mathrm{a}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 2015. volatc \mathrm{i}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d}
\mathrm{F}\mathrm{X} \mathrm{s}\mathrm{p} \mathrm{o}\mathrm{t} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y} \mathrm{d}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{h}\mathrm{e} 24 \mathrm{h}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{o} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}
\mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}-\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{e}\mathrm{r}
\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l} \mathrm{w}\mathrm{a}\mathrm{s} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}
\mathrm{i}\mathrm{n} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 8, \mathrm{b}\mathrm{u}\mathrm{t}, \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{a}\mathrm{k}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{c}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{y}, \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{o}\mathrm{n}\mathrm{l}\mathrm{y} \mathrm{s}\mathrm{h}\mathrm{o}\mathrm{w}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{w}\mathrm{o} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{o}\mathrm{f}
\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}. \mathrm{O}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{o} \mathrm{e}ffi\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{a}\mathrm{s} \mathrm{e}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}. \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}
\mathrm{a}\mathrm{n}\mathrm{d} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{s}. ***, **, * \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} 1\%, 5\% \mathrm{a}\mathrm{n}\mathrm{d} 10\% \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{s}.
Table 6 shows the estimation results for overnight FX swaps and swaps with a maturity of one
month . In columns (1) and (3), we present regression results for estimating Equation 7 (similar to
Table 5) using the modified treatment and control group excluding currency pairs including neither
CHF nor EUR, as well as CHF-EUR swaps, which are virtually identical to the one in Table 5.
Columns (2) and (4) show the results for estimating Equation 8. As shown in Figure 6, there was
25
Electronic copy available at: https://ssrn.com/abstract=3498958
a huge increase in realized volatilities of FX swaps in the direct aftermath of the CHF decoupling
event, which hardly reflects expectations on future volatility. Therefore, our assumption that
historical volatility is one of the major drivers of a dealer's expectation on future volatility might
not be true during the market turmoil immediately after the decoupling event. We therefore focus
only on the impact of volatility on the ``new normal"" spreads. Hence, the main variable of interest
is the triple interaction terms volatc \cdot treatedc \cdot longT ermt , reflecting changes in dealers' sensitivity
to realized volatility in CHF currency pairs after the decoupling event. As before, the interaction
with longT ermt estimates the permanent effect in the ``new normal"". A highly significant and
positive permanent effect, after volatility has settled within a reasonable and higher range, shows
that dealers became more sensitive to realized volatility. A higher price per unit volatility together
with an overall higher volatility level can explain a substantial share of the permanent bid-ask
spread increase for CHF currency pairs. Consequently, both coefficients of treatedc \cdot longT ermt
substantially decrease compared to columns (1) and (2), and for a maturity of one month, the
coefficient even ceases to be statistically significant.
Hypothesis 2 is only supported for the permanent effect of volatility on CHF currency pairs, as
increased sensitivity to volatility explains a significant proportion of increased bid-ask spreads. The
temporary exaggeration cannot be explained by a linear relationship between realized volatility and
bid-ask spreads, so that Hypothesis 2 has to be rejected in the short-run.
4.3
Counterparty risk channel
The volatility channel identified in the previous section drives both inventory holding costs and
XVAs. The counterparty risk channel aims at disentangling inventory holding costs from XVAs in
the swap bid-ask spread. As inventory holding costs according to Stoll (1978) do not depend on
customer characteristics, such as a customer's riskiness, differences in risk premiums charged for
the same product to different customers would therefore provide evidence of XVAs in the bid-ask
spread. In order to disentangle these bid-ask spread components, we make use of the heterogeneity
of customers and evaluate the effect on bid-ask spreads for customers with different risk profiles.
As counterparties are anonymous in our data sample, we cannot resort to balance sheet data or
other customer characteristics, but we can classify them according to risk criteria observable in the
data. The differential increase of risk premiums charged for swaps including CHF is analyzed in a
difference-in-differences-in-differences framework as described by the following equation.
ln(Spreadijtca ) = RHS of Equation 7
+ \beta 6 \cdot shortT ermt \cdot customerT ypej + \beta 7 \cdot longT ermt \cdot customerT ypej
+ \beta 8 \cdot treatedc \cdot shortT ermt \cdot customerT ypej
(9)
+ \beta 9 \cdot treatedc \cdot longT ermt \cdot customerT ypej
The customer segment dummy variable customerT ypej is equal to 1 if the criteria to classify a
26
Electronic copy available at: https://ssrn.com/abstract=3498958
customer as the considered customer type is fulfilled. For example, to estimate the differential effect
for bank customers to corporate customers, customerT ypej is equal to 1 if customer j is a bank and
0 otherwise. Equation 7 is extended by four variables interacted with a dummy variable describing
the respective customer segment.30 The main variables of interest are treatedc \cdot shortT ermt \cdot customerT ypej and treatedc \cdot longT ermt \cdot customerT ypej . Both describe the differential impact of
the CHF-EUR decoupling event on the customer segment described by customerT ypej relative to
the customers that do not fulfill the criteria of the customer segment, e.g., the differential impact on
banks relative to corporate customers, in the post period. The two triple interactions differentiate
again between the temporary and the permanent differential effect. As the triple interactions thus
describe the difference between two customer segments, they are denoted by \Delta treatedc \cdot shortT ermt
and \Delta treatedc \cdot longT ermt in the following.
Table 7
Regression on log(spreads) -- CHF currency pairs vs. major non-CHF currency pairs:
Financial vs. corporate customer
Maturity:
Customer segment:
treatedc \cdot shortT ermt
treatedc \cdot longT ermt
(1)
overnight
all
(2)
overnight
interbank
(3)
overnight
corporate
(4)
1 month
all
(5)
1 month
interbank
(6)
1 month
corporate
2.1811***
(0.0818)
1.0365***
2.1875***
(0.0881)
1.0498***
2.0507***
(0.1620)
0.8840***
1.9083***
(0.0859)
1.1082***
1.8913***
(0.0898)
1.1174***
2.1390***
(0.1435)
1.0031***
\Delta treatedc \cdot shortT ermt
0.0988
(0.1325)
0.2268*
(0.1219)
\Delta treatedc \cdot longT ermt
N
R2
-0.1260
(0.1320)
0.1687
(0.1344)
120642
0.6938
99497
0.6871
6972
0.8154
22203
0.8819
17466
0.8881
3439
0.8944
Volume \& year-end controls
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark Dealer-day FE
Dealer-customer-month FE
Currency-pair FE
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{O}\mathrm{L}\mathrm{S} \mathrm{r}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 7. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s} ln(Spreadijtca ) \mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{l} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m}
\mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}, \mathrm{i}.\mathrm{e}. \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{b} \mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} i \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} j \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} t
\mathrm{f}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} a. treatedc \mathrm{i}\mathrm{s} \mathrm{a} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{s} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}
\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}. \mathrm{T}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{C}\mathrm{H}\mathrm{F} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{n}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}
\mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{s}\mathrm{u}\mathrm{c}\mathrm{h} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s}. shortT ermt \mathrm{i}\mathrm{s}
\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}, \mathrm{b}\mathrm{u}\mathrm{t} \mathrm{b}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e} \mathrm{F}\mathrm{e}\mathrm{b}\mathrm{r}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 1, 2015 \mathrm{t}\mathrm{o} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t}.
\mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} longT ermt \mathrm{w}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{h} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1 \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{J}\mathrm{a}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 2015. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m}
\mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}-\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}.
\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{m}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{u}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{b} \mathrm{e}\mathrm{l}\mathrm{o}\mathrm{w} \mathrm{c}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n} \mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b} \mathrm{e}\mathrm{r}\mathrm{s}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{b}\mathrm{a}\mathrm{n}\mathrm{k} \mathrm{o}\mathrm{r}
\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e} \mathrm{t}\mathrm{o} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{b}\mathrm{a}\mathrm{n}\mathrm{k}\mathrm{s} \mathrm{o}\mathrm{r} \mathrm{c}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s}, \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{y}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{r}\mathrm{o}\mathrm{w}\mathrm{s}
\mathrm{b}\mathrm{e}\mathrm{g}\mathrm{i}\mathrm{n}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h} \mathrm{a} \Delta \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{e}ffi\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{i}\mathrm{p}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}-\mathrm{i}\mathrm{n}-\mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{s}-\mathrm{i}\mathrm{n}-\mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{s}
\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l} \mathrm{i}\mathrm{n} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 9 \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{o}\mathrm{n} \mathrm{b}\mathrm{a}\mathrm{n}\mathrm{k}\mathrm{s} \mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}. \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e}
\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{s}. ***, **, * \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} 1\%, 5\% \mathrm{a}\mathrm{n}\mathrm{d} 10\% \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{s}.
We first analyze potential differences between the interbank and corporate segments. Treatment
and control currency pairs are defined similar to Section 4.1. Table 7 shows the results of estimating
30
The uninteracted customer segment dummy variable is absorbed by customer fixed effects and therefore not
shown in Equation 9.
27
Electronic copy available at: https://ssrn.com/abstract=3498958
Equation 7 for only the interbank segment in columns (2) and (5), and only the corporate segment
in columns (3) and (6). Columns (1) and (4) restate the results for all customer segments from
Table 5 for comparison. The results show that both customer segments pay a substantial premium
after the decoupling event, which is larger for the temporary than for the permanent effect. The
difference between the interbank and the corporate segments using a difference-in-differences-indifferences approach in Equation 9 reveals that this differential impact on banks is only significant
for overnight maturities in the permanent effect.
Table 8
Regression on log(spreads) -- CHF currency pairs vs. major non-CHF currency pairs:
Interbank details on FX exposure and domicile
Maturity:
Sample:
Sub-sample FX exposure:
(1)
overnight
interbank
all
(2)
overnight
interbank
low
(3)
overnight
interbank
high
(4)
1 month
interbank
all
(5)
1 month
interbank
low
(6)
1 month
interbank
high
FX exposure
FX exposure
Domicile
Domicile
Domicile
Domicile
low - high nonCH - CH nonCH - CH low - high nonCH - CH nonCH - CH
customerT ypej :
treatedc \cdot shortT ermt
2.1335***
(0.1856)
1.2371***
(0.1599)
0.0603
(0.1564)
-0.2321*
(0.1383)
2.2037***
(0.1802)
1.3063***
(0.1306)
-0.3281
(0.3524)
-0.1723
(0.2723)
2.2414***
(0.0846)
0.9661***
(0.0864)
-0.2497**
(0.1134)
0.1921
(0.1473)
1.4371***
(0.1351)
0.7309***
(0.1632)
0.5350***
(0.0925)
0.4644***
(0.1207)
2.6149***
(0.2743)
1.5483***
(0.2204)
-0.9459***
(0.3476)
-0.6471***
(0.1697)
2.0405***
(0.0981)
1.1358***
(0.1165)
-0.1649
(0.1237)
0.1225
(0.1380)
99482
0.6872
22547
0.7383
76648
0.6819
17466
0.8893
3126
0.9282
13797
0.8917
Volume \& year-end controls
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark Dealer-day FE
Dealer-customer-month FE
Currency-pair FE
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark treatedc \cdot shortT ermt
\Delta treatedc \cdot shortT ermt
\Delta treatedc \cdot longT ermt
N
R2
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{O}\mathrm{L}\mathrm{S} \mathrm{r}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 9. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p} \mathrm{e}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s} ln(Spreadijtca ) \mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{l} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e}
\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}, \mathrm{i}.\mathrm{e}. \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{b}\mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} i \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} j \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}
\mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} a. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{e}ffi\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{d}\mathrm{i}ff-\mathrm{i}\mathrm{n}-\mathrm{d}\mathrm{i}ff \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{i}\mathrm{p}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e}
\mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}-\mathrm{i}\mathrm{n}-\mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{s}-\mathrm{i}\mathrm{n}-\mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{s} \mathrm{m}\mathrm{o} \mathrm{d}\mathrm{e}\mathrm{l} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t} (\Delta ) \mathrm{o}\mathrm{n} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{c}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{i}fi\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}
\mathrm{F}\mathrm{X} \mathrm{e}\mathrm{x}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{l}\mathrm{e}, \mathrm{i}.\mathrm{e}. customerT ypej . \mathrm{C}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n} (1) \mathrm{a}\mathrm{n}\mathrm{d} (4) \mathrm{s}\mathrm{h}\mathrm{o}\mathrm{w} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{o}\mathrm{n} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h} \mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h} \mathrm{F}\mathrm{X}
\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e} \mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h} \mathrm{l}\mathrm{o}\mathrm{w} \mathrm{F}\mathrm{X} \mathrm{e}\mathrm{x}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e} \mathrm{u}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n} \mathrm{a}\mathrm{g}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{o}\mathrm{f}
\mathrm{a}\mathrm{l}\mathrm{l} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{l}\mathrm{d}. \mathrm{I}\mathrm{n} \mathrm{c}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n}\mathrm{s} (2), (3), (5), \mathrm{a}\mathrm{n}\mathrm{d} (6) \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{o}\mathrm{n} \mathrm{S}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{s} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{t}\mathrm{o}
\mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{S}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{s} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} \mathrm{s}\mathrm{u}\mathrm{b}-\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h} \mathrm{o}\mathrm{r} \mathrm{l}\mathrm{o}\mathrm{w} \mathrm{F}\mathrm{X} \mathrm{e}\mathrm{x}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}. treatedc \mathrm{i}\mathrm{s} \mathrm{a}
\mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{s} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}. \mathrm{T}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y}
\mathrm{C}\mathrm{H}\mathrm{F} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{n}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}
\mathrm{o}\mathrm{f} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s}. shortT ermt \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}, \mathrm{b}\mathrm{u}\mathrm{t} \mathrm{b} \mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e} \mathrm{F}\mathrm{e}\mathrm{b}\mathrm{r}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 1, 2015 \mathrm{t}\mathrm{o}
\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} longT ermt \mathrm{w}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{h} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1 \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{J}\mathrm{a}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y}
2015. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}-\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l}
\mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}. \mathrm{C}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{m}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{e}\mathrm{s}, \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{b}\mathrm{a}\mathrm{n}\mathrm{k} \mathrm{s}\mathrm{u}\mathrm{b}-\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{F}\mathrm{X} \mathrm{e}\mathrm{x}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e}
\mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{b}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{w} \mathrm{c}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n} \mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{s}. \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{s}. ***, **, * \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e}
\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} 1\%, 5\% \mathrm{a}\mathrm{n}\mathrm{d} 10\% \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{s}.
We further zoom in on the interbank segment and split the sample along two dimensions: FX
exposure and country domicile.31 If it is indeed counterparty credit risk driving the above results
31
Note that the corporate segment is much smaller than the interbank sample and not all sample splits estimated
in Table 8 are possible for corporate customers.
28
Electronic copy available at: https://ssrn.com/abstract=3498958
rather than inventory holding costs, we should find an increase in bid-ask spreads in particular
for customers with a large FX exposure that are not headquartered in Switzerland.32 For these
different samples, we rerun the regression model in Equation 9 with customerT ypej being a dummy
variable that is equal to 1 if the customer has an FX exposure above the cross-sectional mean (is
domiciled in Switzerland) and zero otherwise.
We present results in Table 8. The diff-in-diff interaction terms in columns (1) and (4) are shown
to confirm that the decoupling widens FX swap spreads for customers with low FX exposure. An
additional risk premium for customers with a high FX exposure cannot be confirmed for overnight
maturities. For FX-swaps with longer maturities, however, the differential effect (\Delta interaction
terms) shows a significant additional mark-up for customers with a large FX exposure. When
splitting the sample along the exposure dimension into customers with low (columns (2) and (5))
and high (columns (3) and (6)) FX exposure, we find that the spread increase is larger for non-CH
domiciled customers, in particular in the segment of low-FX exposure customers.33 This discount
is stronger in swaps with longer maturities, as we would indeed expect if counterparty credit risk
influences the spread widening. Taken together, customer specific risk seems to play a minor role
for overnight maturities, which is in line with the common perception that overnight markets are
the last risk-free domain in the financial system. More importantly, customer specific risk explains
a substantial share of the risk premium increase of longer maturities, particularly for non-Swiss
customers. Consequently, our results provide evidence for Hypothesis 3.
5
Cross-currency spillover
The previous section has documented a massive and permanent increase of CHF including FX
swap bid-ask spreads following the discontinuation of the CHF currency peg due to an increase in
(the perception of) counterparty credit risk. In this section, we document that dealers changed
also the pricing of FX swaps on other pegged currencies following the CHF decoupling, fearing a
similar jump in the spot market as observed in the CHF-EUR rate.
There are other currencies similarly pegged to the euro, such as, the DKK and the Bulgarian
lev (BGN). Both countries have introduced a fixed exchange rate policy against the euro that they
enforce by way of monetary policy. Both currency pegs to the euro have been in place since the
introduction of the euro in 1999. This section examines whether the decoupling of the Swiss franc
from the euro had an impact on currencies having a similar peg to the euro, even though nothing
regarding the fixed exchange rate policy has changed for them after January 15, 2015. We focus
the analysis on the DKK as there are not enough transactions for the BGN in the platform in order
to derive statistically meaningful conclusions.
32
For customers headquartered in Switzerland, the decoupling might have served as a positive income shock: CHF
is the major currency of Swiss customers and Swiss banks have access to CHF liquidity via the SNB. Their natural
long position in CHF benefits from an appreciation of the Swiss franc and makes positions in foreign currencies for
such customers relatively less expensive.
33
This is shown by a significant risk discount, i.e. negative coefficient, for Swiss customers together with substantially higher coefficients of the diff-in-diff variables, which reflect the wider spreads of non-Swiss customers.
29
Electronic copy available at: https://ssrn.com/abstract=3498958
5.1
The Danish currency peg
Denmark has already been conducting a fixed exchange rate policy to the German mark since
1982, and then against the euro. Denmark uses the European Exchange Rate Mechanism (ERM 2)
as the formal framework for the fixed exchange rate policy, but not with the intention to join the
euro. The exchange rate is fixed at 7.46038 DKK per EUR with a fluctuation band of +/- 2.25\%.
Even in foreign currency crises the DKK exchange rate against the EUR was not adjusted for
economic policy purposes. The EUR-DKK exchange rate in Panel (b) in Figure 7 shows that it has
been very stable at its original level two years before and after the decoupling event in Switzerland
with at most a tiny deviation shortly after the event with no longer run effect. At the same time
there is quite some fluctuation for the DKK-USD currency pair, whose movement is largely identical
to the EUR-USD exchange rate development as expected due to the currency peg against the euro.
Graphical evidence in Panel (b) in Figure 7 suggest that DKK FX spot markets were unaffected
by the CHF-EUR decoupling, which was potentially achieved by a temporary, strong expansion of
the foreign currency reserve assets by the Danmarks Nationalbank (DNB), as indicated in Panel
(a) in Figure 7.
Figure 7
DKK-EUR currency peg
(\bfa ) DNB foreign currency reserves
(\bfb ) DKK exchange rate development
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{v}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{r}\mathrm{e}\mathrm{d} \mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e} \mathrm{m}\mathrm{a}\mathrm{r}\mathrm{k}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{C}\mathrm{H}\mathrm{F}-\mathrm{E}\mathrm{U}\mathrm{R} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{o}\mathrm{n} \mathrm{J}\mathrm{a}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 15, 2015. \mathrm{F}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{n} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{P}\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{l}
(\mathrm{a}) \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{a}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{t} \mathrm{c}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{s}. \mathrm{F}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{o}\mathrm{n} \mathrm{r}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{o}\mathrm{n} \mathrm{F}\mathrm{X} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s} \mathrm{h}\mathrm{a}\mathrm{v}\mathrm{e} \mathrm{b} \mathrm{e}\mathrm{e}\mathrm{n} \mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d} \mathrm{t}\mathrm{o} 100 \mathrm{o}\mathrm{n} \mathrm{J}\mathrm{a}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 2, 2004, \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e}
\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e} \mathrm{s}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{D}\mathrm{a}\mathrm{n}\mathrm{k}\mathrm{m}\mathrm{a}\mathrm{r}\mathrm{k}\mathrm{s} \mathrm{N}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{b}\mathrm{a}\mathrm{n}\mathrm{k} \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e} \mathrm{i}\mathrm{n} \mathrm{P}\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{l} (\mathrm{b}).
\mathrm{S}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{s}: \mathrm{E}\mathrm{C}\mathrm{B} \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a} \mathrm{W}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{s}\mathrm{e}, \mathrm{D}\mathrm{a}\mathrm{n}\mathrm{m}\mathrm{a}\mathrm{r}\mathrm{k}\mathrm{s} \mathrm{N}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{b}\mathrm{a}\mathrm{n}\mathrm{k} \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}
5.2
Identifying spillovers to the Danish krone
We use an approach similar to the analysis of CHF swaps in the previous section to formally
examine the impact for the EUR-DKK currency pair.34 Again, we construct a treatment group out
of currency pairs composed by DKK and major currencies in the trading platform and a control
34
Appendix A.2 describes the development of DKK swap prices and provides descriptive evidence of spillovers.
30
Electronic copy available at: https://ssrn.com/abstract=3498958
Figure 8
FX swap spreads -- DKK currency pairs (treated) vs. major non-DKK currency pairs (control)
(\bfa ) Bid-ask spreads (log) -- Overnight maturity
(\bfb ) Bid-ask spreads (log) -- 1 week maturity
(\bfc ) Bid-ask spreads (log) -- 1 month maturity
(\bfd ) Bid-ask spreads (log) -- 3 months maturity
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{o}\mathrm{f} \mathrm{D}\mathrm{K}\mathrm{K} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} (\mathrm{b}\mathrm{l}\mathrm{u}\mathrm{e} \mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}) \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{s}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{D}\mathrm{K}\mathrm{K} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{A}\mathrm{U}\mathrm{D}, \mathrm{C}\mathrm{A}\mathrm{D}, \mathrm{E}\mathrm{U}\mathrm{R},
\mathrm{G}\mathrm{B}\mathrm{P}, \mathrm{J}\mathrm{P}\mathrm{Y}, \mathrm{o}\mathrm{r} \mathrm{U}\mathrm{S}\mathrm{D}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{o}\mathrm{f} \mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{D}\mathrm{K}\mathrm{K} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} (\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}) \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{s}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{A}\mathrm{U}\mathrm{D}, \mathrm{C}\mathrm{A}\mathrm{D}, \mathrm{E}\mathrm{U}\mathrm{R},
\mathrm{G}\mathrm{B}\mathrm{P}, \mathrm{J}\mathrm{P}\mathrm{Y}, \mathrm{o}\mathrm{r} \mathrm{U}\mathrm{S}\mathrm{D}. \mathrm{O}\mathrm{n}\mathrm{l}\mathrm{y} \mathrm{m}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{u}\mathrm{b}-\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}. \mathrm{A}\mathrm{l}\mathrm{l} fi\mathrm{g}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{s} \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{a}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m}
\mathrm{o}\mathrm{f} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{s} \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}, \mathrm{i}.\mathrm{e}. \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{n} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{b}\mathrm{y} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{a}\mathrm{m}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{d}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{a}
\mathrm{d}\mathrm{a}\mathrm{y}, \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{p} \mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}.
\mathrm{S}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}: \mathrm{F}\mathrm{X} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}
group out of currency pairs consisting of all major currencies excluding DKK. Figure 8 shows
the logarithm of the provider-level bid-ask spreads for the four most relevant maturities on the
trading platform. The four graphs confirm the parallel trend of control and treatment group in
the pre-period and show a divergence of spreads after the Swiss decoupling event across different
maturities.
Descriptive evidence in Figure 8 confirms that all prerequisites to run a diff-in-diff regression
model with the DKK currency pairs as the treatment group and the other major currency pairs
as the control group, similar to the setup in Section 4.1, are fulfilled.35 Results of estimating
Equation 6 for the logarithm of swap bid-ask spreads as dependent variable applying the same
fixed effect and control variable specifications as for the CHF analysis are shown in Table 9. The
35
See Appendix B.1 for a formal confirmation of the parallel trend assumption.
31
Electronic copy available at: https://ssrn.com/abstract=3498958
coefficient of the diff-in-diff variable, which describes the bid-ask spread change of DKK currency
pairs relative to the spread of control currency pairs from pre- to post-period, is positive and
statistically highly significant across all specifications and sample maturities. The magnitude of
the log-spread widening is somewhat lower than for CHF currency pairs, but still immense with a
relative spread increase of 250-450\%. Results are again robust against using the absolute bid-ask
spreads as dependent variable.36
Table 9
Regression on log(spreads) -- DKK currency pairs vs. major non-DKK currency pairs
(1)
overnight
(6)
1 month
(7)
3 months
treatedc \cdot postt
1.2454*** 1.2549*** 1.2563*** 1.2409*** 1.6667*** 1.6376***
(0.1224)
(0.1160)
(0.1164)
(0.1182)
(0.1935)
(0.0837)
1.6670***
(0.0998)
N
R2
111208
0.4629
111048
0.6924
110719
0.7216
110219
0.7675
9510
0.8732
17537
0.8801
8613
0.8612
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark Maturity:
Volume \& year-end controls
Dealer-day FE
Customer-month FE
Dealer-customer FE
Dealer-customer-month FE
Currency-pair FE
(2)
overnight
(3)
overnight
\checkmark \checkmark (4)
overnight
(5)
1 week
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{O}\mathrm{L}\mathrm{S} \mathrm{r}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 6. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p} \mathrm{e}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s} ln(Spreadijtca ) \mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{l} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f}
\mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}, \mathrm{i}.\mathrm{e}. \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{b} \mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} i \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} j \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{f}\mathrm{o}\mathrm{r}
\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} a. treatedc \mathrm{i}\mathrm{s} \mathrm{a} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{s} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}.
\mathrm{T}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{D}\mathrm{K}\mathrm{K} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{n}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l}
\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{s}\mathrm{u}\mathrm{c}\mathrm{h} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s}. postt \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r}
\mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{a}\mathrm{n}\mathrm{d} 0 \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}-\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{p} \mathrm{e}\mathrm{r}
\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}. \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{s}.
***, **, * \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} 1\%, 5\% \mathrm{a}\mathrm{n}\mathrm{d} 10\% \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{s}.
In order to rule out that results are driven by post-decoupling turbulences, we differentiate the
post-period again into a short-term window until the end of January and a longer-term window
starting at the beginning of February similar to Section 4.1. In contrast to the CHF results, we do
not expect a massive exaggeration directly after the decoupling event, as the spot market is not
directly affected by the SNB's decision. However, we expect the market to gradually increase to
a ""new normal"" related to an increase in the risk of a massive spot movement after a decoupling
event. The longer-term effect should therefore -- as for the Swiss franc -- reflect a permanent
impact on the bid-ask spread adjusted for an updated pricing of risk and thus economically reflects
increased FX funding costs for foreign market participants operating in Danish krone and vice
versa. We estimate Equation 7 using the most saturated specification in columns (3) to (6) of
Table 9. Again, the coefficient of the interactions treatedc \cdot shortT ermt and treatedc \cdot longT ermt
reflect the temporary and the permanent impact of the CHF-EUR decoupling event on bid-ask
spreads of DKK currency pairs.
The results shown in Table 10 are statistically and economically significant for both the temporary and the permanent impact across different maturities. As expected, they vary in magnitude,
36
See Table B.3 in the appendix for regression results on absolute bid-ask spreads in pips.
32
Electronic copy available at: https://ssrn.com/abstract=3498958
and while the spread increase is smaller in the short-term, the spreads seem to establish a ""new
normal"" well above the pre-decoupling level in the long-term. The longer-term effect shows a consistent relative increase of bid-ask spreads across the four major maturities by a log-factor of 1.5
to 2.0, which translates into a massive relative spread increase by 350-600\%. The permanent effect
is even larger than the relative long-term bid-ask spread increase of the CHF currency pairs. The
results are robust against using bid-ask spread in absolute terms without taking the logarithm
showing an absolute spread mark-up of up to 33 pips for the permanent effect depending on the
considered maturity, which is consistent with the log-results.37
Table 10
Regression on log(spreads) -- DKK currency pairs vs. major non-DKK currency pairs:
Short-term and longer-term effect
(1)
overnight
(2)
1 week
(3)
1 month
(4)
3 months
0.8146***
(0.1227)
1.4571***
(0.1244)
1.2356***
(0.2086)
2.0339***
(0.2291)
1.0866***
(0.0995)
1.9547***
(0.0954)
1.2076***
(0.1313)
1.9967***
(0.1258)
110219
0.7684
9510
0.8741
17537
0.8826
8613
0.8618
Volume \& year-end controls
\checkmark \checkmark \checkmark \checkmark Dealer-day FE
Dealer-customer-month FE
Currency-pair FE
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark Maturity:
treatedc \cdot shortT ermt
treatedc \cdot longT ermt
N
R2
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{O}\mathrm{L}\mathrm{S} \mathrm{r}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 7. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p} \mathrm{e}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s} ln(Spreadijtca )
\mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{l} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}, \mathrm{i}.\mathrm{e}. \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{b} \mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n}
\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} i \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} j \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{n}
\mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} a. treatedc \mathrm{i}\mathrm{s} \mathrm{a} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{s} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e}
\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}. \mathrm{T}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{D}\mathrm{K}\mathrm{K} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{n}\mathrm{e}
\mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e}
\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{s}\mathrm{u}\mathrm{c}\mathrm{h} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s}. shortT ermt \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o}
1, \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}, \mathrm{b}\mathrm{u}\mathrm{t} \mathrm{b} \mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e} \mathrm{F}\mathrm{e}\mathrm{b}\mathrm{r}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 1, 2015 \mathrm{t}\mathrm{o} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{t}\mathrm{h}\mathrm{e}
\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} longT ermt \mathrm{w}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{h} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1
\mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{J}\mathrm{a}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 2015. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}. \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d}
\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{s}. ***, **, * \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e}
\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} 1\%, 5\% \mathrm{a}\mathrm{n}\mathrm{d} 10\% \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{s}.
The regression results confirm a spillover of the CHF-EUR decoupling event to DKK currency
pairs, as bid-ask spreads substantially widen as response to the decoupling announcement of the
SNB. Since this happens without any monetary policy change by the DNB, results suggest that
the Danish currency peg has lost credibility after the Swiss decoupling event, and dealers price a
higher probability of a similar event and the risk of a connected FX rate jump into the FX swap
spreads. Results lend support to Hypothesis 4 of a jump risk-induced bid-ask spread increase. In
order to confirm that widened bid-ask spreads reflect a lower credibility of the Danish currency
peg, we rule out in the next section that bid-ask spreads are driven by expectations derived from
realized spot market volatility similar to CHF currency pairs.
37
See Table B.4 in the Appendix B.3 for regression results on absolute bid-ask spreads in pips.
33
Electronic copy available at: https://ssrn.com/abstract=3498958
5.3
Jump risk channel
Realized volatility in CHF currency pairs became more important as a determinant of dealers'
market expectation after the decoupling event. Dealers' increased sensitivity to realized volatility,
which translates into higher unit prices for volatility, and an overall higher volatility level explain a
significant share of the additional risk premiums charged by dealers after the CHF-EUR decoupling.
Figure 9 shows that the realized volatility of DKK and corresponding EUR currency pairs in the
platform are largely unaffected by the Swiss decoupling event. Hence, we do not expect to find
evidence for a transmission channel via realized volatility.
Figure 9
Realized volatility of FX spot rates -- DKK and corresponding EUR currency pairs
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{D}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{r}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y} \mathrm{r}\mathrm{e}\mathrm{f}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{t}\mathrm{o} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d} \mathrm{F}\mathrm{X} \mathrm{s}\mathrm{p} \mathrm{o}\mathrm{t} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y} \mathrm{d}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{h}\mathrm{e} 24 \mathrm{h}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{o} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} \mathrm{a}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{o}ff-\mathrm{t}\mathrm{h}\mathrm{e}-\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{l}\mathrm{f} \mathrm{b}\mathrm{y} \mathrm{B}\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{g} \mathrm{f}\mathrm{o}\mathrm{r}
\mathrm{a}\mathrm{l}\mathrm{l} \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s}.
\mathrm{S}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}: \mathrm{B}\mathrm{l}\mathrm{o} \mathrm{o}\mathrm{m}\mathrm{b} \mathrm{e}\mathrm{r}\mathrm{g}
During the whole observation period spot rate volatility of the EUR-DKK currency pair is very
close to zero and other DKK currency pairs very closely track the volatility of the corresponding
EUR currency pair. This behavior does not change after the CHF-EUR decoupling, suggesting
that the Danish currency peg is still effective. In line with Section 4.2, we formally test the
volatility risk channel using DKK currency pairs excluding EUR-DKK as the treatment group and
all corresponding EUR currency pairs as the control group and estimate again Equation 8. Results
for the logarithm of swap bid-ask spreads as the dependent variable, applying the same fixed effects
and control variable specifications as for the CHF analysis in Section 4.2, are shown in Table 11.
The coefficients of the triple interactions, which show dealers' change in sensitivity to realized
volatility of DKK currency pairs relative to other currency pairs in the post-periods, are either
34
Electronic copy available at: https://ssrn.com/abstract=3498958
not significantly different from zero or slightly negative. Together with a largely unaffected overall
volatility level of DKK currency pairs, results suggest that realized volatility does not play a major
role for the spread increase of DKK currency pairs. However, the diff-in-diff variable remains highly
significant after controlling for volatility and still increases in the longer-term. Hence, results hint at
tightening doubts about the Danish currency peg built up with some time delay to the decoupling
event that drove up the swap bid-ask spread of DKK currency pairs. Substantial premiums due
to dealers' increased awareness of jump risks finally confirms Hypothesis 4. The results are again
robust against including non-DKK and non-EUR currency pairs in the control group.
Table 11
Regression on log(spreads) -- DKK currency pairs vs. corresponding EUR currency pairs
Volatility effect
(1)
overnight
(2)
overnight
(3)
1 month
(4)
1 month
1.5849***
(0.1377)
1.5113***
(0.2126)
0.0049
(0.0140)
2.1733***
(0.2117)
4.0405***
(1.1882)
-0.2089*
(0.1229)
44556
0.8737
44556
0.8738
8764
0.9107
8764
0.9112
Volume \& year-end controls
\checkmark \checkmark \checkmark \checkmark Dealer-day FE
Dealer-customer-month FE
Currency-pair FE
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark Maturity:
treatedc \cdot longT ermt
volatc \cdot treatedc \cdot longT ermt
N
R2
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{O}\mathrm{L}\mathrm{S} \mathrm{r}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 7 \mathrm{i}\mathrm{n} \mathrm{c}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n}\mathrm{s} (1) \mathrm{a}\mathrm{n}\mathrm{d} (2) \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 8 \mathrm{i}\mathrm{n}
\mathrm{c}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n}\mathrm{s} (2) \mathrm{a}\mathrm{n}\mathrm{d} (4). \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p} \mathrm{e}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s} ln(Spreadijtca ) \mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{l}
\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}, \mathrm{i}.\mathrm{e}. \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{b} \mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}
\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} i \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} j \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} a. treatedc \mathrm{i}\mathrm{s} \mathrm{a}
\mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{s} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}. \mathrm{T}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}
\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{D}\mathrm{K}\mathrm{K} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{n}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e}
\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m} \mathrm{e}\mathrm{x}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{E}\mathrm{U}\mathrm{R} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{i}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{E}\mathrm{U}\mathrm{R} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}
\mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s}. shortT ermt \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}, \mathrm{b}\mathrm{u}\mathrm{t} \mathrm{b}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e} \mathrm{F}\mathrm{e}\mathrm{b}\mathrm{r}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y}
1, 2015 \mathrm{t}\mathrm{o} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} longT ermt
\mathrm{w}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{h} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1 \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{J}\mathrm{a}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 2015. volatc \mathrm{i}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d}
\mathrm{F}\mathrm{X} \mathrm{s}\mathrm{p} \mathrm{o}\mathrm{t} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y} \mathrm{d}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{h}\mathrm{e} 24 \mathrm{h}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{o} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}
\mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}-\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{e}\mathrm{r}
\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l} \mathrm{w}\mathrm{a}\mathrm{s} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}
\mathrm{i}\mathrm{n} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 8, \mathrm{b}\mathrm{u}\mathrm{t}, \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{a}\mathrm{k}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{c}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{y}, \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{o}\mathrm{n}\mathrm{l}\mathrm{y} \mathrm{s}\mathrm{h}\mathrm{o}\mathrm{w}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{w}\mathrm{o} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{o}\mathrm{f}
\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}. \mathrm{O}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{o} \mathrm{e}ffi\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{a}\mathrm{s} \mathrm{e}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}. \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}
\mathrm{a}\mathrm{n}\mathrm{d} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{s}. ***, **, * \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} 1\%, 5\% \mathrm{a}\mathrm{n}\mathrm{d} 10\% \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{s}.
5.4
Counterparty risk channel
The jump risk channel describes how decreasing credibility of a currency peg drives a dealer's
volatility expectations. Volatility expectation, irrespective of being driven by historic spot volatility
or the belief in a monetary policy instrument, affects both inventory holding costs and XVAs. In
order to disentangle these components again, we run a similar analysis as in Section 4.3. As financial
institutions became particularly at risk for a huge jump risk in the spot after a decoupling event, we
would expect a stronger effect on financial customers if indeed counterparty credit risk drives the
35
Electronic copy available at: https://ssrn.com/abstract=3498958
results. If, however, the widening of bid-ask spreads is purely due to the fear of increasing inventory
holding costs, we would expect a homogeneous increase in bid-ask spreads for both customers banks
and corporates.
Table 12 depicts the results of estimating Equation 7 for the interbank and corporate customer segments using the same treatment and control groups as in Section 5.2. Results show
that the build-up of a jump risk premium is consistent across different customer segments. However, customer banks incur a substantially higher risk premium increase than corporate customers.
Estimating the differential impact on the interbank segment in Equation 9 confirms that banks'
additional risk premiums are statistically significant too.
Table 12
Regression on log(spreads) -- DKK currency pairs vs. major non-DKK currency pairs:
Financial vs. corporate customer
Maturity:
Segment:
treatedc \cdot shortT ermt
treatedc \cdot longT ermt
(1)
overnight
all
(2)
overnight
interbank
(3)
overnight
corporate
(4)
1 month
all
(5)
1 month
interbank
(6)
1 month
corporate
0.8146***
(0.1227)
1.4571***
(0.1244)
0.8435***
(0.1301)
1.5204***
(0.1212)
0.4610***
(0.1320)
0.7308***
(0.1991)
1.0866***
(0.0995)
1.9547***
(0.0954)
1.2814***
(0.1584)
2.2283***
(0.1301)
0.8331***
(0.0963)
1.7546***
(0.0969)
\Delta treatedc \cdot shortT ermt
0.2984*
(0.1582)
0.6975***
(0.1714)
\Delta treatedc \cdot longT ermt
N
R2
0.3229**
(0.1438)
0.4298***
(0.1287)
110219
0.7684
91218
0.7688
6831
0.8708
17537
0.8826
12957
0.8585
3463
0.9383
Volume \& year-end controls
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark Dealer-day FE
Dealer-customer-month FE
Currency-pair FE
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{O}\mathrm{L}\mathrm{S} \mathrm{r}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 7. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s} ln(Spreadijtca ) \mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{l} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m}
\mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}, \mathrm{i}.\mathrm{e}. \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{b} \mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} i \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} j \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} t
\mathrm{f}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} a. treatedc \mathrm{i}\mathrm{s} \mathrm{a} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{s} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}
\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}. \mathrm{T}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{D}\mathrm{K}\mathrm{K} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{n}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}
\mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{s}\mathrm{u}\mathrm{c}\mathrm{h} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s}. shortT ermt \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l}
\mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}, \mathrm{b}\mathrm{u}\mathrm{t} \mathrm{b}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e} \mathrm{F}\mathrm{e}\mathrm{b}\mathrm{r}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 1, 2015 \mathrm{t}\mathrm{o} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} longT ermt \mathrm{w}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{h} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1 \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{J}\mathrm{a}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 2015. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p}
\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}-\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{p} \mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}. \mathrm{C}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}
\mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{m}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{u}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{b} \mathrm{e}\mathrm{l}\mathrm{o}\mathrm{w} \mathrm{c}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n} \mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{s}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{b}\mathrm{a}\mathrm{n}\mathrm{k} \mathrm{o}\mathrm{r} \mathrm{c}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}
\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e} \mathrm{t}\mathrm{o} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{b}\mathrm{a}\mathrm{n}\mathrm{k}\mathrm{s} \mathrm{o}\mathrm{r} \mathrm{c}\mathrm{o}\mathrm{r}\mathrm{p} \mathrm{o}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s}, \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{p} \mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{y}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{r}\mathrm{o}\mathrm{w}\mathrm{s} \mathrm{b}\mathrm{e}\mathrm{g}\mathrm{i}\mathrm{n}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g}
\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h} \mathrm{a} \Delta \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{o} \mathrm{e}ffi\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{i}\mathrm{p}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}-\mathrm{i}\mathrm{n}-\mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{s}-\mathrm{i}\mathrm{n}-\mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{s} \mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l} \mathrm{i}\mathrm{n}
\mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 9 \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{o}\mathrm{n} \mathrm{b}\mathrm{a}\mathrm{n}\mathrm{k}\mathrm{s} \mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}. \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}
\mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{s}. ***, **, * \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} 1\%, 5\% \mathrm{a}\mathrm{n}\mathrm{d} 10\% \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{s}.
To better understand the dynamics behind the effect on financial customers, which is the largest
segment too, we estimate the differential effect of FX exposure in Table 13. Since there are only very
few Danish customers included in the sample, we cannot run a Danish vs. non-Danish customer
analysis in line with the home currency benefit argument in Section 4.3.
Column (1) in Table 13 shows the differential effect of riskier customers with respect to FX
36
Electronic copy available at: https://ssrn.com/abstract=3498958
Table 13
Regression on log(spreads) -- DKK currency pairs vs. major non-DKK currency pairs:
Interbank details on FX exposure
(1)
overnight
interbank
all
Maturity:
Sample:
Sub-sample FX exposure:
FX exposure
low - high
customerT ypej :
treatedc \cdot shortT ermt
-0.0823
(0.3139)
0.9900***
(0.2001)
0.9268***
(0.2856)
0.6023***
(0.1853)
treatedc \cdot shortT ermt
\Delta treatedc \cdot shortT ermt
\Delta treatedc \cdot longT ermt
N
R2
91218
0.7692
Volume \& year-end controls
\checkmark Dealer-day FE
Dealer-customer-month FE
Currency-pair FE
\checkmark \checkmark \checkmark \mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{O}\mathrm{L}\mathrm{S} \mathrm{r}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 9. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s} ln(Spreadijtca ) \mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{l} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m}
\mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}, \mathrm{i}.\mathrm{e}. \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{b}\mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} i \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} j \mathrm{o}\mathrm{n}
\mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} a. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{e}ffi\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{d}\mathrm{i}ff-\mathrm{i}\mathrm{n}-\mathrm{d}\mathrm{i}ff \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{a}\mathrm{n}\mathrm{d}
\mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{i}\mathrm{p}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}-\mathrm{i}\mathrm{n}-\mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{s}-\mathrm{i}\mathrm{n}-\mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{s} \mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t} (\Delta ) \mathrm{o}\mathrm{n}
\mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{c}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{i}fi\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{F}\mathrm{X} \mathrm{e}\mathrm{x}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{l}\mathrm{e}, \mathrm{i}.\mathrm{e}. customerT ypej . \mathrm{C}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n} (1) \mathrm{s}\mathrm{h}\mathrm{o}\mathrm{w}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e}
\mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{o}\mathrm{n} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h} \mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h} \mathrm{F}\mathrm{X} \mathrm{e}\mathrm{x}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e} \mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h} \mathrm{l}\mathrm{o}\mathrm{w} \mathrm{F}\mathrm{X} \mathrm{e}\mathrm{x}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e} \mathrm{u}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}
\mathrm{a}\mathrm{g}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{l}\mathrm{d}. treatedc \mathrm{i}\mathrm{s} \mathrm{a} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y}
\mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{s} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}. \mathrm{T}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d}
\mathrm{b}\mathrm{y} \mathrm{D}\mathrm{K}\mathrm{K} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{n}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y}
\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s}. shortT ermt \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}, \mathrm{b}\mathrm{u}\mathrm{t} \mathrm{b} \mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}
\mathrm{F}\mathrm{e}\mathrm{b}\mathrm{r}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 1, 2015 \mathrm{t}\mathrm{o} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} longT ermt \mathrm{w}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{h} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l}
\mathrm{t}\mathrm{o} 1 \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{J}\mathrm{a}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 2015. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}-\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}
\mathrm{p}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}. \mathrm{C}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{m}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{e}\mathrm{s}, \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{b}\mathrm{a}\mathrm{n}\mathrm{k} \mathrm{s}\mathrm{u}\mathrm{b}-\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{s} \mathrm{o}\mathrm{f}
\mathrm{F}\mathrm{X} \mathrm{e}\mathrm{x}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{b} \mathrm{e}\mathrm{l}\mathrm{o}\mathrm{w} \mathrm{c}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n} \mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{s}. \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e}
\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{s}. ***, **, * \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} 1\%, 5\% \mathrm{a}\mathrm{n}\mathrm{d} 10\% \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{s}.
exposure, defined similar to Section 4.3, relative to less risky customers with respect to FX exposure.
Riskier customers incur a substantially higher bid-ask spread increase than less risky customers,
which is statistically significant at the 1\% level. In the short-term, risky customers with high FX
exposure can explain almost the whole bid-ask spread increase in the temporary effect, which is
indicated by a no longer statistically significant coefficient for treatedc \cdot shortT ermt . Counterparty
risk plays an even more important role for the spillover impact on DKK currency pairs than for the
direct impact of the decoupling event on CHF currency pairs. Risky banks with high FX exposure
are the major driver behind the temporary bid-ask spread increase and can also explain a substantial
share of the permanent risk premium increase. Therefore, results fully confirm Hypothesis 5.
Overall, the CHF-EUR decoupling reminded dealer banks of the consequences of terminating a
fixed exchange rate regimes. Dealers increased bid-ask spreads in the absence of actual spot market
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Electronic copy available at: https://ssrn.com/abstract=3498958
reactions. At first, dealers charge jump risk premiums to risky clients with high FX exposure, i.e.
XVAs, and increase charges for inventory holding costs in the permanent spread adjustment.
6
Conclusion
In this paper, we provide evidence for the pricing of counterparty credit risk in FX swap
derivative markets. Using a novel dataset of dealer-specific bid-ask quotes and employing the
Swiss franc decoupling from the euro on January 15, 2015 as an exogenous event, we describe three
channels that affect dealers' risk pricing and lead to a widening of bid-ask spreads through both
increased inventory holding costs and costs related to CCR, i.e. XVAs.
First, the removal of the peg increased both the level of volatility and dealers' sensitivity to
volatility for the FX spot prices of all currency pairs including CHF. Second, we document that
the peg removal remembered market participants of a potential jump risk for pegged currencies
that emerges whenever a fixed exchange rate regime is terminated. In this way, the SNB action
spilled over to other pegged currencies, such as, for instance, the Danish krone. Dealers started to
include substantial jump risk premiums into the bid-ask spreads of currency pairs including DKK,
even though FX sport prices or FX spot volatility hardly changed for these currency pairs. Finally,
both effects are substantially driven by the customer specific risk profile. Riskier customers with a
higher overall exposure to FX movements pay significantly higher premiums, especially for longer
maturities for which customers' default risk is more relevant than for overnight maturities. The
relevance of CCR is confirmed by a risk discount for Swiss customers during the temporary market
turmoil in CHF currency pairs.
The increase in bid ask-spreads for currency pairs including CHF is also economically immense
and equivalent to a substantial increase of loan margins by 5.0-7.5\%. Therefore, results also suggest
that there was a central bank-induced risk discount through credible currency pegs.
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Electronic copy available at: https://ssrn.com/abstract=3498958
Appendix
Appendix A
A.1
Swap markets around the decoupling event
EUR-CHF swaps
The announcement by the SNB to discontinue the currency peg of the Swiss franc to the euro
is inherently affecting the FX market of CHF products. By focusing on the FX swap market, we
extend the descriptive results of Cielinska et al. (2017) who primarily describe the short-term -especially intra-day -- reaction following the de-pegging announcement by a longer-term view using
dealer-individual bid-ask spread data as outlined above. Considering the executed EUR-CHF FX
swap transactions, we observe a sharp increase in total number of transactions following the de-peg,
with a particular increase in the buy-side on the event date. As supply in the uncertain environment
is expected to be rather impaired than expanded, the increase is most likely demand-side driven.
While corresponding total traded notional amounts are not increasing to the same extent, the
average trade-size is noticeable smaller. This effect, potentially indicating higher uncertainty in the
market, is persistent for approximately 2 weeks before slowly returning to a pre-event level.
Figure A.1
EUR-CHF executed swap transaction
(\bfa ) Buy and sell volume by requester type
(\bfb ) Number of executed transactions
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{F}\mathrm{i}\mathrm{g}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{n}\mathrm{l}\mathrm{y} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{E}\mathrm{U}\mathrm{R}-\mathrm{C}\mathrm{H}\mathrm{F} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{m}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{o}\mathrm{n} \mathrm{b}\mathrm{u}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s} \mathrm{d}\mathrm{a}\mathrm{y}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}. \mathrm{B}\mathrm{u}\mathrm{y}
\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{v}\mathrm{i}\mathrm{s}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{p}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{s}\mathrm{e}\mathrm{l}\mathrm{l} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}\mathrm{s} \mathrm{a}\mathrm{s} \mathrm{n}\mathrm{e}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{b}\mathrm{a}\mathrm{r}\mathrm{s}. \mathrm{P}\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{l} (\mathrm{a}) \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{s} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}\mathrm{s}, \mathrm{w}\mathrm{h}\mathrm{i}\mathrm{l}\mathrm{e} \mathrm{P}\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{l} (\mathrm{b})
\mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b} \mathrm{e}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}, \mathrm{b}\mathrm{o}\mathrm{t}\mathrm{h} \mathrm{a}\mathrm{g}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{o}\mathrm{n} \mathrm{a} \mathrm{d}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{y} \mathrm{b}\mathrm{a}\mathrm{s}\mathrm{i}\mathrm{s} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{s}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{t} \mathrm{b}\mathrm{y} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{y}\mathrm{p} \mathrm{e}, \mathrm{i}.\mathrm{e}. \mathrm{b}\mathrm{a}\mathrm{n}\mathrm{k}, \mathrm{i}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}, \mathrm{a}\mathrm{n}\mathrm{d}
\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}.
\mathrm{S}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}: \mathrm{F}\mathrm{X} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}
Figure A.2 presents the average bid- and ask quote of EUR-CHF FX swaps and reveals two
closely related effects following the decoupling event. The blue and red lines in Panel (a) and
Panel (b) show a level reduction of the bid and ask quote, respectively, and thus, reflect a shift
of the mid-price induced by EUR-CHF spot rate change as well as by the decrease in rCHF . In
addition, however, there is a widening of dealer specific bid-ask spreads, which is separately shown
(log transformed) in Panel (c) and Panel (d), which is not directly driven by a change in the FX
39
Electronic copy available at: https://ssrn.com/abstract=3498958
spot rate or interest rate cut, but driven by a change in risk pricing following the announcement.
Figure A.2
EUR-CHF swap prices
(\bfa ) Bid and ask quotes -- Overnight maturity
(\bfb ) Bid and ask quotes -- 1 month maturity
(\bfc ) Bid-ask spreads (log) -- Overnight maturity
(\bfd ) Bid-ask spreads (log) -- 1 month maturity
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{F}\mathrm{i}\mathrm{g}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{n}\mathrm{l}\mathrm{y} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{E}\mathrm{U}\mathrm{R}-\mathrm{C}\mathrm{H}\mathrm{F} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{u}\mathrm{b}-\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{e}\mathrm{r}\mathrm{s}. \mathrm{P}\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{l}\mathrm{s} (\mathrm{a}) \mathrm{a}\mathrm{n}\mathrm{d} (\mathrm{b})
\mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{a}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s} \mathrm{d}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{a} \mathrm{d}\mathrm{a}\mathrm{y}. \mathrm{P}\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{l}\mathrm{s} (\mathrm{c}) \mathrm{a}\mathrm{n}\mathrm{d} (\mathrm{d}) \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{a}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e}
\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{s} \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}, \mathrm{i}.\mathrm{e}. \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{s} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{b}\mathrm{y} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{d}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{a} \mathrm{d}\mathrm{a}\mathrm{y}.
\mathrm{S}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}: \mathrm{F}\mathrm{X} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}
A.2
EUR-DKK swaps
Even though the DNB managed to keep the EUR-DKK FX spot rate large unaffected from the
Swiss decoupling event, EUR-DKK swap prices in Figure A.3 show that FX derivatives markets
still seem to be affected by the event. Bid and ask quotes of overnight swaps in Panel (a) do not
exhibit a level change after the decoupling event, but quotes for longer maturities, such as one
month in Panel (b), do exhibit a decreasing trend until mid of February 2015. As swap prices can
be explained by spot and forward rates,38 investors seem to expect a future appreciation of DKK,
which is priced into the forward leg of the swap pushing down bid and ask rates of swaps. Panels
(c) and (d) graphically confirm that there is also more uncertainty regarding the EUR-DKK FX
38
See Section 2.2 for details.
40
Electronic copy available at: https://ssrn.com/abstract=3498958
Figure A.3
EUR-DKK swap prices
(\bfa ) Bid and ask quotes -- Overnight maturity
(\bfb ) Bid and ask quotes -- 1 month maturity
(\bfc ) Bid-ask spreads (log) -- Overnight maturity
(\bfd ) Bid-ask spreads (log) -- 1 month maturity
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{F}\mathrm{i}\mathrm{g}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{n}\mathrm{l}\mathrm{y} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{E}\mathrm{U}\mathrm{R}-\mathrm{D}\mathrm{K}\mathrm{K} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{u}\mathrm{b}-\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{e}\mathrm{r}\mathrm{s}. \mathrm{P}\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{l}\mathrm{s} (\mathrm{a}) \mathrm{a}\mathrm{n}\mathrm{d}
(\mathrm{b}) \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{a}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s} \mathrm{d}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{a} \mathrm{d}\mathrm{a}\mathrm{y}. \mathrm{P}\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{l}\mathrm{s} (\mathrm{c}) \mathrm{a}\mathrm{n}\mathrm{d} (\mathrm{d}) \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{a}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{o}\mathrm{f}
\mathrm{t}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{s} \mathrm{o}\mathrm{n} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}, \mathrm{i}.\mathrm{e}. \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{n} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{b}\mathrm{y} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{a}\mathrm{m}\mathrm{e}
\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r} \mathrm{d}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{a} \mathrm{d}\mathrm{a}\mathrm{y}.
\mathrm{S}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}: \mathrm{F}\mathrm{X} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}
rate, which is indicated by increasing swap bid ask spreads after the decoupling event. Despite
temporarily heavy monetary intervention by the DNB, investors seem to question the credibility of
the Danish currency peg after the Swiss decoupling event.
Appendix B
B.1
Robustness tests
Parallel trends
The validity of results further requires the parallel trend assumption, which we formally test by
estimating the following equation:
41
Electronic copy available at: https://ssrn.com/abstract=3498958
ln(Spreadijtca ) = \alpha it + \alpha ijt + \alpha c + \beta 1 \cdot treatedc
+ \beta 2 \cdot treatedc \cdot pre(8w)t + ... + \beta 8 \cdot treatedc \cdot pre(2w)t
+ \beta 9 \cdot treatedc \cdot post(1w)t + ... + beta1 6 \cdot treatedc \cdot post(8w)t
(B.1)
+ \gamma \cdot volumea + \delta \cdot \bfitY c + \epsilon ijtca
The pre and post variables are split into weekly indicators for an eight week period before and
after the decoupling on January 15, 2015. The week before the event is excluded and taken as
reference point for the analysis. We use the most saturated fixed-effects specification in line with
columns (4) to (7) in Table 4.39 The parallel trend is confirmed if all pre-reform period interactions
do not exhibit a significant divergence from zero -- and especially no positive one -- while the
post-reform period interactions diverge from zero, in our case in the positive direction.
Figure B.1
Parallel trend test, coefficient estimates and 90\% confidence intervals
(\bfa ) CHF currency pairs, overnight maturity
(\bfb ) DKK currency pairs, overnight maturity
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{C}\mathrm{o}\mathrm{e}ffi\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s} \mathrm{a}\mathrm{n}\mathrm{d} 90\% \mathrm{c}\mathrm{o}\mathrm{n}fi\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} treatedc \cdot pret /postt \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t} \mathrm{w}\mathrm{e}\mathrm{e}\mathrm{k}\mathrm{s} \mathrm{b} \mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d}
\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t} \mathrm{w}\mathrm{e}\mathrm{e}\mathrm{k}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}-\mathrm{p}\mathrm{e}\mathrm{g}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{r}\mathrm{e}\mathrm{d} \mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}.
\mathrm{S}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}: \mathrm{F}\mathrm{X} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}
The estimated coefficients and 90\% confidence intervals on a weekly basis around the decoupling event are depicted in Figure B.1. We exemplarily show the parallel trend estimation for the
overnight maturity, as results are consistent across maturities.40 Results in Figure B.1 confirm the
parallel trend assumption with no or slightly negative divergence from zero before the CHF-EUR
decoupling event for CHF currency pairs. The parallel trend is confirmed for DKK currency pairs,
too. Positive divergence before the decoupling event come form the year-end effect and return to
the normal pre-period level before the event takes place.
39
We replace dealer \times day fixed effects by dealer \times week fixed effects in order to absorb less observations.
Even with dealer \times week fixed effects some coefficients are absorbed by fixed effects. Weekly coefficients that can
be estimated with availabe observation in the dataset for longer maturities are consistent with the overnight results.
40
42
Electronic copy available at: https://ssrn.com/abstract=3498958
B.2
Additional robustness of CHF currency pairs
Table B.1
Regression on spreads -- CHF currency pairs vs. major non-CHF currency pairs
(1)
overnight
(6)
1 month
(7)
3 months
treatedc \cdot postt
1.0066*** 1.0122*** 1.0033*** 0.9469*** 3.3688*** 5.6386***
(0.1946)
(0.1957)
(0.1969)
(0.1832)
(0.5144)
(1.3093)
10.1554***
(2.0821)
N
R2
121608
0.0753
121475
0.1619
121125
0.1923
120642
0.2434
11633
0.6546
22203
0.5892
12127
0.7022
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark Maturity:
Volume \& year-end controls
Dealer-day FE
Customer-month FE
Dealer-customer FE
Dealer-customer-month FE
Currency-pair FE
(2)
overnight
(3)
overnight
(4)
overnight
\checkmark \checkmark (5)
1 week
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{O}\mathrm{L}\mathrm{S} \mathrm{r}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 6. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s} Spreadijtca \mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{i}\mathrm{p}\mathrm{s},
\mathrm{i}.\mathrm{e}. \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{b} \mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} i \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} j \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} a.
treatedc \mathrm{i}\mathrm{s} \mathrm{a} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{s} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}. \mathrm{T}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s}
\mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{C}\mathrm{H}\mathrm{F} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{n}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d}
\mathrm{b}\mathrm{y} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{s}\mathrm{u}\mathrm{c}\mathrm{h} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s}. postt \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{a}\mathrm{n}\mathrm{d} 0 \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}.
\mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}-\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l}
\mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}. \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{s}. ***, **, * \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e}
1\%, 5\% \mathrm{a}\mathrm{n}\mathrm{d} 10\% \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{s}.
Table B.2
Regression on spreads -- CHF currency pairs vs. major non-CHF currency pairs:
Short-term and longer-term effect
(1)
overnight
(2)
1 week
(3)
1 month
(4)
3 months
1.8799***
(0.3964)
0.3369***
(0.1035)
4.7586***
(0.7161)
1.6152***
(0.3298)
8.2622***
(1.7135)
3.1226***
(0.9157)
12.9379***
(2.2425)
6.2747***
(2.1280)
120642
0.2541
11633
0.6681
22203
0.6105
12127
0.7118
Volume \& year-end controls
\checkmark \checkmark \checkmark \checkmark Dealer-day FE
Dealer-customer-month FE
Currency-pair FE
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark Maturity:
treatedc \cdot shortT ermt
treatedc \cdot longT ermt
N
R2
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{O}\mathrm{L}\mathrm{S} \mathrm{r}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 7. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p} \mathrm{e}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s} Spreadijtca \mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{e}\mathrm{d}
\mathrm{a}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{i}\mathrm{p}\mathrm{s}, \mathrm{i}.\mathrm{e}. \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{b} \mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}
\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} i \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} j \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} a. treatedc \mathrm{i}\mathrm{s}
\mathrm{a} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{s} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}. \mathrm{T}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}
\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{C}\mathrm{H}\mathrm{F} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{n}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n}
\mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{s}\mathrm{u}\mathrm{c}\mathrm{h}
\mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s}. shortT ermt \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t},
\mathrm{b}\mathrm{u}\mathrm{t} \mathrm{b} \mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e} \mathrm{F}\mathrm{e}\mathrm{b}\mathrm{r}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 1, 2015 \mathrm{t}\mathrm{o} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t}
\mathrm{i}\mathrm{s} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} longT ermt \mathrm{w}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{h} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1 \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{J}\mathrm{a}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 2015. \mathrm{T}\mathrm{h}\mathrm{e}
\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}-\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{p} \mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}
\mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}. \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}
\mathrm{a}\mathrm{n}\mathrm{d} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{s}. ***, **, * \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} 1\%, 5\% \mathrm{a}\mathrm{n}\mathrm{d} 10\% \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{s}.
43
Electronic copy available at: https://ssrn.com/abstract=3498958
Figure B.2
Realized volatility of FX spot rates -- Non-EUR and non-CHF currency pairs
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{D}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{r}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y} \mathrm{r}\mathrm{e}\mathrm{f}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{t}\mathrm{o} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d} \mathrm{F}\mathrm{X} \mathrm{s}\mathrm{p} \mathrm{o}\mathrm{t} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}
\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y} \mathrm{d}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{t}\mathrm{h}\mathrm{e} 24 \mathrm{h}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{o} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} \mathrm{a}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{o}ff-\mathrm{t}\mathrm{h}\mathrm{e}-\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{l}\mathrm{f} \mathrm{b}\mathrm{y}
\mathrm{B}\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{g} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{d}\mathrm{e}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s}.
\mathrm{S}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}: \mathrm{B}\mathrm{l}\mathrm{o} \mathrm{o}\mathrm{m}\mathrm{b} \mathrm{e}\mathrm{r}\mathrm{g}
B.3
Additional robustness of DKK currency pairs
Table B.3
Regression on spreads -- DKK currency pairs vs. major non-DKK currency pairs
(1)
overnight
Maturity:
(2)
overnight
(3)
overnight
(4)
overnight
(5)
1 week
(6)
1 month
(7)
3 months
treatedc \cdot postt
4.8262*** 4.8713*** 4.9041*** 4.9429*** 9.5441*** 16.0615*** 27.5896***
(0.8377)
(0.8437)
(0.8589)
(0.8612)
(2.3980)
(1.4813)
(2.9055)
N
R2
111208
0.2383
111048
0.2948
110719
0.3179
110219
0.3525
9510
0.6739
17537
0.6739
8613
0.8597
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark Volume \& year-end controls
Dealer-day FE
Customer-month FE
Dealer-customer FE
Dealer-customer-month FE
Currency-pair FE
\checkmark \checkmark \mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{O}\mathrm{L}\mathrm{S} \mathrm{r}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 6. \mathrm{D}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s} Spreadijtca \mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{i}\mathrm{p}\mathrm{s}, \mathrm{i}.\mathrm{e}.
\mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{b} \mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} i \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} j \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} a.
treatedc \mathrm{i}\mathrm{s} \mathrm{a} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{s} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}. \mathrm{T}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s}
\mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{D}\mathrm{K}\mathrm{K} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{n}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d}
\mathrm{b}\mathrm{y} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{s}\mathrm{u}\mathrm{c}\mathrm{h} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s}. postt \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{a}\mathrm{n}\mathrm{d} 0 \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}.
\mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}-\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l}
\mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}. \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{s}. ***, **, * \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e}
1\%, 5\% \mathrm{a}\mathrm{n}\mathrm{d} 10\% \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{s}.
44
Electronic copy available at: https://ssrn.com/abstract=3498958
Table B.4
Regression on spreads -- DKK currency pairs vs. major non-DKK currency pairs:
Short-term and longer-term effect
(1)
overnight
(2)
1 week
(3)
1 month
(4)
3 months
3.3012***
(0.8264)
5.7759***
(0.9623)
7.2078**
(3.2279)
11.5343***
(1.9831)
9.1401***
(1.2257)
20.0458***
(1.9722)
20.2344***
(3.6004)
32.8679***
(3.8514)
120642
0.3568
11633
0.6804
22203
0.6981
12127
0.8675
Volume \& year-end controls
\checkmark \checkmark \checkmark \checkmark Dealer-day FE
Dealer-customer-month FE
Currency-pair FE
\checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark \checkmark Maturity:
treatedc \cdot shortT ermt
treatedc \cdot longT ermt
N
R2
\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}: \mathrm{O}\mathrm{L}\mathrm{S} \mathrm{r}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} 7. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{p} \mathrm{e}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s} Spreadijtca \mathrm{d}\mathrm{e}fi\mathrm{n}\mathrm{e}\mathrm{d}
\mathrm{a}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{b}\mathrm{i}\mathrm{d}-\mathrm{a}\mathrm{s}\mathrm{k} \mathrm{s}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{i}\mathrm{p}\mathrm{s}, \mathrm{i}.\mathrm{e}. \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}ff\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{b}\mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n} \mathrm{a}\mathrm{s}\mathrm{k} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{b}\mathrm{i}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}
\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} i \mathrm{t}\mathrm{o} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r} j \mathrm{o}\mathrm{n} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{n} \mathrm{a}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} a. treatedc \mathrm{i}\mathrm{s} \mathrm{a}
\mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} c \mathrm{i}\mathrm{s} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}. \mathrm{T}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}
\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{C}\mathrm{H}\mathrm{F} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{o}\mathrm{n}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n}
\mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p} \mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{s}\mathrm{u}\mathrm{c}\mathrm{h}
\mathrm{m}\mathrm{a} \mathrm{j}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{s}. shortT ermt \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1, \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t},
\mathrm{b}\mathrm{u}\mathrm{t} \mathrm{b} \mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e} \mathrm{F}\mathrm{e}\mathrm{b}\mathrm{r}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 1, 2015 \mathrm{t}\mathrm{o} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t}. \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m} \mathrm{e}ff\mathrm{e}\mathrm{c}\mathrm{t}
\mathrm{i}\mathrm{s} \mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{y} longT ermt \mathrm{w}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{h} \mathrm{i}\mathrm{s} \mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{o} 1 \mathrm{i}\mathrm{f} \mathrm{d}\mathrm{a}\mathrm{y} t \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{J}\mathrm{a}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{y} 2015. \mathrm{T}\mathrm{h}\mathrm{e}
\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{a}\mathrm{p} \mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}-\mathrm{e}\mathrm{n}\mathrm{d} \mathrm{d}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{y} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}
\mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}. \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\mathrm{s} \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}
\mathrm{a}\mathrm{n}\mathrm{d} \mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{i}\mathrm{n} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{s}. ***, **, * \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{i}fi\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e} 1\%, 5\% \mathrm{a}\mathrm{n}\mathrm{d} 10\% \mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{s}.
45
Electronic copy available at: https://ssrn.com/abstract=3498958
Journal of Financial Economics 103 (2012) 280–293
Contents lists available at SciVerse ScienceDirect
Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec
Counterparty credit risk and the credit default swap market$
Navneet Arora a, Priyank Gandhi b, Francis A. Longstaff b,c,n
a
American Century Investments, United States
UCLA Anderson School, United States
c
NBER, United States
b
a r t i c l e in f o
abstract
Article history:
Received 19 February 2010
Received in revised form
8 April 2011
Accepted 9 June 2011
Available online 19 October 2011
Counterparty credit risk has become one of the highest-profile risks facing participants
in the financial markets. Despite this, relatively little is known about how counterparty
credit risk is actually priced. We examine this issue using an extensive proprietary data
set of contemporaneous CDS transaction prices and quotes by 14 different CDS dealers
selling credit protection on the same underlying firm. This unique cross-sectional data
set allows us to identify directly how dealers’ credit risk affects the prices of these
controversial credit derivatives. We find that counterparty credit risk is priced in the
CDS market. The magnitude of the effect, however, is vanishingly small and is
consistent with a market structure in which participants require collateralization of
swap liabilities by counterparties.
& 2011 Elsevier B.V. All rights reserved.
JEL classification:
G12
G13
G24
Keywords:
Counterparty credit risk
Credit default swaps
Collateralization
1. Introduction
During the past several years, counterparty credit risk
has emerged as one of the most important factors driving
financial markets and contributing to the global credit crisis.
Concerns about counterparty credit risk were significantly
heightened in early 2008 by the collapse of Bear Stearns, but
then skyrocketed later in the year when Lehman Brothers
declared Chapter 11 bankruptcy and defaulted on its debt
$
The authors are grateful for the comments of Darrell Duffie, Chris
Jones, Peter Knez, Peter Meindl, Derek Schaeffer, Victor Wong, and
seminar participants at the 2010 NYU Moody’s Conference, the 2010
Moody’s Risk Practitioner Conference in San Francisco, the 2010 SIAM
conference on Financial Mathematics and Engineering, and the 2010
USC/UCLA Financial Research Conference. We are particularly grateful
for the comments and advice of the editor Bill Schwert and an
anonymous referee. All errors are our responsibility.
n
Corresponding author at: UCLA Anderson School, United States.
E-mail address: francis.longstaff@anderson.ucla.edu (F.A. Longstaff).
0304-405X/$ - see front matter & 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.jfineco.2011.10.001
and swap obligations.1 Fears of systemic defaults were so
extreme in the aftermath of the Lehman bankruptcy that
Euro-denominated CDS contracts on the U.S. Treasury
were quoted at spreads as high as 100 basis points.
Despite the significance of counterparty credit risk in
the financial markets, however, there has been relatively
little empirical research about how it affects the prices of
contracts and derivatives in which counterparties may
default. This is particularly true for the $57.3 trillion
notional credit default swap (CDS) market in which
defaultable counterparties sell credit protection (essentially insurance) to other counterparties.2 The CDS markets
have been the focus of much attention recently because it
was AIG’s massive losses on credit default swap positions
1
Lehman Brothers filed for Chapter 11 bankruptcy on September
15, 2008. During the same month, American International Group (AIG),
Merrill Lynch, Fannie Mae, and Freddie Mac also failed or were placed
under conservatorship by the U.S. government.
2
The size of the CDS market as of June 30, 2008 comes from
estimates reported by the Bank for International Settlements.
N. Arora et al. / Journal of Financial Economics 103 (2012) 280–293
that led to the Treasury’s $182.5 billion bailout of AIG.
Furthermore, concerns about the extent of counterparty
credit risk in the CDS market underlie recent proposals to
create a central clearinghouse for CDS transactions.3
This paper uses a unique proprietary data set to
examine how counterparty credit risk affects the pricing
of CDS contracts. Specifically, this data set includes contemporaneous CDS transaction prices and quotations
provided by 14 large CDS dealers for selling protection
on the same set of underlying reference firms. Thus, we
can use this cross-sectional data to measure directly how
a CDS dealer’s counterparty credit risk affects the prices at
which the dealer can sell credit protection. A key aspect of
the data set is that it includes most of 2008, a period
during which fears of counterparty defaults in the CDS
market reached historical highs. Thus, this data set
provides an ideal sample for studying the effects of
counterparty credit risk on prices in derivatives markets.
Four key results emerge from the empirical analysis.
First, we find that there is a significant relation between
the credit risk of the dealer and the prices at which the
dealer can sell credit protection. As would be expected,
the higher the dealer’s credit risk, the lower is the price
that the dealer can charge for selling credit protection.
This confirms that prices in the CDS market respond
rationally to the perceived counterparty risk of dealers
selling credit protection.
Second, although there is a significant relation
between dealer credit risk and the cost of credit protection, we show that the effect on CDS spreads is vanishingly small. In particular, an increase in the dealer’s credit
spread of 645 basis points only translates into a onebasis-point decline on average in the dealer’s spread for
selling credit protection. This small effect is an order of
magnitude smaller than what would be expected if swap
liabilities were uncollateralized. In contrast, the size of
the pricing effect is consistent with the standard practice
among dealers of having their counterparties fully collateralize swap liabilities.
Third, the Lehman bankruptcy in September 2008 was
a major counterparty credit event in the financial markets. Accordingly, we examine how the pricing of counterparty credit risk was affected by this event. We find that
counterparty credit risk was priced prior to the Lehman
bankruptcy. After the Lehman event, the point estimate of
the effect increases but remains very small in economic
terms. The increase is significant at the 10% level (but not
at the 5% level).
Fourth, we study whether the pricing of counterparty
credit risk varies across industries. In theory, the default
correlation between the firm underlying the CDS contract
and the CDS dealer selling protection on that firm should
affect the pricing. Clearly, to take an extreme example, no
investor would be willing to buy credit protection on
Citigroup from Citigroup itself. Similarly, to take a less
extreme example, we might expect the pricing of CDS
3
For example, see the speech by Federal Reserve Board Chairman
Ben S. Bernanke at the Council on Foreign Relations on March 10, 2009.
For an in-depth discussion of the economics of CDS clearinghouse
mechanisms, see Duffie and Zhu (2009).
281
dealers’ credit risk to be more evident in selling credit
protection on other financial firms. Surprisingly, we find
that counterparty credit risk is priced in the CDS spreads
of all firms in the sample except for the financials.
These results have many implications for current proposals to regulate the CDS market. As one example, they
argue that market participants may view current CDS risk
mitigation techniques such as the overcollateralization of
swap liabilities and bilateral netting as largely successful in
addressing counterparty credit risk concerns. Thus, proposals to create a central CDS exchange may not actually be
effective in reducing counterparty credit risk further.
This paper contributes to an extensive literature on the
effect of counterparty credit risk on derivatives valuation.
Important research in this area includes Cooper and Mello
(1991), Sorensen and Bollier (1994), Duffie and Huang
(1996), Jarrow and Yu (2001), Hull and White (2001),
Longstaff (2004, 2010), and many others. The paper most
closely related to our paper is Duffie and Zhu (2009) who
study whether the introduction of a central clearing
counterparty into the CDS market could improve on
existing credit mitigation mechanisms such as bilateral
netting. They show that a central clearing counterparty
might actually increase the amount of credit risk in the
market. Thus, our empirical results support and complement the theoretical analysis provided in Duffie and Zhu.
The remainder of this paper is organized as follows.
Section 2 provides a brief introduction to the CDS market.
Section 3 discusses counterparty credit risk in the context
of the CDS markets. Section 4 describes the data. Section 5
examines the effects of dealers’ credit risk on spreads in
the CDS market. Section 6 summarizes the results and
presents concluding remarks.
2. The credit default swap market
In this section, we review briefly the basic features of a
typical CDS contract. We then discuss the institutional
structure of the CDS market.
2.1. CDS contracts
A CDS contract is best thought of as a simple insurance
contract on the event that a specific firm or entity defaults
on its debt. As an example, imagine that counterparty A
buys credit protection on Amgen from counterparty B by
paying a fixed spread of, say, 225 basis points per year for
a term of five years. If Amgen does not default during this
period of time, then B does not make any payments to A. If
there is a default by Amgen, however, then B pays A the
difference between the par value of the bond and the
post-default value (typically determined by a simple
auction mechanism) of a specific Amgen bond. In essence,
the protection buyer is able to put the bond back to the
protection seller at par in the event of a default. Thus, the
CDS contract ‘‘insures’’ counterparty A against the loss of
value associated with default by Amgen.4
4
For a detailed description of CDS contracts, see Longstaff, Mithal,
and Neis (2005).
282
N. Arora et al. / Journal of Financial Economics 103 (2012) 280–293
2.2. The structure of the CDS market
Like interest rate swaps and other fixed income derivatives, CDS contracts are traded in the over-the-counter
market between large financial institutions. During the
past 10 years, CDS contracts have become one of the
largest financial products in the fixed-income markets. As
of June 30, 2008, the total notional amount of CDS
contracts outstanding was $57.325 trillion. Of this
notional, $33.083 trillion is with dealers, $13.683 trillion
with banks, $0.398 trillion with insurance companies,
$9.215 trillion with other financial institutions, and
$0.944 trillion with nonfinancial customers.5
Early in the development of the CDS market, participants recognized the advantages of having a standardized
process for initiating, documenting, and closing out CDS
contracts. The chartering of the International Swaps and
Derivatives Association (ISDA) in 1985 led to the development of a common framework which could then be
used by institutions as a uniform basis for their swap and
derivative transactions with each other. Currently, ISDA
has 830 member institutions. These institutions include
virtually every participant in the swap and derivatives
markets. As the central organization of the privately
negotiated derivatives industry, ISDA performs many
functions such as producing legal opinions on the enforceability of netting and collateral arrangements, advancing the understanding and treatment of derivatives and
risk management from public policy and regulatory capital perspectives, and developing uniform standards and
guidelines for the derivatives industry.6
3. Counterparty credit risk
In this section, we first review some of the sources of
counterparty credit risk in the CDS market. We then
discuss ways in which the industry has attempted to
mitigate the risk of losses stemming from the default of a
counterparty to a CDS contract.
3.1. Sources of counterparty credit risk
There are at least three ways in which a participant in
the CDS market may suffer losses when their counterparty enters into financial distress. First, consider the case
in which a market participant buys credit protection on a
reference firm from a protection seller. If the reference
firm underlying the CDS contract defaults, the protection
buyer is then owed a payment from the counterparty. If
the default was unanticipated, however, then the protection seller could suddenly be faced with a large loss. If the
loss was severe enough, then the protection seller could
potentially be driven into financial distress. Thus, the
protection buyer might not receive the promised protection payment.
5
Data obtained from Table 4 of OTC Derivatives Market Activity for
the First Half of 2008, Bank for International Settlements.
6
This discussion draws on the information about ISDA provided on
its Web site www.isda.org.
Second, even if the reference firm underlying the CDS
contract does not default, a participant in the CDS market
could still experience a substantial loss in the event that
the counterparty to the contract entered financial distress.
The reason for this is that while CDS contracts initially
have value of zero when they are executed, their mark-tomarket values may diverge significantly from zero over
time as credit spreads evolve. Specifically, consider the
case where counterparty A has an uncollateralized markto-market liability of X to counterparty B. If counterparty
A were to enter bankruptcy, thereby canceling the CDS
contract and making the liability immediately due and
payable, then counterparty B’s only recourse would be to
attempt to collect its receivable of X from the bankruptcy
estate. As such, counterparty B would become a general
unsecured creditor of counterparty A. Given that the debt
and swap liabilities of Lehman Brothers were settled at
only 8.625 cents on the dollar, this could result in
counterparty B suffering substantial losses from the
default of counterparty A.7
A third way in which a market participant could suffer
losses through the bankruptcy of a counterparty is
through the collateral channel. Specifically, consider the
case where counterparty A posts collateral with counterparty B, say, because counterparty B is counterparty A’s
prime broker. Now imagine that the collateral is either
not segregated from counterparty B’s general assets (as
was very typical prior to the Lehman default), or that
counterparty B rehypothecates counterparty A’s collateral
(also very common prior to the Lehman default). In this
context, a rehypothecation of collateral is the situation in
which counterparty B transfers counterparty A’s collateral
to a third party (without transferring title to the collateral) in order to obtain a loan from the third party.
Buhlman and Lane (2009) argue that under certain circumstances, the rehypothecated securities become part of
the bankruptcy estate. Thus, if counterparty B filed for
bankruptcy after rehypothecating counterparty A’s collateral, or if counterparty A’s collateral was not legally
segregated, then counterparty A would become a general
unsecured creditor of counterparty B for the amount of
the collateral, again resulting in large potential losses. An
even more precarious situation would be when the
rehypothecated collateral itself was seized and sold by
the third party in response to counterparty B’s default on
the loan obtained using the rehypothecated securities as
collateral. Observe that because of this collateral channel,
counterparty A could suffer significant credit losses from
counterparty B’s bankruptcy, even if counterparty B does
not actually have a mark-to-market liability to counterparty A stemming from the CDS contract.
3.2. Mitigating counterparty credit risk
One of the most important ways in which the CDS
market attempts to mitigate counterparty credit risk is
7
The settlement amount was based on the October 10, 2008
Lehman Brothers credit auction administered by Creditex and Markit
and participated in by 14 major Wall Street dealers. See the Lehman
auction protocol and auction results provided by ISDA.
N. Arora et al. / Journal of Financial Economics 103 (2012) 280–293
283
through the market infrastructure provided by ISDA. In
particular, ISDA has developed specific legal frameworks
for standardized master agreements, credit support
annexes, and auction, closeout, credit support, and novation protocols. These ISDA frameworks are widely used by
market participants and serve to significantly reduce the
potential losses arising from the default of a counterparty
in a swap or derivative contract.8
Master agreements are encompassing contracts between
two counterparties that detail all aspects of how swap and
derivative contracts are to be executed, confirmed, documented, settled, etc. Once signed, all subsequent swaps and
derivative transactions become part of the original master
swap agreement, thereby eliminating the need to have
separate contracts for each transaction. An important
advantage of this structure is that it allows all contracts
between two counterparties to be netted in the event of a
default by one of the counterparties. This netting feature
implies that when default occurs, the market value of all
contracts between counterparties A and B are aggregated
into a net amount, leaving one of the two counterparties
with a net liability to the other. Without this feature,
counterparties might have incentives to demand payment
on contracts on which they have a receivable, but repudiate
contracts on which they have a liability to the defaulting
counterparty.
Credit support annexes are standardized agreements
between counterparties governing how credit risk mitigation mechanisms are to be structured. For example, a
specific type of credit risk mitigation mechanism is the
use of margin calls in which counterparty A demands
collateral from counterparty B to cover the amount of
counterparty B’s net liability to counterparty A. The credit
support annex specifies details such as the nature and
type of collateral to be provided, the minimum collateral
transfer amount, how the collateral amount is to be
calculated, etc.
ISDA protocols specify exactly how changes to master
swap agreements and credit support annexes can be
modified. These types of modifications are needed from
time to time to reflect changes in the nature of the
markets. For example, the increasing tendency among
market participants to closeout positions through novation rather than by offsetting positions motivated the
development of the 2006 ISDA Novation Protocol II.
Similarly, the creation of a standardized auction mechanism for settling CDS contracts on defaulting firms motivated the creation of the 2005–2009 ISDA auction
protocols and the 2009 ISDA closeout amount protocol.
An important second way in which counterparty credit
risk is minimized is through the use of collateralization.
Recall that the value of a CDS contract can diverge
significantly from zero as the credit risk of the reference
firm underlying the contract varies over time. As a result,
each counterparty could have a significant mark-to-market liability to the other at some point during the life of
the contract. In light of the potential credit risk, full
collateralization of CDS liabilities has become the market
standard. For example, the ISDA Margin Survey (2009)
reports that 74% of CDS contracts executed during 2008
were subject to collateral agreements and that the estimated amount of collateral in use at the end of 2008 was
approximately $4.0 trillion. Typically, collateral is posted
in the form of cash or government securities. Participants
in the Margin Survey indicate that approximately 80% of
the ISDA credit support agreements are bilateral, implying
two-way transfers of collateral between counterparties. Of
the 20 largest respondents to the survey (all large CDS
dealers), 50% of their collateral agreements are with hedge
funds and institutional investors, 15% are with corporations, 13% are with banks, and 21% are with others.
The data set used in this study represents the CDS
spreads at which the largest Wall Street dealers actually
sell, or are willing to sell, credit protection. Both discussions with CDS traders and margin survey evidence
indicate that the standard practice by these dealers is to
require full collateralization of swap liabilities by both
counterparties to a CDS contract. In fact, the CDS traders
we spoke with reported that the large Wall Street dealers
they trade with typically require that their non-dealer
counterparties overcollateralize their CDS liabilities
slightly. This is consistent with the ISDA Margin Survey
(2009) that documents that the 20 largest firms
accounted for 93% of all collateral received, but only 89%
of all collateral delivered, suggesting that there was a net
inflow of collateral to the largest CDS dealers. Furthermore, the degree of overcollateralization required can
vary over time. As an example, one reason for the liquidity
problems at AIG that led to emergency loans by the
Federal Reserve was that AIG would have been required
to post additional collateral to CDS counterparties if AIG’s
credit rating had downgraded further.9
At first glance, the market standard of full collateralization seems to suggest that there may be little risk of a
loss from the default of a Wall Street credit protection
seller. This follows since the protection buyer holds
collateral in the amount of the protection seller’s CDS
liability. In actuality, however, the Wall Street practice of
requiring non-dealer protection buyers to slightly overcollateralize their liabilities actually creates a subtle
counterparty credit risk. To illustrate this, imagine that a
protection buyer has a mark-to-market liability to the
protection seller of $15 per $100 notional amount.
Furthermore, imagine that the protection seller requires
the protection buyer to post $17 in collateral. Now
consider what occurs if the protection seller defaults.
The bankruptcy estate of the protection seller uses $15
of the protection buyer’s collateral to offset the $15 markto-market liability. Rather than returning the additional
$2 of collateral, however, this additional capital becomes
part of the bankruptcy estate. This implies that the
protection buyer is now an unsecured creditor in the
8
Bliss and Kaufman (2006) provide an excellent discussion of the
role of ISDA and of netting, collateral, and closeout provisions in
mitigating systemic credit risk.
9
For example, see the speech by Federal Reserve Chairman Ben S.
Bernanke before the Committee on Financial Services, U.S. House of
Representatives, on March 24, 2009.
284
N. Arora et al. / Journal of Financial Economics 103 (2012) 280–293
amount of the $2 excess collateral. Thus, in this situation,
the protection buyer could suffer a significant loss even
though the buyer actually owed the defaulting counterparty on the CDS contract.
This scenario is far from hypothetical. In actuality, a
number of firms experienced major losses on swap contracts in the wake of the Lehman bankruptcy because of
their net exposure (swap liability and offsetting collateral)
to Lehman.10
4. The data
Fixed-income securities and contracts are traded primarily in over-the-counter markets. For example, Treasury bonds, agency bonds, sovereign debt, corporate bonds,
mortgage-backed securities, bank loans, interest rate
swaps, and CDS contracts are all traded in over-thecounter markets. Because of the inherent decentralized
nature of these markets, however, actual transaction
prices are difficult to observe. This is why most of the
empirical research in the financial literature about fixedincome markets has typically been based on the quotation
data available to participants in these markets.
We were fortunate to be given access to an extensive
proprietary data set of CDS prices by one of the largest
fixed-income asset management firms in the financial
markets. A unique feature of this data set is that it contains
both actual CDS transaction prices for contracts entered
into by this firm as well as actionable quotations provided
to the firm by a variety of CDS dealers. These quotations
are actionable in the sense that the dealers are keenly
aware that the firm expects to be able to trade (and often
does) at the prices quoted by the dealers (and there are
implicit sanctions imposed on dealers who do not honor
their quotations). Thus, these quotations should more
closely represent actual market prices than the indicative
quotes typically used in the fixed-income literature.
In this paper, we study the spreads associated with
contracts in which 14 major CDS dealers sell five-year
credit protection to the fixed-income asset management
firm on the 125 individual firms in the widely followed
CDX index. The sample period for the study is March 31,
2008 to January 20, 2009. This period covers the turbulent
Fall 2008 period in which Fannie Mae, Freddie Mac,
Lehman Brothers, AIG, etc. entered into financial distress
and counterparty credit fears reached their peak. Thus,
this sample period is ideally suited for studying the effects
of counterparty credit risk on financial markets.
The transactions data in the sample are taken from a
file recording the spreads on actual CDS contracts executed by the firm in which the firm is buying credit
protection. There are roughly 1,000 transactions in this
file. The average transaction size is $6.5 million and the
average maturity of these contracts is 4.9 years. All 14 of
the major CDS dealers to be studied in this paper are
10
From the October 7, 2008 Financial Times: ‘‘The exact amount of
any claim is determined by the difference between the value of the
collateral and the cost of replacing the contract.. . . Moreover, many
counterparties to Lehman who believe it owes them money have joined
the ranks of unsecured creditors.’’
included in this file. Thus, all 14 of these dealers sold
credit protection to the asset management firm during the
sample period. Of these transactions, however, most
involve either firms that are not in the CDX index, or
contracts with maturities significantly different from five
years. Screening out these trades results in a sample of
several hundred observations.
To augment the sample, we also include quotes provided directly to the firm by the CDS dealers selling
protection on the firms in the CDX index. As described
above, these quotes represent firm offers to sell protection
and there can be sanctions for dealers who fail to honor
their quotes. For example, if the asset management firm
finds that a dealer is often not willing to execute new
trades (or unwind existing trades) at quoted prices, then
that dealer could be dropped from the list of dealers that
the firm’s traders are willing to do business with. Given
the large size of the asset management firm providing the
data, the major CDS dealers included in the study have
strong incentives to provide actionable quotes.
There are a number of clear indications that the dealers respond to these incentives and provide reliable
quotes. First, the dealers included in the study frequently
update their quotes throughout the trading day. The total
number of quotations records in the data set for firms in
the CDX index is 673,060. This implies an average of 2.19
quotations per day per dealer for each of the firms in the
sample. Thus, quotes are clearly being refreshed throughout the trading day. Second, the fact that all 14 of the CDS
dealers sold protection to the asset management firm
during the sample period suggests that each was active in
providing competitive and actionable quotes during this
period. Third, we compare our sample of transaction
prices directly to the quotes available in the market on
the same day. This comparison is necessarily a little noisy
since the transaction prices are not time-stamped within
the day, and we are comparing them to quotes available
in the market at roughly 11:30 AM. Despite this, however,
the average transaction price is only 0.26 basis points
below the minimum quote available in the market. The
standard deviation of the difference is 5.87 basis points
and the difference between the mean transaction price
and minimum quote is not statistically significant.
As mentioned, dealers frequently update their quotations throughout the day to insure that they are current.
Since our objective is to study whether the cross-sectional
dispersion in dealer prices is related to counterparty
credit risk, it is important that we focus on dealer prices
that are as close to contemporaneous as possible. To this
end, we extract quotes from the data set in the following
way. First, we select 11:30 AM as the reference time. For
each of the 14 CDS dealers, we then include the quote
with time-stamp nearest to 11:30 AM, but within 15
minutes (from 11:15 to 11:45 AM). In many cases, of
course, there may not be a quote within this 30-minute
period. Thus, we will generally have fewer than 14 prices
or quotes available for each firm each day. For a firm to be
included in the sample for a particular day, we require
that there be two or more prices or quotes for that firm.
We repeat this process for all days and firms in the
sample.
N. Arora et al. / Journal of Financial Economics 103 (2012) 280–293
This algorithm results in a set of 13,383 observation
vectors of synchronous prices or quotations by multiple CDS
dealers for selling protection on a common underlying
reference firm. Since there are 212 trading days in the
sample period, this implies that we have data for multiple
CDS dealers for an average of 63.13 firms each day. Table 1
presents summary statistics for the data. As shown, the
number of synchronous quotes ranges from two to nine. On
average, an observation includes 3.073 dealer quotes for the
reference firm for that day. Table 1 also shows that the
variation in the quotes provided by the various dealers is
relatively modest. For most of the observations, the range of
CDS quotations is only on the order of two to three basis
points, and the median range is three basis points.
In addition to the prices and quotes provided by the
dealers selling protection, we also need a measure of
the counterparty credit risk of the dealers themselves. To
this end, we obtain daily midmarket five-year CDS quotes
referencing each of the 14 major CDS dealers in the study.
The midmarket spreads for these CDS contracts are obtained
285
from the Bloomberg system and reflect the market’s perception of the counterparty credit risk of the dealers selling
credit protection to the asset management firm.
Table 2 reports summary statistics for the CDS spreads
for these dealers. As shown, the average CDS spread
ranges from a low of 59.40 basis points for BNP Paribas
to a high of 355.10 basis points for Morgan Stanley. Note
that CDS data for Lehman Brothers and Merrill Lynch are
included in the data set even though these firms either
went bankrupt or merged during the sample period. The
reason for including these firms is that both were actively
making markets in selling credit protection through much
of the sample period. Thus, their spreads may be particularly informative about the impact of perceived counterparty credit risk on CDS spreads.
5. Empirical analysis
In this section, we begin by briefly describing the
methodology used in the empirical analysis. We then test
Table 1
The distribution of dealer prices and quotations.
This table provides summary statistics for the distribution of dealer prices or quotations for CDS contracts referencing the firms in the CDX index. The
panel on the left summarizes the distribution in terms of the number of dealer prices and quotations on a given day for a CDS contract referencing a
specific firm. The panel on the right summarizes the distribution in terms of the range R of prices and quotations (measured in basis points) provided by
dealers on a given day for a CDS contract on a specific reference firm. Only days on which two or more simultaneous prices or quotations are available for
a specific firm are included in the sample as an observation. The sample period is March 31, 2008 to January 20, 2009.
Number
Observations
Percentage
Range
Observations
Percentage
2
3
4
5
6
7
8
9
4907
4518
2566
1012
267
84
21
8
36.66
33.78
19.17
7.56
1.99
0.62
0.16
0.06
0
0oRr1
1oRr2
2oRr3
3oRr4
4oRr5
5 o R r 10
10 o R r 20
20 o R
1175
1952
2298
1925
1065
1800
2209
748
211
8.78
14.59
17.17
14.38
7.96
13.44
16.51
5.59
1.58
Total
13,383
100.00
Total
13,383
100.00
Table 2
Summary statistics for CDS contracts referencing dealers.
This table provides summary statistics for the CDS spreads (in basis points) for contracts referencing the dealers listed below. The spreads are based on
daily observations obtained from the Bloomberg system. N denotes the number of days on which Bloomberg quotes are available for the indicated dealer.
The sample period is March 31, 2008 to January 20, 2009.
Dealer
Mean
Standard
deviation
Minimum
Median
Maximum
N
Barclays
BNP Paribas
Bank of America
Citigroup
Credit Suisse
Deutsche Bank
Goldman Sachs
HSBC
JP Morgan
Lehman
Merrill Lynch
Morgan Stanley
Royal Bank of Scotland
UBS
122.65
59.40
121.60
180.67
111.66
96.88
230.58
75.41
110.86
291.79
243.19
355.10
116.45
139.09
43.33
13.29
35.77
71.13
37.20
29.70
110.62
21.94
27.96
89.01
71.34
236.22
45.16
56.81
53.27
34.24
61.97
87.55
57.59
51.92
79.83
41.84
62.54
154.04
114.35
108.06
55.17
55.45
122.17
59.08
119.75
162.90
101.40
90.11
232.69
67.59
107.68
285.12
218.43
244.98
110.69
126.24
261.12
107.21
206.85
460.54
194.22
172.00
545.14
128.30
196.34
641.91
472.72
1360.00
304.89
320.80
212
212
209
207
212
212
177
212
209
84
193
187
212
212
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N. Arora et al. / Journal of Financial Economics 103 (2012) 280–293
whether counterparty credit risk is reflected in the prices
of CDS contracts. Finally, we study whether the pricing of
counterparty credit risk by dealers varies by industry as
would be implied by a correlation-based credit model.
5.1. Methodology
For each reference firm and for each date t in the
sample, we have simultaneous prices from multiple CDS
dealers for selling five-year credit protection on that firm.
Thus, we can test directly whether counterparty credit risk
is priced by a straightforward regression of the price of
protection sold or quoted by a dealer for a reference firm
on the price of protection for the dealer itself providing
that quotation. In this panel regression framework, we
allow for reference-firm-specific date fixed effects. Specifically, we estimate the following regression:
CDSi,j,t ¼ ai,t þ b Spreadj,t1 þ Ei,j,t ,
Table 3
Results from the regression of CDS spreads on the CDS spread of the
corresponding dealer.
This table reports the results from the regressions of CDS prices or
quotations for the firms in the CDX Index on the CDS spread of the dealer
providing the CDS price or quotation. The sample period is March 31,
2008 to January 20, 2009. Regression specification II includes a dummy
variable IL that takes value one for the post-Lehman period beginning
September 15, 2008, and zero otherwise. The t-statistics are based on
the White (1980) heteroskedasticity-consistent estimate of the covariance matrix. The superscript nn denotes significance at the 5% level; the
superscript n denotes significance at the 10% level.
I:
CDSi,j,t ¼ ai,t þ b Spreadj,t1 þ Ei,j,t ,
II :
CDSi,j,t ¼ ai,t þ b Spreadj,t1 þ gIL,t Spreadj,t1 þ Ei,j,t :
Regression specification I
Regression specification II
with post-Lehman dummy
Variable
Coefficient
t-Statistic
Coefficient
t-Statistic
Spread
IL Spread
0.001548
7.31nn
0.000991
0.000713
3.73nn
1.92n
ð1Þ
where CDSi,j,t denotes the CDS spread for credit protection
on reference firm i sold or quoted by dealer j at date t, ai,t
is a fixed effect parameter specific to firm i at time t, and
Spreadj,t1 is the CDS spread for dealer j as of the end of
the previous day.11 Under the null hypothesis that counterparty credit risk is not priced, the slope coefficient b is
zero. The t-statistics for b reported in the tables are based
on the White (1980) heteroskedastic-consistent estimate
of the covariance matrix.
As shown in Table 1, there are a total of 13,383
observation vectors in the sample. On average, each
observation vector consists of 3.073 distinct quotations
for selling credit protection on the reference firm, giving a
total of 41,122 observations collectively. Thus, there are
339.85 observations on average for each of the 121
reference firms in the sample.
5.2. Is counterparty credit risk priced?
Although a formal model of the relation between a
dealer’s credit risk and the price at which the dealer could
sell credit protection could be developed, the underlying
economics of the transaction makes it clear that there
should be a negative relation between the two. Specifically, as the credit risk of a protection seller increases, the
value of the protection being sold is diminished and
market participants would not be willing to pay as much
for it. Thus, if counterparty credit risk is priced in the
market, the slope coefficient b in the regressions should
be negative.
Table 3 reports the results from estimating the regression in Eq. (1) (which is designated specification I). The
slope coefficient b is 0.001548 with a t-statistic of
7.31. Thus, the empirical results strongly support the
hypothesis that counterparty credit risk is priced in the
11
We use the dealer’s spread as of t1 rather than t since the dealer
data are as of the end of the day while the CDS quotation data are taken
from a narrow timeframe centered at 11:30 AM. Thus, using the dealer’s
spread as of the end of day t1 avoids using ex post data in the
regression.
N
41,122
41,122
CDS market. Furthermore, the sign of the coefficient is
negative, consistent with economic intuition.
We acknowledge, however, that we cannot completely
rule out the possibility that the relation between CDS
spreads and the credit risk of protection sellers may
actually be due to some other factor that is correlated
with dealer spreads.12 For example, since CDS contracts
are traded in over-the-counter markets, the search costs
associated with finding trading partners could play a role
in determining equilibrium CDS spreads (see Duffie,
Gârleanu, and Pedersen, 2002, 2005, 2008 and others). If
these search costs were inversely related to dealer CDS
spreads, then they could potentially affect CDS spreads in
a way consistent with the results reported in Table 3. We
will explore some of these possibilities in a later section
on robustness.
5.3. Why is the effect so small?
Although statistically very significant, the slope coefficient is relatively small in economic terms. In particular,
the value of 0.001548 implies that the credit spread of a
CDS dealer would have to increase by nearly 645 basis
points to result in a one-basis-point decline in the price of
credit protection. As shown in Table 2, credit protection
on most of CDS dealers in the sample never even reached
645 basis points during the period under study. These
results are consistent with the results in Table 1 suggesting that the cross-sectional variation in the dealers’
quotes for selling credit protection on a specific reference
firm is only on the order of several basis points.
A number of papers have explored the theoretical
magnitude of counterparty credit risk on the pricing of
interest rate swaps. Important examples of this literature
12
We are grateful to the referee for raising this issue.
N. Arora et al. / Journal of Financial Economics 103 (2012) 280–293
include Cooper and Mello (1991), Sorensen and Bollier
(1994), and Duffie and Huang (1996). Typically, these
papers find that since the notional amount is not exchanged
in an interest rate swap, the effect of counterparty credit
risk on an interest rate swap is very small, often only a basis
point or two.
Unlike an interest rate swap, however, a CDS contract
could involve a very large payment by the protection
seller to the protection buyer. For example, sellers of
protection on Lehman Brothers were required to pay
$91.375 per $100 notional to settle their obligations to
protection buyers. Thus, the results from the interest rate
swap literature may not necessarily be directly applicable
to the CDS market.
A few recent papers have focused on the theoretical
impact of counterparty credit risk on the pricing of CDS
contracts. Important examples of these papers include
Jarrow and Yu (2001), Hull and White (2001), Brigo and
Pallavicini (2006), Kraft and Steffensen (2007), Segoviano
and Singh (2008), and Blanchet-Scalliet and Patras (2008).
In general, estimates of the size of the effect of counterparty credit risk in this literature tend to be orders of
magnitude larger than those in the literature for interest
rate swaps. For example, estimates of the potential size of
the pricing effect range from 7.0 basis points in Kraft and
Steffensen to more than 20 basis points in Hull and White,
depending on assumptions about the default correlations
of the protection seller and the underlying reference firm.
Thus, this literature tends to imply counterparty credit
risk pricing effects many times larger than those we find
in the data.
It is crucial to recognize, however, that this literature
focuses almost exclusively on the case in which CDS
contract liabilities are not collateralized. As was discussed
earlier, the standard market practice during the sample
period would be to require full collateralization by both
counterparties to a CDS contract. This would be particularly true for CDS contracts in which one counterparty
was a large Wall Street CDS dealer.
In theory, full collateralization of CDS contract liabilities would appear to imply that there should be no
pricing of counterparty credit risk in CDS contracts. In
reality, however, there are several reasons why there
might still be a small pricing effect even if counterparties
require full collateralization. First, as became clear after
the Lehman bankruptcy, counterparties who post collateral in excess of their liabilities risk becoming unsecured
creditors of a defaulting counterparty for the amount of
the excess collateral. As discussed earlier, however, Wall
Street CDS dealers often require a small amount of overcollateralization from their counterparties (typically on
the order of several percent) thus creating the possibility
of a slight credit loss (ironically, however, only when the
counterparty owes the bankrupt firm money). Second, the
Lehman bankruptcy also showed that there were a number of legal pitfalls that many market participants had not
previously appreciated. These include the risk of unsegregated margin accounts or the disposition of rehypothecated collateral.
In summary, the size of the counterparty pricing effect
in the CDS market appears too small to be explained by
287
models that abstract from the collateralization of CDS
contracts. Rather, the small size of the pricing effect
appears more consistent with the standard market practice of full collateralization, or even overcollateralization,
of CDS contract liabilities.
5.4. Did pricing of counterparty credit risk change?
The discussion above suggests that the Lehman bankruptcy event may have forced market participants to
reevaluate the risks inherent in even fully collateralized
counterparty relationships. If so, then the pricing of
counterparty credit after the Lehman bankruptcy might
differ from the pricing in the CDS market previous to the
bankruptcy. To explore this possibility, we reestimate the
regression described above using a dummy slope coefficient for the post-Lehman period. Specifically, we estimate the regression
CDSi,j,t ¼ ai,t þ b Spreadj,t1 þ g IL,t Spreadj,t1 þ Ei,j,t ,
ð2Þ
where IL is a dummy variable that takes value one for the
post-Lehman period beginning September 15, 2008, and
zero otherwise. Table 3 also reports the results from this
regression (which is designated specification II). Note that
in this specification, the coefficient b represents the
regression slope during the pre-Lehman period, while
the coefficient g measures the change in the slope after
the Lehman bankruptcy. Thus, we can test for whether
there was a significant change in the pricing of counterparty credit risk after the Lehman bankruptcy by simply
testing whether g is statistically significant. The regression slope during the post-Lehman period can be obtained
by simply summing the pre-Lehman slope coefficient b
and the post-Lehman change in the slope coefficient g.
The results provide some support for the hypothesis that
the pricing of counterparty credit risk changed after the
Lehman bankruptcy. Specifically, the pre-Lehman slope
coefficient is 0.000991 and has a t-statistic of 3.73.
After the Lehman bankruptcy, the change in the slope
coefficient is 0.000713, making the pricing of counterparty credit risk in the post-Lehman period roughly twice
as large as in the pre-Lehman period. The t-statistic for the
change, however, is only 1.92. Thus, the change is
significant at the 10% level, but not the 5% level.
5.5. Robustness of the results
To provide some robustness checks for these results,
we also estimate several alternative specifications. In the
first of these, we include the total number of trades
executed by each dealer each day as a control for trading
activity. Specifically, we estimate the following regression
specifications:
CDSi,j,t ¼ ai,t þ b Spreadj,t1 þ Z Volumej,t þ Ei,j,t ,
ð3Þ
CDSi,j,t ¼ ai,t þ b Spreadj,t1 þ gIL,t Spreadj,t1
þ Z Volumej,t þ Ei,j,t ,
ð4Þ
where Volumej,t denotes the total number of trades
executed by dealer j on date t. Table 4 reports the results
from the regressions.
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N. Arora et al. / Journal of Financial Economics 103 (2012) 280–293
Table 4
Results from the regression of CDS spreads on the CDS spread of the
corresponding dealer with control for dealer trading volume.
This table reports the results from the regressions of CDS prices or
quotations for the firms in the CDX index on the CDS spread of the dealer
providing the CDS price or quotation and on the total number of trades
executed by the dealer in all CDX index firms that day as a control
variable (denoted as volume). The sample period is March 31, 2008 to
January 20, 2009. Regression specification II includes a dummy variable
IL that takes value one for the post-Lehman period beginning September
15, 2008, and zero otherwise. The t-statistics are based on the White
(1980) heteroskedasticity-consistent estimate of the covariance matrix.
The superscript nn denotes significance at the 5% level; the superscript n
denotes significance at the 10% level.
I:
CDSi,j,t ¼ ai,t þ b Spreadj,t1 þ Z Volumej,t þ Ei,j,t ,
II :
CDSi,j,t ¼ ai,t þ b Spreadj,t1 þ gIL,t Spreadj,t1 þ Z Volumej,t þ Ei,j,t :
Table 5
Results from the regression of CDS spreads on the CDS spread of the
corresponding dealer with fixed effects for individual dealers.
This table reports the results from the regression of CDS prices or
quotations for the firms in the CDX index on the CDS spread of the dealer
providing the CDS price or quotation. The regression also includes a
separate fixed effect dummy variable for each dealer (except for the
dealer with the largest number of quotes, arbitrarily designated dealer
14). The sample period is March 31, 2008 to January 20, 2009. Regression specification II includes a dummy variable IL that takes value one for
the post-Lehman period beginning September 15, 2008, and zero
otherwise. The t-statistics are based on the White (1980) heteroskedasticity-consistent estimate of the covariance matrix. The superscript nn
denotes significance at the 5% level; the superscript n denotes significance at the 10% level.
I:
Regression specification II
with post-Lehman dummy
Spread
IL Spread
Volume
Coefficient
t-Statistic
Coefficient
t-Statistic
0.001548
nn
0.000990
0.000714
0.009988
3.73nn
1.92n
0.14
0.008122
N
7.30
0.12
41122
41122
Even after controlling for dealer trading activity,
Table 4 shows the regression coefficients and t-statistics
for the dealers’ CDS spreads are virtually the same as they
are in Table 3. Thus, the results provide evidence that the
dealer spread is not simply proxying for dealer liquidity
effects.
As another robustness check, we reestimate the
regressions in Table 3, but with dummy variables for
individual dealers. This specification controls for dealer
fixed effects. Thus, the relation between CDS spreads for
the firms in the CDX index and dealer CDS spreads is
identified using only the times-series variation in spreads.
The regressions estimated are
CDSi,j,t ¼ ai,t þ b Spreadj,t1 þ
13
X
dj Ij þ Ei,j,t ,
ð5Þ
j¼1
CDSi,j,t ¼ ai,t þ b Spreadj,t1 þ gIL,t Spreadj,t1
þ
13
X
j¼1
dj Ij þ
13
X
Zj Ij IL þ Ei,j,t ,
ð6Þ
j¼1
where Ij is the dummy variable for the j-th dealer. Note
that we only include 13 dealer dummies rather than all
14. This is because inclusion of all 14 dummies results in a
collinearity with the firm and date fixed effects. Thus, the
regression coefficients for dealer dummies have the interpretation of the marginal effect relative to that of the
omitted dealer, which is chosen to be the dealer with the
highest trading activity throughout the sample period.
The results from these regressions are reported in Table 5.
The results indicate that the previous results are
robust to the inclusion of dealer fixed effects. The coefficient for dealer CDS spread is 0.001338 for the first
specification, which is only slightly less than the
dj Ij þ Ei,j,t ,
CDSi,j,t ¼ ai,t þ b Spreadj,t1 þ gIL,t Spreadj,t1
þ
13
X
j¼1
Variable
13
X
j¼1
II :
Regression specification I
CDSi,j,t ¼ ai,t þ b Spreadj,t1 þ
dj Ij þ
13
X
Zj Ij IL þ Ei,j,t :
j¼1
Regression specification I
Variable
Spread
I1
I2
I3
I4
I5
I6
I7
I8
I9
I10
I11
I12
I13
Coefficient
t-Statistic
Coefficient
t-Statistic
0.001338
1.4154
0.6574
0.1707
0.4062
0.2106
0.0326
0.4728
0.6006
0.1701
0.1041
0.1862
0.9453
0.1922
nn
0.001786
0.1130
0.7774
0.1923
0.5837
0.0086
0.0461
0.4227
0.2026
0.1136
0.3960
0.1982
0.6462
0.0659
2.35nn
0.23
4.34nn
1.88n
7.50nn
0.09
0.82
2.07nn
2.28nn
0.82
3.75nn
3.05nn
3.74nn
0.65
0.000347
1.4112
1.0839
0.0857
0.7415
0.4342
0.7280
0.5204
1.6748
–
1.1010
0.0423
0.6155
2.6544
0.36
2.21nn
2.78nn
0.30
2.90nn
1.47
2.58nn
0.32
4.68nn
–
4.79nn
0.17
2.08nn
1.87n
4.49
3.87nn
4.17nn
1.56
4.95nn
1.95n
0.64
2.28nn
6.03nn
1.66n
1.49
3.60nn
6.96nn
1.64
IL Spread
I1 IL
I2 IL
I3 IL
I4 IL
I5 IL
I6 IL
I7 IL
I8 IL
I9 IL
I10 IL
I11 IL
I12 IL
I13 IL
N
Regression specification II
with post-Lehman dummy
41,122
41,122
corresponding estimate in Table 3. The t-statistic for
dealer CDS spread in this regression is 4.49. In the
second specification with the post-Lehman dummy variable, the CDS spread of the dealer is again significantly
negative during the pre-Lehman period, and there is no
significant change in the variable after the Lehman bankruptcy. This again provides support for the result that
dealer credit risk is priced in the market, although the
effect is very small.
N. Arora et al. / Journal of Financial Economics 103 (2012) 280–293
The coefficients for the individual dealer dummy variables are also interesting. Although many of the coefficients in the first specification are significant, almost all of
them are much less than one basis point in magnitude.
The same is also true for the pre-Lehman coefficients for
the second specification. On the other hand, the results
indicate that a number of the coefficients change in the
post-Lehman period by one or more basis points. These
changes, however, are essentially equally divided
between positive and negative values. Thus, these results
provide some evidence of greater heterogeneity in dealer
fixed effects in the post-Lehman period.13
5.6. Are there differences across firms?
289
Table 6
Results from regression of CDS spreads on the CDS spreads of the
corresponding dealer interacted with sector dummy variables for the
underlying firms.
This table reports the results from the regression of CDS prices or
quotations for the firms in the CDX index on the CDS spread of the dealer
providing the CDS price or quotation interacted with five sector dummy
variables where the dummy variables take value one if firm i is in the
consumer, energy, financial, industrial, or technology sectors, respectively, and zero otherwise. The sample period is March 31, 2008 to
January 20, 2009. Regression specification II includes a dummy variable
IL that takes value one for the post-Lehman period beginning September
15, 2008, and zero otherwise. The t-statistics are based on the White
(1980) heteroskedasticity-consistent estimate of the covariance matrix.
The superscript nn denotes significance at the 5% level; the superscript n
denotes significance at the 10% level.
I:
5
X
CDSi,j,t ¼ ai,t þ
bk ISectork Spreadj,t1 þ Ei,j,t ,
k¼1
A number of recent papers have emphasized the role
that the default correlation between the protection seller
and the reference firm should play in determining CDS
spreads. To illustrate the importance of correlation, let us
take it to an extreme and imagine that Citigroup is willing
to sell credit protection against the event that Citigroup
itself defaults. Clearly, no one would be willing to pay
Citigroup for this credit protection.14 Similarly, a financial
institution selling credit protection on another financial
institution might not be able to charge as much as a
nonfinancial seller might.15
To explore the effects of correlation on the price of
credit protection, we do the following. First, we classify
the firms in the CDX index that are in our sample into one
of five broad industry sectors or categories: consumer,
energy, financials, industrials, and technology. We then
reestimate the regressions using the following specifications:
CDSi,j,t ¼ ai,t þ
5
X
bk ISectork Spreadj,t1 þ Ei,j,t ,
ð7Þ
II :
CDSi,j,t ¼ ai,t þ
5
X
bk ISectork Spreadj,t1
k¼1
þ
5
X
gk ISectork IL Spreadj,t1 þ Ei,j,t :
k¼1
Regression
specification I
Variable
IConsumer Spread
IEnergy Spread
IFinancial Spread
IIndustrial Spread
ITechnology Spread
Regression specification II
with post-Lehman
dummy
Coefficient t-Statistic
Coefficient
t-Statistic
4.83nn
7.25nn
0.77
3.61nn
5.41nn
0.000015
0.002253
0.000910
0.001245
0.003173
0.04
5.14nn
0.67
2.42nn
4.69nn
0.001719
0.000079
0.003183
0.000096
0.000674
3.65nn
0.09
1.27
0.14
0.80
0.001161
0.002313
0.001097
0.001324
0.002553
IConsumer IL Spread
IEnergy IL Spread
IFinancial IL Spread
IIndustrial IL Spread
ITechnology IL Spread
k¼1
N
CDSi,j,t ¼ ai,t þ
5
X
5
X
41,122
bk ISectork Spreadj,t1
k¼1
þ
41,122
gk ISectork IL Spreadj,t1 þ Ei,j,t ,
ð8Þ
k¼1
where ISectork are dummy variables that take value one if
firm i is in sector k, and zero otherwise. The regression
results are reported in Table 6.
As shown in the first specification, counterparty credit
risk is priced for the consumer, energy, industrial, and
technology firms in the sample. The t-statistics for the
corresponding coefficients are 4.83, 7.25, 3.61, and
5.41, respectively. These results are clearly consistent
with the previous results.
13
We are grateful to the referee for suggesting the robustness
checks discussed in this section.
14
It is interesting to note, however, that a number of European
banks sell credit protection on the iTraxx index which includes these
banks as index components.
15
Examples of recent papers discussing the role of correlation in the
pricing of CDS contracts include Hull and White (2001), Jarrow and Yu
(2001), Longstaff, Mithal, and Neis (2005), Yu (2007), and many others.
The most puzzling result, however, is that for the
financial sector. As described above, the correlation argument suggests that the counterparty credit risk for the
CDS dealers should be most evident when they are selling
protection on firms in the financial industry. In contrast to
this intuition, however, the results show that the CDS
dealers’ counterparty credit risk is not priced in the
spreads of CDS contracts on financial firms. Furthermore,
likelihood ratio tests strongly reject the hypotheses that
the slope coefficient for the financial sector is equal to
that of the consumer, energy, industrial, and technology
sectors, with p-values of 0.00026, 0.00000, 0.00012, and
0.00000, respectively. Thus, the pricing of counterparty
credit risk for financial firms is significantly different from
that of the other four categories of firms in the sample. In
summary, far from being the most sensitive to counterparty credit risk, financial firms in the CDX index represent the only category in the sample for which
counterparty credit risk is not priced.
These patterns are repeated in the second specification. As shown, counterparty credit risk is significantly
290
N. Arora et al. / Journal of Financial Economics 103 (2012) 280–293
priced for the energy, industrial, and technology firms
during the pre-Lehman period. Furthermore, there is no
significant change in how counterparty credit risk is
priced for these firms in the post-Lehman period. Counterparty credit risk for firms in the consumer sector is not
priced during the pre-Lehman period, but there is a
significant change in pricing for these firms after the
Lehman event. The results also show that counterparty
credit risk for the financial firms is not priced in the preLehman period, and that there is no significant change in
this relation after the Lehman event.
What factors might help account for the evidence that
counterparty credit risk is not priced for the financial
firms? First of all, the financial firms in the CDX index
consist primarily of insurance firms, industrial lenders,
consumer finance firms, and real estate companies. Thus,
it is possible that the default risk of these firms in the CDX
index may actually be much less correlated with that of
the CDS dealers than one might expect based on their
designation as financials. Second, counterparty credit risk
might not be priced in the cost of selling protection on the
large financial firms in the CDX index if the market
believed that the CDS dealers would not fail when the
large financial firms in the CDX index became vulnerable
to default. Thus, this possibility suggests that there might
be a state-contingent aspect to the default risk of CDS
dealers. Finally, it is important to acknowledge that there
is actually little empirical evidence in the literature about
default correlations. Thus, while intuition suggests that
the default correlation between financial firms should be
higher than the default correlation between financial and
nonfinancial firms, there is no direct empirical evidence
supporting this intuition. For this reason, the analysis in
this section should be viewed more as an exploratory
investigation, rather than as a test rejecting specific
empirical hypotheses about default correlations.
6. Comparison to model-implied values
The empirical results demonstrate that counterparty
credit risk is priced by the market, but that the size of the
effect is very small. A natural question to ask is whether
these empirical results can be reconciled with those
implied by theoretical models of counterparty credit
risk.16
There is a large and rapidly growing literature on the
valuation of counterparty credit risk in CDS contracts
which is far too extensive for us to review fully here.
Gregory (2010) provides an excellent summary of the
literature and discusses a number of the modeling
approaches that have been applied to the problem of
valuing counterparty credit risk. In this section, we
compare our empirical results with those implied by a
simple simulation-based model of the effects of counterparty credit risk. A key feature of this framework is that
it allows us to quantify the size of the effect when
CDS counterparties collateralize their mark-to-market
liabilities.
16
We are grateful to the referee for raising this issue.
In this model, we take the perspective of the protection
buyer and model the losses arising from the default of the
protection seller. To model default, we use the reducedform framework of Duffie and Singleton (1997, 1999) in
which the default of a firm is triggered by the realization
of a jump process. Let lt and nt denote the risk-neutral
intensity processes of the firm underlying the CDS contract and the firm selling credit protection (the CDS
counterparty), respectively. The risk-neutral dynamics
for these intensity processes are given by,
pffiffiffi
dl ¼ ðablÞdt þ s l dZ l ,
ð9Þ
pffiffiffi
dn ¼ ðmgnÞdt þs n dZ n ,
ð10Þ
where a, b, s, m, g, and s are constant parameters, and Corr
ðdZ l ,dZ n Þ ¼ x. Given this model, the marginal distribution
for the default time of the underlying firm has a hazard
function equal to the realized path of the intensity (see
Lando, 1998), and similarly for the firm selling default
protection. Modeling the simultaneous distribution of
defaults would require a specification of the probability
of simultaneous defaults. We will specify the joint distribution of defaults in our discrete-time simulation.
Following Gregory (2010), we distinguish between
three types of default scenarios. The first is the case in
which the underlying firm defaults but not the counterparty. In this case, the protection buyer receives the
protection payment from the protection seller and does
not suffer any counterparty credit losses.
The second case is when the counterparty defaults, but
the underlying firm does not. For simplicity, we assume
that both counterparties are required to post full collateral daily for CDS liabilities, where the mark-to-market
liability is computed under the assumption that both
counterparties are default free.17 In addition, we assume
that there is zero recovery of uncollateralized liabilities in
the event that the protection seller defaults.18 Given the
square-root dynamics in Eq. (9), the value of a CDS
contract can be obtained directly from the CDS valuation
model in Longstaff, Mithal, and Neis (2005, pp. 2221–
2222). There are now two ways in which a protection
buyer can suffer a loss when the protection seller defaults.
If the mark-to-market value is positive, but the collateral
posted the previous day (which equals the previous day’s
mark-to-market value of the CDS contract) is insufficient,
then the buyer’s loss is the difference between the two. As
discussed earlier, however, the buyer can also lose from a
counterparty default when he owes the counterparty on
the CDS contract and the amount of collateral posted with
the defaulting protection seller exceeds the amount of the
buyer’s liability. In this situation, the excess collateral
becomes part of the bankruptcy estate and represents the
protection buyer’s loss. Note that the loss of excess
collateral does not occur when CDS liabilities are
17
This assumption greatly simplifies the analysis but has virtually
no effect on the total amount of collateral required.
18
This is consistent with the Lehman default in which CDS contracts
referencing Lehman were settled at 8.625 cents on the dollar.
N. Arora et al. / Journal of Financial Economics 103 (2012) 280–293
uncollateralized. Thus, there are states in which a protection buyer may be worse off with full bilateral collateralization of CDS liabilities.
The third case occurs when both the underlying firm
and the counterparty default at the same time. We will
make the assumption that joint default occurs if both the
firm and the counterparty default within a two-businessday timeframe. This assumption reflects the reality that a
discrete period of time is required operationally to post
collateral and settle trades. With collateralization, the
protection buyer’s loss is the difference between the loss
on the underlying firm and the amount of collateral held.
Again, since the buyer may have posted collateral with
the defaulting counterparty, the buyer could actually be
worse off in some states in this joint default scenario than
without collateralization.
Since we are simulating changes in the intensity
processes and the realization of defaults at each time
step, we only need to specify local or one-step joint
probabilities to simulate joint default events. In particular, conditional on no default having occurred before time
t, the marginal probability of the underlying firm defaulting between time t and t þ Dt is lt Dt. Similarly, the
marginal probability of the firm selling credit protection
defaulting between time t and t þ Dt is nt Dt. Let a, b, c, and
d denote the joint probabilities that neither firm defaults,
that only the underlying firm defaults, that only the firm
selling credit protection defaults, and that both firms
default between time t and t þ D, respectively. The Appendix shows that these joint probabilities are completely
determined by the two marginal probabilities and a
default correlation parameter r. Thus, we are in essence
assuming that the local joint distribution of default events
is given by a simple multinomial distribution. Furthermore, this approach explicitly allows for correlated
defaults to occur. Given these joint probabilities, we
simulate the model in steps of Dt and sample the four
joint events based on their multinomial probabilities. We
repeat this process at each time step along a simulated
path until the first default occurs.19
Turning to the issue of calibration, it is important to
stress that our objective is simply to provide general
estimates of the size of counterparty default effects rather
than to model specific contracts. As such, we adopt a
generic parameterization and estimate counterparty
default costs under a broad range of assumptions about
default intensities and correlations. The average value of
the CDX index during the sample period is 95 basis points,
while the average CDS spread for the dealers during the
same period is 145 basis points. These values, of course,
are high by historical standards but they do provide a
realistic benchmark for the calibration of the risk-neutral
intensity processes. Accordingly, we parameterize the
long-run values of lt and nt to be 100 and 150 basis
points, respectively. Furthermore, we assume b ¼ g ¼ 0:50
and s ¼ s ¼ 0:20. These parameters are consistent with
19
Note that the limiting distribution of this multinomial distribution would likely be of the form of a bivariate exponential distribution as
the number of time steps increases (see Johnson and Kotz, 1972). We are
grateful to the referee for this insight.
291
the longer-term properties of the CDX index.20 We also
assume that the spread correlation parameter x takes on
values of 2%, 6%, or 10%. Similarly, we assume that the
default correlation r takes on values of 2%, 6%, or 10%.
These values essentially bracket the default correlations
reported by Longstaff and Rajan (2008) implied from the
prices of CDX index tranches and the CDS spreads for the
constituents of the CDX index.21
Table 7 reports the estimated basis-point cost of
counterparty default for a range of scenarios. Specifically,
we compute the cost of events in which only the counterparty defaults, the cost of joint events in which both the
underlying firm and the counterparty default, and the
total of these two costs. The default intensity for the
underlying firm takes values of 100 or 300 basis points,
essentially bracketing the CDX index values during the
sample period. Similarly, the default intensity for the
counterparty selling protection takes values of 100, 300,
and 500 basis points, again paralleling the behavior of
broker CDS spreads during the sample period. The results
are based on 100,000 simulations for a five-year CDS
contract. The details on how the joint distribution of
defaults is simulated are described in the Appendix.
The results in Table 7 imply counterparty credit risk
pricing effects that are very consistent with those documented in previous sections of this paper. For example, a
400-basis-point increase in the CDS spread of the protection
seller from 100 to 500 basis points maps into an increase in
counterparty credit costs of roughly 0.5, 1.0, and 2.0 basis
points in the cases where the default correlation is 2%, 6%,
and 10%, respectively. Thus, the empirical estimates of the
size of the effect of counterparty credit risk on CDS spreads
given in this paper harmonize well with those implied by a
model in which average default correlations are in the range
of, say, zero to 4%.
7. Conclusion
We examine the extent to which the credit risk of a
dealer offering to sell credit protection is reflected in the
prices at which the dealer can sell protection. We find
strong evidence that counterparty credit risk is priced in
the market; the higher the credit risk of a dealer, the
lower is the price at which the dealer can sell credit
protection in the market. The magnitude of the effect,
however, is extremely small. In particular, an increase in
the credit spread of a dealer of about 645 basis points
maps into only a one-basis-point decline in the price of
credit protection.
The price of counterparty credit risk appears to be too
small to be explained by models that assume that CDS
liabilities are unsecured. The pricing of counterparty
credit risk, however, seems consistent with the standard
market practice of requiring full collateralization, or even
the overcollateralization of CDS liabilities. These results
20
Specifically, the moments of normalized monthly changes in the
CDX index from 2004 to 2009 imply b ¼ 0:54 and s ¼ 0:18.
21
For a few of the 100,000 simulated paths, we assume a smaller
value of r to insure that simulated joint default probabilities remain
positive. See the discussion in the Appendix.
292
N. Arora et al. / Journal of Financial Economics 103 (2012) 280–293
Table 7
Basis point cost of CDS counterparty credit risk
This table reports the basis point cost to the protection buyer from the potential default of the protection seller. The central panel reports the costs
when CDS liabilities are not collateralized; the right panel reports the costs when CDS liabilities are collateralized. CP default cost denotes the cost of
events where only the counterparty defaults. Joint default cost denotes the cost of events where both the underlying firm and the counterparty default
together. Total cost denotes the sum of the costs of the two types of events. The parameter r denotes the default correlation between the underlying firm
and the counterparty. The parameters l and Z denote the basis point default intensities for the underlying firm and the counterparty, respectively.
Parameters
Uncollateralized
Collateralized
r
l
Z
CP
default
cost
0.02
100
100
300
500
0.69
0.98
1.31
0.89
1.02
1.21
1.58
2.00
2.52
0.07
0.10
0.14
0.88
1.00
1.18
0.95
1.10
1.32
300
100
300
500
0.68
1.16
1.62
1.16
1.50
1.56
1.84
2.66
3.18
0.08
0.13
0.18
1.14
1.48
1.53
1.22
1.61
1.71
100
100
300
500
0.68
0.99
1.32
2.50
3.35
3.52
3.18
4.34
4.83
0.07
0.10
0.13
2.43
3.27
3.43
2.50
3.37
3.56
300
100
300
500
0.69
1.16
1.63
3.24
4.15
4.48
3.93
5.31
6.11
0.08
0.13
0.18
3.18
4.07
4.38
3.26
4.20
4.56
100
100
300
500
0.71
1.02
1.35
3.82
5.17
5.99
4.53
6.19
7.34
0.07
0.10
0.13
3.73
5.04
5.87
3.80
5.14
6.00
300
100
300
500
0.69
1.15
1.65
5.11
6.89
7.70
5.80
8.04
9.35
0.08
0.13
0.18
5.00
6.75
7.55
5.08
6.88
7.73
0.06
0.10
Joint
default
cost
Total
cost
CP
default
cost
Joint
default
cost
Total
cost
also have implications for current proposals about
restructuring derivatives markets. For example, since
market participants appear to price counterparty credit
risk as if it were only a relatively minor concern, this
suggests that attempts to mitigate counterparty credit
risk through alternative approaches, such as the creation
of a central clearinghouse for CDS contracts, may not be as
effective as might be anticipated. This implication parallels and complements the conclusions in the recent paper
by Duffie and Zhu (2009).
Appendix A
To simulate correlated defaults in the model presented
in Section 6, we do the following. First, we define the
discretization interval for the simulation to be two days;
Dt ¼ 2=260 (there are approximately 260 trading days per
year). Let I1 denote a random binomial variable that takes
value one if the underlying firm defaults during the twoday window, and zero otherwise. Similarly, let I2 denote a
random binomial variable that takes value one if the
counterparty defaults during the two-day window, and
zero otherwise. Let p1 ¼ lDt denote the probability that
the underlying firm defaults during the two-day window,
and p2 ¼ nDt denote the probability that the counterparty
defaults during the two-day window. Thus, with this
notation, E½I1 ¼ p1 and E½I2 ¼ p2 . Also, Var½I1 ¼ p1 p21
and Var½I2 ¼ p2 p22 .
Now let a denote the probability that neither the
underlying firm nor the counterparty defaults during the
two-day window. Let b denote the probability that the
underlying firm defaults during the two-day window, but
the counterparty does not. Let c denote the probability
that the counterparty defaults during the two-day window, but the underlying firm does not. Finally, let d
denote the probability that both the underlying firm and
the counterparty default during the two-day window. It is
easily shown that the correlation r between I1 and I2 is
given by
dp1 p2
Corr½I1 ,I2 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi :
ðp1 p21 Þðp2 p22 Þ
Solving this expression for d gives,
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
d ¼ r p1 p2 ð1p1 Þð1p2 Þ þ p1 p2 :
ðA:1Þ
ðA:2Þ
Since the marginal probabilities of default are p1 and p2 ,
and since the total probability must equal one, we have
a ¼ 1bcd,
ðA:3Þ
b ¼ p1 d,
ðA:4Þ
c ¼ p2 d:
ðA:5Þ
Thus, given l, n, and r, we can solve for the probabilities a,
b, c, and d that define the joint default distribution for
each two-day window.
To simulate default outcomes for a five-year CDS
contract, we simulate a path for the default intensity
processes l and n using the dynamics given in Eqs. (9) and
(10). In doing this, we use two-day discretization
N. Arora et al. / Journal of Financial Economics 103 (2012) 280–293
intervals. For each two-day window along the path, we
then apply the above algorithm to simulate the joint
default outcome (neither defaults, both default, etc.). We
then use the simulated joint default probabilities to define
the cash flows along the path and evaluate the default
costs. We repeat this process using 100,000 simulated
paths.
Finally, we note that there is a minor restriction on r
that is needed to insure that b and c take positive values:
ro
minðp1 ð1p2 Þ, p2 ð1p1 ÞÞ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi :
p1 p2 ð1p1 Þð1p2 Þ
ðA:6Þ
Whenever r exceeds this bound for a two-day window,
we set r equal to this bound in solving for the joint
default probabilities for that two-day window. This
restriction, however, only affects a small fraction of the
100,000 simulated paths.
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Journal of Mathematical Finance, 2017, 7, 1-38
http://www.scirp.org/journal/jmf
ISSN Online: 2162-2442
ISSN Print: 2162-2434
Counterparty Credit Risk in OTC Derivatives
under Basel III
Mabelle Sayah1,2,3
Group Risk Management, Bank Audi S.A.L., Beirut, Lebanon
LSAF, Univ Lyon, UCBL, Lyon, France
3
Mathematics and Applications Laboratory, EGFEM, Saint Joseph University, Beirut, Lebanon
1
2
How to cite this paper: Sayah, M. (2017)
Counterparty Credit Risk in OTC Derivatives under Basel III. Journal of Mathematical Finance, 7, 1-38.
http://dx.doi.org/10.4236/jmf.2017.71001
Received: October 18, 2016
Accepted: December 26, 2016
Published: December 30, 2016
Copyright © 2017 by author and
Scientific Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution International
License (CC BY 4.0).
http://creativecommons.org/licenses/by/4.0/
Open Access
Abstract
Recent financial crises were the root of many changes in regulatory implementations in the banking sector. Basel previously covered the default capital
charge for counterparty exposures however, the crisis showed that more than
two third of the losses related to this risk emerged from the exposure to the
movement of the counterparty’s credit quality and not its actual default
therefore, Basel III divided the required counterparty risk capital into two
categories: The traditional default capital charge and an additional counterparty credit valuation adjustment (CVA) capital charge. In this article, we explain the new methodologies to compute these capital charges on the OTC
market: The standardized approach for default capital charge (SA-CCR) and
the basic approach for CVA (BA-CVA). Based on historical calibration and
future estimations, we built internal models in order to compare them with
the amended standardized approach. Up till June 2015, interest rate and FX
derivatives constituted more than 90% of the traded total OTC notional
amount; we constructed our application on such portfolios containing and
computed their total counterparty capital charge. The analysis reflected different impacts of the netting and collateral agreements on the regulatory capital depending on the instruments’ typologies. Moreover, results showed an
important increase in the capital charge due to the CVA addition doubling it
in some cases.
Keywords
Counterparty Credit Risk, SA-CCR, CVA, OTC Derivatives, Basel III
1. Introduction
Derivatives market witnessed an important bloom in recent decades due to their
increasing utility in our financial markets. Several typologies and complexity leDOI: 10.4236/jmf.2017.71001 December 30, 2016
M. Sayah
vels of such instruments are used either in a regulated exchange traded manner
or in an over the counter fashion. Instruments could be swaps, options, futures,
forwards... Exchange traded activity started in 1970 following certain rules and
“standardized” formats whereas over the counter (OTC) market came in 1990 as
an “irregular” market with various customizable trades; therefore it is a more
risk vulnerable environment. OTC market has a larger volume due to the higher
profit margin and wider bid-ask spreads. Trying to reduce the risk on the OTC
market, clearing houses were created in order to give all the counterparties a
guarantee not to have any open positions and to force applications of the agreed
upon rules.
Derivatives hold several types of risks such as market, liquidity and credit,
however the credit risk in such instruments is not the typical credit risk that we
encounter when passing a loan; it is the counterparty credit risk. The counterparty credit risk differs from the traditional credit risk by two points: The bilateral risk profile and the variation of the exposure depending on market and
counterparty behavior. Counterparty credit risk is the risk taking into account
the exposure of the financial institution to the counterparty if this latter defaults
or has its credit quality devaluated. Recent crises emphasized the faulty practices
regarding the OTC derivatives capital charge computation from a counterparty
credit risk point of view: Starting with the collapse of Lehman Brothers and several near and full collapses of banks all over the United States, United Kingdom
and Europe, the counterparty risk gained now the same importance as the major
well-known risks (market, liquidity, operational…). Counterparty credit risk has
gained importance making it a central need in several areas of the banking
workflow: Pricing OTC products, computing the capital charges, managing exposures to different counterparties and finally stating the conditions of a certain
deal concerning the initial margin or collateral… Basel II had implemented methods to compute the default capital charge of the counterparty credit risk beard
in derivatives however in the subprime crisis two thirds of the losses did not result from such category of counterparty risk. A new risk source was highlighted:
the risk resulting from the credit valuation of the counterparty noted the credit
valuation adjustment risk (CVA). In this paper our aim is to describe the current
OTC market, to briefly note the previously applied regulatory methods for the
counterparty credit risk then to explain and apply the new methods in order to
compute the capital requirements on typical portfolios. The paper proposes also
an internal approach to compute the same figures based on historical behavior
and future market experts’ estimations. Section I introduces the counterparty
credit risk, Section II details the default capital charge whereas Section III details
the CVA risk capital charge. Section IV presents the application of such techniques compared to internal approaches on sample portfolios and finally Section
V concludes on the results.
2. Counterparty Credit Risk
Counterparty Credit risk is a major risk faced on the OTC market. It covers two
2
M. Sayah
facts: the defaults of the counterparty or the decrease in its credit quality as described in [1]. In both scenarios, the bank would try to replace the instrument
held or re-evaluate its worthiness. In order to compute this “replacement cost”
and “potential future exposure” different factors are involved such as: Mark-tomarket exposure, liquidity risk following a counterparty’s default, operational
risk as in the process of managing the positions after a change had occurred or
even in managing the margins or collaterals of a certain agreement and finally
legal risk related to enforcement for the application of the deals conditions. As
the use of derivatives has grown, especially on the OTC market, regulators are
continuously trying to implement new approaches that reflect as adequately as
possible the counterparty risk englobed by these instruments and therefore
making their approaches more and more sophisticated, see [2].
2.1. Transition to Basel
In an attempt of improving capital framework for OTC derivatives under Basel
III method presented in [3], several reforms were put in place:
• Wrong way Risk is more adequately evaluated by not taking recoveries in the
loss given default (LGD) computation (the amount lost in case of the counterparty’s default).
• The computation of the portfolio exposure is required to take into account a
stressed period values (in LGD calibration).
• New method for collateralized transactions evaluations to capture the exposure over a full year of inception.
• Standards for initial margining have been strengthen.
• The asset value correlation parameter was increased by 25% to reflect the
correlations between financial institutions raising the risk weights.
Another important change in Basel III is the addition of a credit valuation
adjustment (CVA) capital charge to capture the risk of mark to market losses
on the expected counterparty credit risk, this is amply described in [4]. Total
losses from CVA were double the losses from defaults (66% from CVA and
only 33% of the losses are due to defaults). The CVA capital charge is expected
to double the capital charge for derivatives however, banks are not going to be
asked to put any additional CVA charge if the derivatives are centrally cleared:
This is an incentive to clear through a central counterparty clearing house
(CCP).
2.2. Default Capital Charge Computation
All banks are required to hold capital against the variability in the market value
of their OTC instruments: They need to capitalize for default risk. As it is well
known for Basel amended approaches two possibilities are entitled: A standardized approach and an internal model implementation. In the following, we are
going to discuss briefly the characteristics and method scheme of each of these
methods in order to apply them in the following part of this work and compare
their figures.
3
M. Sayah
2.2.1. Standardized Counterparty Credit Risk Approach (SA-CCR)
SA-CCR is the new standardized approach for computing default counterparty
credit risk presented in the BCBS document [5]. It was presented and revised by
April 2014 and is in order to be implemented by January 2017. Different papers
described this method such as [6], in our work we try to summarize and apply it
on different portfolios under different conditions in order to understand the behavior of this practice.
Main objectives of this method implementation were to be:
• Suitable to be applied on different kinds and specifications of derivatives
transactions
• Easy and simple implementation techniques
• Better than the methods that preceded
• More risk sensitivity reflection
Computing the capital charge is our main aim and this figure is given by:
Default Counterparty Capital Charge
= Exposure at default × Risk weight × 8% (1)
Where the SA-CCR EAD (Exposure at default) is our key figure, the risk
weight is amended by Basel and the 8% reflects the pillar 1 obligation.
Computing the EAD would need to be held on each netting set level on a
hedging set basis:
EAD =1.4 × ( RC+ PFE )
(2)
where RC is the replacement cost and PFE the potential future exposure.
The concept of Equation (2) is referring to is the fact that the exposure to an
instrument is the sum of its present value and the future potential values. The
alpha factor is added as an insurance to cover the risk and the value of alpha is
calibrated based on several internally generated models (seen in previous counterparty credit risk models), therefore this coefficient is kept constant all through
the computation.
Hedging sets are defined as follows (details in pages 12 - 13 of document [5]):
1) Interest rate: a hedging set is defined for one same currency further divided
into maturities, long and short positions fully offset within maturity categories, across maturity categories partial offset is recognized
2) Foreign exchange: same currency pairs form same hedging sets, full offset is
only permitted within a same pair
3) Credit derivatives and Equity derivatives: in these two categories each asset
class forms a hedging set, full offset is permitted for a same entity (index or
name) whereas partial offset between derivatives is applied when referring to
different entities
4) Commodity derivatives: four hedging sets: energy, metals, agriculture and
others. No offset among these categories. In a same hedging set, full offset for
same commodity is permitted and partial offset is applied when handling
different commodities.
The EAD formula changes in case the trade is margined or un-margined:
• If margined: RC represents the exposure if the counterparty defaults at time
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M. Sayah
t = 0 assuming the close-out does not take time and PFE is the change in
value during the period between the default and the deployment of the collateral.
• If un-margined: RC is the present exposure and PFE is the potential increase
in exposure over a one-year time horizon.
Replacement Cost
The RC is computed following two formulas: if the trade is margined or not
(more details in [7], pp. 4-7.
For un-margined transactions:
=
RC max ( 0;V − C )
(3)
where V is the current market value of the derivatives and C is the net haircut
collateral held. Not having any margin, at time t = 0 the replacement cost
would depend on two possible outcomes: the instrument’s value is in our favor
or not. If the value of the instrument is higher than the collateral a default of the
counterpart would result in a loss equal to V-C the value of the instrument minus the collateral value, if not, no loss is included: which explains the RC formulation in the un-margined case.
For margined transactions:
RC
= max ( 0;V − C ; TH + MTA − NICA )
(4)
where TH is the positive threshold before the counterparty send the bank collateral, MTA is the minimum transfer amount applicable to the counterparty and
NICA any collateral posted by the counterparty minus the one posted by the
bank (net value). In this case the margin should be taken into account for the
computation of the replacement cost: if the value of the instrument is inferior to
the value of the collateral and the collateral posted by the bank is inferior to the
one posted by the counterparty, the loss will be null. However, if any of the previously denoted figures is positive the replacement cost will be equal to it: if the
posted collateral is more than the collateral of the counterparty or if the value of
the instrument is higher than the total collateral the bank would have to cover
these differences as a replacement cost.
Potential Future Exposure
PFE is given by:
PFE
= multiplier × Add − On Aggregate
where the multiplier recognizes excess of collateral and negative mark-tomarket, and the add-ons are calculated for each asset class.
Computing the multiplier also detailed in [7], with a floor of 5% is computed
as follows:



V −C
multiplier
= min 1; floor + (1 − floor ) × exp 

2
1
floor
Add
on^
aggregate
×
−
×
−
(
)
{
}  


The multiplier formula is built in a way to account for over-collaterization:
The multiplier is normally at 1 however, if the bank chooses to over-collaterize
the instrument they are holding, this multiplier will be inferior to 1 therefore
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M. Sayah
giving the bank the advantage of their extra-safety arrangement.
And the add-on computation follows these steps:
1) Define the transaction primary risk factor.
2) Allocate it to an asset class: Interest rate (IR), Foreign exchange (FX), equity,
credit or commodity
3) Compute the adjusted notional amount (for IR and credit duration is included).
4) Get the maturity factor (whether margined or not).
5) Multiply the supervisory delta by the adjusted notional (+ or − 1 if long or
short).
6) Multiply it by the given supervisory factor to reflect volatility.
7) Aggregate by hedging sets and asset-class level.
For more details on the specific computation of the Add-on for each asset
class, please refer to the Basel document [7].
The SA-CCR add-on computation method is based on a set of assumptions in
order to result in the previously cited formulas. These assumptions are the following:
• All trades are at the money (MtM = 0).
• The banks neither hold nor post collateral.
• No cash flows are present before the one-year horizon.
• The evolution process of instruments follows a Brownian motion with zero
drift and fixed volatility.
We note the important impact of the maturity factor on the computation: this
latter depends on the portfolio: margined or not. If the portfolio is un-margined,
the maturity factor (MF) applied is equal to:
MFun − margined =
min (1year, Maturity )
1year
(5)
However, if the portfolio is margined, MF depends on the remargining frequency. Basel amends a certain margin period of risk (MPOR) depending on the
characteristics of the deals considered, this margin represents the closing time
between the default of the counterparty and the margin payment. This concept is
described in [5].
MFmargined =
3 MPOR
2
250
(6)
where MPOR is defined by the frequency: for daily re-margining MPOR is
equivalent to 10. The general formula for an N remargining per day frequency is:
MPOR = 10 + N − 1
(7)
A daily re-margin is the most conservative, therefore we chose this frequency
as a base of our application portfolios (in Section II.7).
However, we note that the 3 2 multiplier maintained by Basel in order to
approach the EE of a margined transactions to the one of an un-margined
transaction for MPOR (reflected in [7]) is resulting in double accounting for the
shock (1.5 × 1.4).
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M. Sayah
Several comments were presented to try and remove this multiplier, such as
the comments by Deutche bank, however, the multiplier remains present in the
finalized version of the method.
A brief description of the SA-CCR mentioned above is shown in Figure 1.
2.2.2. Internal Model Method (IMM)
As the habit went, all internal models to be applied for banks should be accepted
by the supervisor entitled for this bank (the national regulator). The bank in our
case study is free to choose to model internally the EAD for the OTC derivatives.
Having this in mind, Basel implemented in its third version [3] requirements
that should be respected in order to get approval for the proposed internal model. Please note that due to several different approaches that could be considered
in the internal model approach, in a consultative document, refer to [8], Basel
proposed to floor the IMM capital charge to a certain percentage of the SA-CCR
capital charge or better yet remove the IMM as an approved method to compute
and report capital charges under the counterparty credit risk. However, all OTC
instruments that were not included in the internal model or that could not assume approval to be globalized under the internal model should be treated
through the standardized approach. We shall briefly describe the requirements
for the EAD internal model but we note that these requirements are required on
a permanent basis and continuous check-ups will be put in place in order to ensure the fully compliance to these rules all through the period of application of
the chosen internal model.
In an attempt to make this more pleasant for readers and easier to discuss the
conditions for the implementation of an internal model will be represented as
Figure 1. SA-CCR capital charge computation process.
7
M. Sayah
bullet points under each categories of requirements:
• The model should specify a forecasting distribution for changes in market
value such as interest rate or foreign exchange rate.
• For margined counterparties, the model should also capture the future behavior of the collateral in question. Note that no particular form of model is
required.
• Determining the default capital charge should be based on the greater computation using: once the current market data to calibrate the projection models and once a stressed calibration. In both cases the time frame should be
three years and in the stressed conditions it should cover a stressed period in
between (three years containing a stress among them).
• The computation will follow these given steps: the Exposure at Default
(EAD) is the product of a previously calibrated (and negotiated) α factor
and the Effective Expected Positive Exposure:
EAD= α × EEPE
(8)
Effective Expected Positive Exposure (EEPE) relies on internal model to predict counterparty exposures, typically simulating underlying market risk factors
out to long horizons and revaluating counterparty exposures at future dates
along the paths simulated, it is the weighted average of the Effective Expected
Exposure (EEE).
=
EEPE
min (1year,maturity )
∑
k =1
EEE k × ∆ k
(9)
The EEE is the increasing function of the Expected Exposure (EE): this
amends a more restrictive approach, once an exposure is hit the method does
not permit a decrease in the exposure for future dates.
EEE k = max ( EEE k −1 , EE k )
(10)
where ∆ k = tk − tk −1 and EE k being the average exposure at future date k
across possible future values of relevant market risk factors, and alpha set for 1.4
however a discussion permitting lower or greater alpha is possible (floored at
1.2). A more detailed look on these formulas is clearly presented in Pykhtin’s article [9].
• The exposure should not only be limited for a given time horizon (ex: one
year), it should cover the entire life of the portfolio (the OTC portfolio).
• Again for margined transactions, the internal model should account for the
re-margining period, the mark-to-market valuation and a sets of floors set for
the time horizons of deals.
• An independent management unit responsible for calculating and making
calls for margin should be put in place.
• The bank must present: adequate documentation for the counterparty credit
risk (CCR) management process, validation of the models, organizational
approval, accurate reporting and reflective results.
• Before starting to use the model, a bank should calculate it for at least one
year before implementation in order to have a set of observed outcomes of
8
M. Sayah
the chosen approach.
In the rest of this paper, we will choose for each case a given forecasting model
in order to project the risk factors (interest rate and foreign exchange risk), calibrate it twice: once on a normal market and once in stress conditions, compute
the EE and going up the formulas recover the EAD for the instrument in question in the both cases, the maximum EAD will be our IMM exposure at default.
We note that the calibration, the re-evaluation and the models chosen for the
IMM could change the capital charge amended by such approaches: the relative
variability for IMM appears to be considerable between banks. Basel committee
conducted an exercise in an attempt to compare the outcome of such models
between banks and recommend a best practice for the IMM in the counterparty
credit risk framework, this exercise can be found in [10].
3. CVA Capital Charge Computation
The CVA capital charge applies to all derivative transactions that are subject to
the risk that a counterparty could default. However, the scope of application
does not include derivatives cleared through a clearing (central) counterparty. It
also encompasses securities financing transactions that are fair-valued by a bank
for accounting purposes. CVA risk could be seen as a strong link between the
counterparty and the market risk however it is by nature more complex than
market risk on the trading book leading to different frameworks and choices
about precise implementation. Reference [11] discusses this issue precisely. Recent Basel approaches amended two frameworks for the computation of this
capital charge: The Fundamental Review of the Trading Book CVA framework
(FRTB-CVA) and a Basic CVA approach (BA-CVA) as shown in Figure 2. Under the FRTB concept, banks are asked to compute the CVA sensitivities requiring the simulation of all exposures to a large panel of market risk factors. This
procedure is very demanding, therefore some banks are enable to cover this calculation and therefore the basic approach presented in [12] is an option for these
reasons. In February 2016, a QIS was sent by Basel to be calculated by banks on a
voluntarily basis in order to measure the impact of these different approaches on
the computation of the CVA capital charge, QIS found in [13].
Figure 2. CVA capital charge computation methodologies.
9
M. Sayah
3.1. Standardized CVA (SA-CVA, FRTB)
Eligibility Criteria:
1) Ability to compute CVA sensitivities.
2) Methodology to approximate credit spreads for all counterparties (including
illiquid ones).
3) Existence of an independent CVA risk management function.
Eligible hedges: Single-name instruments, proxy hedges and market risk
hedges.
CVA calculation:
At least a monthly computation is entitled: For each counterparty (even if only one derivative is included).
The SA-CVA capital is the sum of delta and Vega risks. Each one of these categories are divided into sub-categories depending on the risk types as shown below in Figure 3. For each type, a certain methodology is used to bucket the assets and to compute their sensitivity.
For each risk type in both categories we compute (refer to BCBS (2015) p.
16-25):
• Sensitivity of the aggregate CVA
• Sensitivities of all eligible hedges
• Compute weighted sensitivities: Risk weights are given by Basel for each risk
type.
• The net weighted sensitivity is the sum of the CVA weighted sensitivities and
their hedges.
• Within each bucket, weighted sensitivities are aggregated to form the bucket’s cc.
• Across buckets computation results in the total capital (detailed description
in [14]).
3.2. Advanced Internal Model Method IMM-CVA FRTB
The use of this method is conditioned upon approval of supervisor’s authority.
Briefly citing the conditions: regular back testing, a trial period, expected shortfall approach, 97.5 confidence level, cover delta and vega risks, stressed period
Figure 3. Standardized CVA categorization.
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M. Sayah
calibration. The methodology is to compute internally the CVA expected shortfall (netted assumptions) and then to compute this figure for each asset types:
interest rate, FX, credit spread, equity and commodities in order to sum all of
them and get the gross expected shortfall. The average of the two expected
shortfalls is considered and a regressive formula is put in place in order to compute the required capital charge.
3.3. Basic CVA (BA-CVA)
The basic CVA approach is for banks that are not able to compute the CVA sensitivity or does not have the approval of their authorities to use the FRTB-CVA
introduced in [12]. However, this approach is known to be very demanding and
very conservative in terms of risk weights placed by Basel.
Before detailing the computation of the capital charge it is important to cite
very briefly the eligible hedges in this framework: single-name CDS that references the counterparty directly, or references an entity legally attached to it or
references an entity that belongs to the same sector and region of this counterparty; single-name contingent CDS and index CDS.
(
The basic CVA capital charge is given by the sum of the spread capital
K spread and the expected exposure capital ( K EE ) :
)
(11)
K
=
K spread + K EE
CVA
The formulation of the capital charge is intuitive because the CVA is the risk a
bank is facing in case of a fluctuation in the credit quality of the counterparty
therefore the two main factors are the credit quality represented by K spread and
the expected exposure amount parallel to this change: K exposure . Differentiation
in computation apply if the portfolio is hedged or not (hedging the CVA risk or
not). Considering that no hedging strategies were put in place for hedging this
kind of risk, which is the case for the majority of small and medium banks having the CVA as a relatively new capital charge computation, we will apply the
following formula:
2


2
2
 ρ ∑Sc  + 1 − ρ ∑Sc
c
 c 
unhedged
K
=
spread
(
)
(12)
where Sc is the supervisory expected shortfall of CVA of counterparty c and
ρ is the supervisory correlation between the credit spread of a counterparty
and the systematic factor set to ρ = 50% .
The second term of Equation (8) is given by a simple scaling of K spread :
unhedged
K EE
= 0.5 × K spread
(13)
Therefore the computation is held in the Sc term:
Sc =
RWb( c )
α
∑ M NS EAD NS
NS ∈c
(14)
α is non-other than the α = 1.4 discussed earlier, EAD are the EAD internally computed earlier on a netting set level, M NS is the effective maturity of the
11
M. Sayah
netting set and RWb ( c ) is the risk weight set by Basel for the risk bucket b( c ) .
The different weights are shown in Basel paper [12].
4. Application
4.1. Data Used
In the following, we chose to work on three different portfolios composed each
time of one unique instrument: an interest rate swap, an FX forward and a FX
plain vanilla call respectively. No netting is considered and no collateral nor
margin agreements are added in this first step.
In each scenario, we computed the capital charge of the portfolio for different
maturities of the instrument (going from 6 months to 5 years) in order to see the
progression in time of the capital charge (in standardized or internal approaches).
The choice was made due to different causes:
• To cover several asset classes.
• To study differences between instruments with or without optionality.
• The interest rate segment accounts for the majority of OTC derivatives activity and represented around 80% of the global OTC derivatives market by
June 2015.
• Foreign exchange derivatives make up the second largest segment of the
global OTC derivatives market with around 13% of the market by mid-2015,
and FX forwards make up half of the notional amount outstanding in this
asset class.
We detail the three considered portfolio in this section:
IR swaps: We start by considering a portfolio containing one interest rate
swap denoted in USD: one floating leg and one fixed leg of 100 USD as notional
with semi-annual payments. The fixed coupon rate is defined in a way for the
present MtM of the swap to be null. We will consider different versions of this
portfolio by changing the maturity of the swap: from a 6-month interest rate
swap to a five-year swap.
FX forward: We consider a portfolio containing one FX forward USD-EUR.
The forward rate is computed in such way that the present MtM is null. As we
did earlier, we will consider different cases of this portfolio by changing the maturity of the forward: from a 6 month FX forward to a five year FX forward.
Plain vanilla option: We consider a portfolio with a single FX plain vanilla
call (USD/EUR), long position, with maturities going from 6 months up till 5
years, a notional of 100 EUR, a strike price of 1.4 (the actual spot is 1.0963). The
MtM of the call is not null and it is priced using the Black and Scholes formula
with the market implied volatility.
The data used are fetched from Bloomberg platform: (see Appendix 2 for the
plots)
• USD swap curve, EURO swap curve and the FX spot rate (USD-EUR).
• For each swap curve the observed tenors are 1 month up till 50 years.
• Daily frequency.
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M. Sayah
• Historical observed dates: since end of April 2004 until end of April 2007.
• Swap curve number of observations: 1536 per tenor (112,128 observations).
• FX curve: 1565 observations.
4.2. Capital Charge Computation
4.2.1. Default Capital Charge
Considering a risk weight of 100% and the pillar 1 factor as 8%, by multiplying
the obtained EAD by these two components we would be able to compute the
capital charge to cover the counterparty credit default risk (as seen in Equation
(1)). Therefore, in the following we will just demonstrate the EAD results, final
computation will be added in the next section.
4.2.2. SA-CCR
IR swaps
Explaining step by step the computation will result in the following:
EAD =1.4 × ( RC + PFE )
In an attempt to replicate the SA-CCR assumptions, we considered interest
rate swaps with an initial RC equal to 0 (we compute the fixed coupons in a way
that is equivalent to the floating leg cash flows). As for the PFE, it is the product
of the multiplier and a given Add-on. The multiplier is here to add the characteristics neglected in the add-on assumption: referring to the assumptions of the
SA-CCR add-on computation formulas p.16, no collateral is considered, therefore the multiplier is added to the formulas in order to incorporate the collaterization effect. Moreover, the multiplier is floored at 5 % in order to always account for the PFE even when we have a very important collaterization. In our
case, no collateral is recognized therefore the multiplier is one.
PFE
= multiplier × Add − on
multiplier
= 1
The Add-on depends on the asset type, for the interest rate the Add-on is
computed as the product of a maturity factor, a supervisory factor, an adjusted
notional and a directional delta. The adjusted notional of the IR bucket is equal
to the notional amount multiplied by the duration of the instrument for a given
rate of 5%. Basel justifies the supervisory factor of 0.5% as the one-year volatility
of the swap rate.
=
Add − on Supervisory factor for IR × Effective Notional
Supervisory factor = 0.50%
Effective Notional = δ i × di × MFi
δi =
+1, di =
Notional × SDi
SDi =
MFi =
exp ( −0.05* Si ) − exp ( −0.05* Ei )
0.05
min (1year, Maturity )
1year
where Si is equal to 0 in our case and Ei is equal to the maturity for each case
and MFi is defined as if in order to scale down the supervisory factor (meaning
13
M. Sayah
Table 1. IR swap SA-CCR results.
Maturity (years)
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
EAD (% of notional)
0.24
0.68
1.01
1.33
1.65
1.95
2.25
2.54
2.82
3.10
Figure 4. Interest rate swap EAD under SA-CCR.
to reduce the volatility for instruments of less than one year). Results for the
EAD of this instrument are shown in Table 1 and Figure 4.
Not having any optionality, the IR swap only “variable” is the effective notional. This latter is computed as a continuous version of a bond duration with a
maturity equivalent to the maturity of the interest rate swap (details can be
found in Appendix 1). The duration being an increasing function of the maturity, the curve is expected to have an increasing trend. An additional supervisory
factor is multiplied in order to “evaluate” the risk of such asset class. Note that
the supervisory factor for the interest rate risk is the lowest for only 0.5
FX forwards
The RC and multiplier reasoning are the same as the one previously explained
in the IR case:
EAD =1.4 × ( RC + PFE )
RC = 0
PFE
= multiplier × Add − on
multiplier = 1
As for the Add-on, the difference in the FX type is: the effective notional
(representing the one-year volatility) is independent of the maturity therefore
the effective notional is simply the notional amount.
=
Add − on Supervisory factor for FX × Effective Notional
Supervisory factor = 4.0%
Effective Notional = δ i × di × MFi
δ i = +1
14
M. Sayah
di = Notional and MFi =
min (1year, Maturity )
1year
Not having any optionality, nor implying the maturity into computation the
FX forward EAD curve seen in Figure 5 is divided into two parts: before the
one-year maturity and after one year. The computation is rather simple multiplying the notional amount, supervisory factor and capped maturity presented in
Table 2. Note that the supervisory factor for the foreign exchange bucket is
much more important than the interest rate amended factor (by 8 times) and it
is equal to 4.0 % justified by the regulator as the first year instrument volatility.
Plain vanilla call
EAD =1.4 × ( RC + PFE )
RC = 0
PFE
= multiplier × Add − on
multiplier
= 1
=
Add − on Supervisory factor for FX × Effective Notional
Supervisory factor = 4.0%
Effective Notional = δ i × di × MFi


 Pi 
2
 ln ln   + 0.5 × σ i × Ti 
 Ki 

δ i = +Φ 

σ i × Ti






=
Pi underlying
=
spot 1.0693
Table 2. FX forward SA-CCR results.
Maturity (years)
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
EAD (% of notional)
3.96
5.60
5.60
5.60
5.60
5.60
5.60
5.60
5.60
5.60
Figure 5. FX forward EAD under SA-CCR.
15
M. Sayah
=
= 1.3
K i strike
σ i = 15% supervisory volatility
=
di Notional
= 100
Ti = maturity
MFi =
min (1year, Maturity )
1year
This is another example in the FX bucket therefore the supervisory factor is
4.0%. On the first hand, we note that in this case the replacement cost is not null:
it is computed as the price of the option (black and Scholes). On another hand,
due to the optionality of this instrument an additional factor is added: the delta.
When handling instruments with no optionality, the delta factor is equal to 1 or
−1 in order to reflect if we are short or long on the transactions. However, in this
case the delta is computed as the normal cumulative function of a given figure.
This is the risk-adjusted probability of exercise derived from the Black and
Scholes formula in [15]. In the delta computation, a 15% volatility is amended by
the regulator. Results are reflected in Table 3 and Figure 6.
Table 3. FX plain vanilla call SA-CCR results.
Maturity (years)
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
EAD (% of notional)
0.28
1.12
1.84
2.47
3.04
3.52
3.97
4.37
4.75
5.09
Figure 6. FX plain vanilla call EAD under SA-CCR.
16
M. Sayah
Internal Model Method
We build our models reflecting historical observations and incorporate expert
opinions along with forecasting visions respecting in parallel the recommended
practices amended by Basel such as the daily steps, the numerous simulations...
Detailed explanation on both models: interest rate and FX rates are found here
below.
Interest rate models
USD interest rate model
After the sub-prime crisis and European debt period, we are in a very low interest rate environment (even negative) and all expectations vote for an increase
in the rates (interest rates or FX rates).
The Federal Open Market Committee (FOMC) forecasting schema is one of
the most used and trusted interest rates projections because it is based on experts’ opinion trying to reflect and anticipate the market behavior. These projections found in [16] and represented in Figure 7, are those of Federal Reserve
Board members and Federal Reserve Bank presidents.
The data we are using ends at t = 0, 27 December 2015, therefore we chose
the forecasting of the FOMC in order to get an idea of the expert opinion projection of the market. FOMC presents several projections however we represent the
most stressed anticipations starting December 2015 here-below:
We can notice that the market tendency is to go up: 1.5% after one year, 2.3%
after two years, 3.15% after three years and a 3.5% rate on the long run. Therefore, we need to calibrate our historical model on an upward trend period. We
chose to calibrate our internal approach to the period of rates increase of
2004-2007 and chose the best fit calibration: calibrating the models to a historical period, projecting today’s yield curve based on these projections and com-
Figure 7. FOMC USD short rates most stressed projections.
17
M. Sayah
Figure 8. Calibration period on the USD short rates.
paring our IMM yields with the FOMC most stressed rates in order to choose
the best fit.
Doing so, the stressed period chosen was: 30 April 2004 till 30 April 2007 to
calibrate our IMM, represented in Figure 8. As an interest rate model we chose
to use the well-known Vasicek approach.
The chosen model that we found adequately representative of the market is
the Vasicek model: This is an easy model, incorporating the drift and implemented in most of the banking solutions. Choosing the simplest model was set
to simplify the most this interpretation. However, Vasicek is a very sensitive
model and differs amply with its calibrations however, following the previously
cited technique we were able to choose a calibration that fits the market today
following three main steps. These three steps should be repeated once on the
stressed market calibration and once again on the current market conditions,
comparing the EAD results we chose the maximum between both calibrations as
our IMM given EAD. The results are as follow:
• Step 1: Calibrate Vasicek models on the historical stressed (resp. actual) period and get the parameters as per Table 4; the calibration is based on [17].
• Step 2: In order to fit the yield curves, we only change the speed of adjustment k in order to find the new speed at which our yields curve today would
converge to the calibration conditions. Keeping all other parameters constant
reflects the market and investors’ behavior in the calibration times (notably
in times of stress). However, by changing the speed of adjustment in order to
fit the actual yield curve, we change the long run of our model, results are
represented in Table 5.
• Step 3: Based on these curves we evaluate our instruments and discount the
cash flows in order to compute the required capital charges and EAD: The
18
M. Sayah
maximum EAD is chosen as the IMM EAD.
EUR interest rate model
The same approach is used for the EUR interest rate model: Vasicek is calibrated on the same historical upwards choc then re-parameterized to fit today’s
yields. The calibration and trend of the EUR curve is shown below in Figure 9.
Foreign Exchange model
As for FX models, we use GARCH (1,1) model to reflect the volatility of these
rates: it is calibrated at the same time-frame and projected. We note that the
projection results of our model are in sync with Bloomberg’s forecasting scenarios (most stressed) for the upcoming years. As for the pricing models for the FX
options we chose to price based on the well-known Black and Scholes formula
incorporating the volatility deducted from the GARCH (1,1) model. On a final
note, in the FX instruments both interest rates and FX models are used. In order
to remain homogeneous between models the same random variable is used in all
Table 4. Vasicek parameters for USD short rates.
k
θ
σ
λ
θ*
r0
Stressed
0.4050
0.07299
0.0015429
5.1172
0.053500
0.0535
Actual
0.00347
0.09629
0.0005517
−0.44712
0.006031
0.00603
Table 5. Vasicek parameters for USD yields generation.
k
θ
σ
λ
θ*
r0
Stressed
0.21129
0.07299
0.001543
5.1172
0.035627
0.0535
Actual
0.05309
0.096298
0.000552
−0.44712
0.008116
0.00603
Figure 9. Calibration period on the EUR short rates.
19
M. Sayah
models used for one given scenario.
PORTFOLIO 1: Interest rate swaps
The EAD value will be deduced following formulas (3), (4) and (5) of Section
II. As previously detailed, we started to model the IR swap curve for the USD on
normal conditions and on stressed market conditions in order to get the EAD as
the maximum of these two sets of calibrations (see Appendix 3 for a detailed
presentation of this approach and of the parameters estimations). We have
modeled the behavior of the interest rate swap based on this model, we have
1
projected in the future the EE, then the EEE. Afterwards, with a ∆ =
(daily
250
basis) we have computed the EEPE and the α = 1.4 resulted in obtaining the
EAD figure. As mentioned above, this was done twice and the resulting EAD is
the maximum exposure for both sets of conditions.
We highlight the fact that in our models, an increase in rates is amended
therefore among counterparties there will always be one party with a higher exposure than another whereas in Basel the standardized approach asks for the
same capital charge for both positions. In our IMM, the maximum exposure of
both long and short positions is asked from both counterparties in order not to
perturb the market equilibrium. Trying to better clarify this previous assumption: Let us consider two counterparties with the same risk profile, if these two
parties enter an interest rate swap we will have one institution paying fixed and
receiving floating and the other one doing exactly the opposite.
Trying to reflect the exposure of each, one party will be paying almost null
capital charge whereas the other will be paying an important amount.
To keep the market equilibrium (not to add a risk premium on the instrument
price) and not to manipulate with the market, both counterparties are asked to
place the same capital charge. This defined capital charge, in order to be the
most restrictive is going to be the maximum of the short and long exposures.
The application of this process is shown in Table 6 (in % of notional), comparing it to the previously computed standardized approach EAD and following
different maturities in years:
Figure 10 shows that following a Vasicek model we can resemble the standardized approach behavior on the maturities going from 0.5 year up to almost 5
years which is the most frequent maturities encountered in such instruments for
our portfolios. However, we can notice that the IMM gives slightly lower EAD
for all of these maturities. The IMM-EAD is almost equivalent to 80 % of the
SA-CCR-IMM.
PORTFOLIO 2: FX forwards
Again following the EAD computation technique explained in the IMM section we shall apply our own chosen models to compute the EE of an FX forward
(USD-EUR). The methodologies used will need a part to project the yield curve
and another part to project the FX rate.
Choosing the Vasicek model for the yield curves (both USD and EUR) is followed to keep consistency with the IR swap. However, for the FX rate a GARCH
20
M. Sayah
Table 6. IR interest rate swap internal model results.
Maturity
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
SA-CCR
0.244
0.68
1.01
1.33
1.64
1.95
2.25
2.54
2.82
3.09
IMM
0.098
0.43
0.82
1.08
1.36
1.58
1.84
2.05
2.30
2.51
Figure 10. Interest rate swap EAD under the IMM.
(1,1) was calibrated to the model and the rates were projected following this approach (refer to Appendix 4 for the GARCH model details).
Again with a daily step and an alpha factor of 1.4 the results, Table 7 and
Figure 11 reflect the EAD as a percentage of the notional amount of the forward:
We had previously seen the two different stages of the standardized approach
EAD following the maturity of the instrument (before and after one year). Here,
the internal model will also differ between these two stages computing the EPE
as an average on the first year.
We can notice that the behavior of the internal model resembles the one described by the SA-CCR computation however the IMM is less demanding than
the SA-CCR when using models based on one factor Vasicek and Garch (1,1).
Both approaches converge to a 5.6% EAD to notional amount. However, on a
certain time range the IMM “explodes” due to the time limits of the GARCH
approach.
PORTFOLIO 3: FX plain vanilla call
The third portfolio contains a plain vanilla FX call option: measuring the EAD
will demand a forecast for two risk factors: the FX rate and the interest rate
(EUR and USD). Based on the same logic as previous applications, we applied a
Vasicek model for the interest rates and a Garch approach for the forecast of the
foreign exchange rate. Adding to that a Black-Scholes traditional pricing formulation was used based on the GARCH-computed volatilities at each time t.
21
M. Sayah
Table 7. FX forward EAD internal model EAD results.
Maturity (years)
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
SA_CCR
3.96
5.60
5.60
5.60
5.60
5.60
5.60
5.60
5.60
5.60
IMM
3.09
4.33
4.48
4.46
4.61
4.87
5.21
5.50
5.84
6.24
Figure 11. FX forward EAD under the IMM.
Table 8. FX options EAD internal model EAD results.
Maturity (years)
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
SA-CCR
0.28
1.12
1.84
2.47
3.04
3.52
3.97
4.37
4.75
5.09
IMM
0.31
1.13
1.65
2.10
2.48
2.84
3.15
3.43
3.69
3.94
Figure 12. FX plain vanilla call EAD under the IMM.
Computing the EE then following the IMM process, we obtain in Table 8 and
Figure 12 the EAD as a percentage of the notional amount of the option:
We can notice here that the internal model is equivalent to the supervisory
22
M. Sayah
capital for low maturities however after a maturity of one year we have a tendency towards approximately 80% of the standardized approach. We note that
this might be due to the assumptions taken on the SA-CCR level assuming a 15%
volatility factor whereas the GARCH approach begins by assuming lower observed volatilities on the stressed period (approximately converging towards
13%) therefore this explains the difference in behaviors depending on the maturities.
4.2.3. CVA Capital Charge
Based on Equations ((8)-(10)) we compute the capital charge for the CVA risk
under the basic approach, using the following: RW = 10.2% considering that the
counterpart is a financial institution, M is the effective maturity of the portfolio
(here it is below or equal to one year therefore it is equal to one), EAD is the exposure at default computed using the IMM method on a netting set level and
α = 1.4 . Table 9 shows the computation for a one-year instrument in each asset
type.
The previous table units are as the notional amounts of each instrument type.
The CVA capital charge being a function of the effective maturity and the
EAD, we can simply apply the equations on the internally computed EAD on a
netting set level in order to get this CVA charge. Having assumed that no hedging is in place for the CVA risk, from Equations ((8)-(10)) applying the coefficients of our cases, we can get the following shortcut formula:
CVA=
0.5464 × M × EAD IMM
CC
(15)
4.2.4. Adding Netting and Margin Effects
Having discussed the benefits of adding netting agreements and margins to our
portfolio, in this section we materialize this in an actual calculation for different
conditions on three given portfolios. We reconsider the same instruments seen
previously, however now we will handle three composed portfolios in order to
show the added effect of netting agreements and margin contracts. Trying to
consider a hedging set and the effect of choosing between the standardized and
internal approach, we consider that in each portfolio all the instruments are held
with the same counterparty. Adding to that, we assume the probability of default
of the counterparty to be 0.05% (equivalent to an AA rating).
Portfolio 1: Two IR USD swaps, one long and another short, with maturities
0.5 and 2.5 years and notional amounts of 100 USD each. This consideration was
based on the statistics of the IR swaps in the OTC market that reflects the fact
that 75% of the swaps have maturities less than 5 years.
Table 9. CVA capital charge for one year instruments.
CVA Capital Charge
One year IR swap
0.047
One year FX forward
0.47
One year FX call option
0.12
23
M. Sayah
Portfolio 2: Three FX forwards deals USD/EUR: one long with a residual
maturity of 0.5 years and the others short with 1 and 2.5 years’ residual maturities. All forwards have the same notional 100 EUR. The choice is also attributed
to the distribution of concentration based on maturities in the FX OTC instruments: <90% have maturities less than 5y .
Portfolio 3: Two options a long position on a call of 0.5 years as maturity and
a short position on another call with a residual maturity of 2.5 years (both have a
100 notional).
Tables 10-12 show respectively the composition of Portfolio 1, 2 and 3.
Not to accumulate numerous variables, we consider the threshold and the
minimum transferable amount null. In other words, any positive exposure will
trigger the margin agreement. As for the collateral, we implemented ISDA method in order to compute the collateral amount as the 99th percentile of the exposure on a 10-days remargining frequency explained in [18]. No independent
amount was considered for the following exercises considering that both counterparties have the same profile therefore the netted collateral value is null. We
hold cash collateral. These are our assumptions for the upcoming applications.
The frequency term denotes the margin re-evaluation frequency; this criterion
will define the maturity factor used to compute the exposure at default under the
standardized approach (refer to paragraph Potential future exposure p.17). In
general, daily frequencies are used therefore we applied this on our portfolios
and used the 10 days MPOR amended by Basel for such remargining frequency.
Applying all the above, summaries for the margin agreement are found in
Tables 13-15.
Table 10. Portfolio 1 composition.
Trade
Type
Currency
Position
Notional
Residual
Maturity
MtM0
1
IR swap
USD
Short
100
0.5
0
2
IR swap
USD
long
100
2.5
0
Table 11. Portfolio 2 composition.
Trade
Type
Currency
Position
Notional
Residual
Maturity
MtM0
1
FX forward
USD/EUR
Short
100
0.5
0
2
FX forward
USD/EUR
long
100
1
0
3
FX forward
USD/EUR
long
100
2.5
0
Table 12. Portfolio 3 composition.
24
Trade
Type
Currency
Position
Notional
Residual
Maturity
MtM0
1
FX option call
USD/EUR
Short
100
0.5
−0.03
2
FX option call
USD/EUR
long
100
2.5
1.07
M. Sayah
Table 13. Portfolio 1 margin agreement.
Frequency
Threshold
MTA
Independent Amount
Net Collateral
Daily
0
0
0
0.12
Table 14. Portfolio 2 margin agreement.
Frequency
Threshold
MTA
Independent Amount
Net Collateral
Daily
0
0
0
1.48
Table 15. Portfolio 3 margin agreement.
Frequency
Threshold
MTA
Independent Amount
Net Collateral
Daily
0
0
0
0.80
Default capital charge
Portfolio 1
• Step 1: Netting but no margin. A simple summation of the exposures at
default of the previously computed results in the non-netted results. For the
netting sets, SA-CCR formula for the IR class amends an aggregation of the
effective notional in such a way to account for different maturity buckets:
Effective notional
=
Eff ⋅ notional12 + Eff ⋅ notional22 + 1.4Eff ⋅ notional1Eff ⋅ notional2
(16)
This is specified by the correlation parameters supposed by Basel between
maturity buckets in the IR asset type (cf. BCBS (2014b) paragraph 4.1). The internal model is less demanding than the SA-CCR in both cases (netted or not).
However, the netting effect decreases the exposure of the SA-CCR by an average
rate of 22% whereas the IMM only decreases by 7%.
• Step 2: Margin but no netting. Applying the conditions of the margin
agreement cited previously on each of the trades in the portfolio, we compute
the EAD for un-netted but margined portfolio. For the SA-CCR approach,
the RC follows Equation (4) and the maturity factor is restrained because we
have a daily computation (MPOR = 10). For the IMM, the EAD was recomputed following the margin agreement. When the collateral increases, the
EAD decreases. We can notice that both methods decreased the capital
charge by 72%. Note the importance of the maturity factor change: In the
SA-CCR the MF is dependent of the MPOR chosen amended as 10 days for
the daily margin. For the IMM, the 1.5 factor added in the SA-CCR is translated as a different MPOR for the IMM: 1.5 × 1.5 × 10 therefore applying the
IMM margin agreement with a MPOR of 22.5 days would be coherent with
the standardized method. If we chose to add only a margin agreement with
daily remargining, no collateral, no threshold, no initial margin nor minimum transferable amount, the SA-CCR EAD would be reduced by 67%
(from the initial EAD “nothing”). With the collateral addition, the SA-CCR
reduces the capital charge by 72.8% whereas the IMM by 72.3% retaining the
25
M. Sayah
ratio between the IMM to the SA-CCR EAD at 78%.
• Step 3: Netting and margin. As a final step we merge collateral and netting
agreement to compute the capital charge.
Figure 13 resumes the EAD of Portfolio 1 under several conditions:
Portfolio 2
• Step 1: Netting but no margin. For the netting sets, SA-CCR formula for
the FX class amends the absolute value of the aggregation of effective notional following:
Effective notional = Eff ⋅ notional1 + Eff ⋅ notional2 + Eff ⋅ notional3
(17)
The internal model is less demanding than the SA-CCR in the non-netted and
almost equivalent in the netted portfolios however, not by much: the netting effect is more recognized in the SA-CCR. In terms of ratios, the EAD decreases the
standard exposure by a rate of 52% whereas it decreases the IMM EAD by 38%.
• Step 2: Margin but no netting. As for step 2, the needed modifications are
put in place to recomputed the EAD for the standardized approach. For both
models, the margin agreement decreased the EAD (therefore the capital
charge) by almost the same amount: 79% in SA-CCR and 77% in IMM.
• Step 3: Netting and margin. Merging collateral and netting agreement.
Figure 14 resumes the EAD of Portfolio 2 under several conditions:
Portfolio 3
Step 1: Netting but no margin. This portfolio is also in the FX bucket
therefore the same computation as portfolio 2 is used in order to define the
EAD of the whole portfolio under the SA-CCR approach. The internal model
reflects the SA-CCR behavior in terms of reduction: the netting effect reduces
EAD by 16 % in the SA-CCR and in the IMM.
• Step 2: Margin but no netting. For the SA-CCR the EAD computation re-
Figure 13. Capital charge portfolio 1.
26
M. Sayah
Figure 14. Capital charge portfolio 2.
Figure 15. Capital charge portfolio 3.
sults in lower EAD, as estimated, the collateral will amply reduce the amount
of the EAD: 80% SA-CCR and 81% IMM.
• Step 3: Netting and margin. Merging collateral and netting agreement in
order to compute the capital charge of our portfolio.
Figure 15 resumes the EAD of Portfolio 3 under several conditions:
CVA capital charge
Applying Equations ((7) to (11)) we compute the basic CVA capital charge.
27
M. Sayah
We apply the computation on the previously considered portfolios: Portfolio 1, 2
and 3.
Considering that the counterparty we considered is a financial institution, the
RW amended by Basel for this CVA approach would be 5%. Not having any
hedging, Table 16 demonstrate the CVA capital charge deducted following Equation (12) denoted earlier.
iv. Comparative Analysis
• Default Capital Charge:
Starting our comparison with the default capital charge section, we need to
compare the IMM to the SA-CCR on the three portfolios level:
o SA-CCR: Focusing on the SA-CCR we have to emphasis the importance of
netting and margin agreements:
The EAD amounts reflected in Table 17 is for the standardized approach applied on the three portfolios (portfolio 1 the IR swaps, portfolio 2 the FX forwards and portfolio 3 the FX options). Trying to make sense of these variations,
Table 18 presents the ratios of the EAD for each portfolio over the EAD not
having any collateral or netting (the “nothing” case).
In order to interpret the results, we will divide this table twice: once based on
the portfolio therefore on the asset typologies, and another time based on the
hedging strategies added (netting, margin agreements, none or both).
We start by discussing the results based on the asset types: For the IR type
(portfolio 1), the EAD decreases by 20% upon applying netting agreements: this
Table 16. CVA capital charge.
CVA capital charge
Portfolio 1
0.370
Portfolio 2
2.025
Portfolio 3
0.626
Table 17. EAD under the SA-CCR.
Portfolio 1
Portfolio 2
Portfolio 3
nothing
1.889
15.159
3.275
netting
1.484
7.240
2.758
margin
0.433
3.135
0.641
both
0.293
0.915
0.464
Portfolio 1
Portfolio 2
Portfolio 3
nothing
100%
100%
100%
netting
79%
48%
84%
margin
23%
21%
20%
both
15%
6%
14%
Table 18. EAD percentage of the “nothing” case.
28
M. Sayah
is due to the fact that the notional amount is reduced when aggregated (Equation (15)) and bucketing is taken into account under the SA-CCR method. Regarding the margin additions change is due to the collateral add-ons and the
maturity factors change: even if we do not add any collateral amount, having a
margining agreement with daily frequency and the given threshold and MTA,
the EAD will decrease per example in the netting case by 70% due to the change
in the maturity factor. Then again adding the collateral will reduce the multiplier
to less than 1 in order to reflect the collaterization effect reducing furthermore
the EAD figure by almost 80%. When having only a collateral (and no netting),
75% reduction is observed and finally when having both hedging policies in
place the reduction will increase to be 85% which is coherent with Basel suggestions that with adequate hedging techniques the capital charge could be reduced
up till 90%. The FX typology is seen in Portfolio 2 and Portfolio 3: Grosso modo
we can see that the impact of netting sets in this asset type is depending on the
portfolios: for portfolio 2 we have three instruments where in portfolio 3 we
have a strategy resembling portfolio 1 therefore the effect of netting here could
be compared to the 80% observed in portfolio 1 whereas the impact is much
higher for portfolio 2. One explanation of such differences might be the method
of computation for the netting set effective notional on one hand (Equation
(16)) and for the fact that in this bucket maturities are not really considered
therefore this could be applied for any maturities (going form 10 days up till five
years). Netting reduces the exposure to a half, and the collateral to 20% in portfolio 2 and 80% and 20% under portfolio 3, whereas when applying both hedges
the reduction is much more important hitting 95% for Portfolio 2 and 85% for
Portfolio 3.
Based on hedging techniques applied, we discuss the following: Across all
portfolios, the results of the netting techniques are various: for the first portfolio,
the netting permitted a reduction of 20% whereas this reduction was far higher
for the second portfolio 60% then again a 15% for the third one. Margining also
had different impacts however, having chosen to suppose a collateral that covers
the 99% percentile exposure, the important reduction was the expected and homogeneous between all portfolios: an average of 80% reduction. The last case is
having both margin and netting applied, this results in a 15 % for the IR portfolio, 6% for the FX forward portfolio and 14% for the FX option portfolio.
o IMM: Only analyzing the internal model based on the same approach previously applied for the SA-CCR results in Table 19 figures in term of EAD:
Table 20 is the same table in percentage of the non-hedged portfolios EAD:
A similar look to this table could show the differences of impact between the
two assets types and the additional difference between instruments with or
without optionality.
o SA-CCR vs IMM: Comparing the IMM to SA-CCR, as per Table 21, several
remarks could be presented, in order to facilitate the representation, the following table sets the ratios of the IMM required capital to the SA-CCR required capital in the same category:
29
M. Sayah
Table 19. EAD under the IMM
Portfolio 1
Portfolio 2
Portfolio 3
nothing
1.463
12.030
2.936
netting
1.354
7.413
2.473
margin
0.263
2.811
0.581
both
0.200
1.399
0.547
Portfolio 1
Portfolio 2
Portfolio 3
nothing
100%
100%
100%
netting
93%
62%
84%
margin
18%
23%
20%
both
14%
12%
19%
Table 20. EAD percentage of the “nothing” case.
Table 21. EAD ratio IMM/SA-CCR.
IMM/SA-CCR
Portfolio 1
Portfolio 2
Portfolio 3
nothing
77%
79%
90%
netting
91%
102%
90%
margin
61%
90%
91%
both
68%
153%
118%
Based on assets’ type, we discuss the following:
• Portfolio 1 shows that: the IMM is less demanding than the SA-CCR in all
scenarios and along with the entity of hedging techniques. This could be interpreted by several causes: the restrictive 5% floor in the multiplier of the
standardized approach or the supervisory factor of 0.5% intended to reflect
the one-year volatility of the rates and which is a bit too restrictive for our
USD case. In the case of margining and netting addition (when applying both
techniques) the IMM always amends less capital.
• Portfolio 2 reflects a different ideology. Not applying neither netting nor collateral, the IMM represents 80% of the SA-CCR EAD, adding the netting our
IMM converges away from the SA-CCR figure (such was not the case in
Portfolio 1 but here the computation of the netting sets differs in the
SA-CCR) and amends similar capital requirements. When adding the margin
agreement only, our model is less demanding by (representing only 90%).
Last step, netting and margining the portfolio would result, in a more
easy-going SA-CCR in a sort that the IMM requests the standardized capital
times 1.5. This could be interpreted by the motivation given by Basel to apply
such techniques therefore by the important reduction in the standardized
model making the IMM much more demanding.
• Portfolio 3 slightly differs from the previous portfolios due to the effect of the
optionality on the netting and margining computations: having the SA-CCR
30
M. Sayah
recommending less capital charges for optionality embedded instruments,
our internal model seems to be a bit too restrictive. No hedging implies a
90% capital charge (IMM to EAD) and applying both methods would result
in a 118%. We can deduce that for the FX options portfolio, the SA-CCR is
less demanding than our internal model and requires a lower capital charge.
Plus, we note that this is applied for the EUR-USD FX pair with an initial volatility of 13% in our internal models (increasing) whereas Basel amends a
15% volatility factor.
Based on hedging techniques applied, we discuss the following:
• When nothing is applied, our internal model is representing 80% of the
SA-CCR figures.
• Netting effects vary between portfolios depending on the composition of
each: in the IR and FX options where we net a 2.5 years by a 0.5 years’ instrument, the capital charge decreases by 10%. However, in the second portfolio the SA-CCR was less demanding (a ratio of 102%).
• The margin agreement effect was more recognized in the IR swap due to the
low fluctuations of such instruments (re-evaluated quarterly) making the
IMM equal to only 60% of the standardized figure. On another hand, in the
FX portfolios, the fluctuations were considered through the lower and higher
bonds of the margin agreement reducing more significantly the demanded
capital charge (up to 90%).
• Finally, having both effects, Basel “rewards” such techniques and reduces the
capital in a way that makes our IMM more demanding than the SA-CCR for
the FX bucket. This is expected because one motivation of this new SA-CCR
is to motivate banks to margin and net their deals.
CVA Capital Charge: In terms of ratio, Table 22 resumes the results:
For the singular portfolios, having an effective maturity of one year the ratio is
constant and equal approximately to 55% to 65% for the default counterparty
capital charge therefore doubling the capital charge for the counterparty credit
risk. For the mixed portfolios, the add-on of the CVA capital charge depends on
the effective maturity and the EAD therefore, for our considered example, the
capital charge of the CVA consists of around 55% to 58% of the total counterparty capital requirement resulting in an additional 20% to 30% on the default
capital charge amount amended in earlier version of Basel requirements.
Table 22. Capital charge ratio of total counterparty credit risk.
CVA Capital Charge
CCR netting without collateral
CVA/CCR
Singular 1
35.33%
64.67%
0.54
Singular 2
35.33%
64.67%
0.54
Singular 3
35.33%
64.67%
0.54
Portfolio 1
57.74%
42.26%
1.36
Portfolio 2
56.32%
43.67%
1.29
Portfolio 3
55.87%
44.13%
1.27
31
M. Sayah
5. Conclusions
This work permits comparison between the standardized approaches used by
Basel and suggests internal model methodology based on historical and futuristic
observations through various applications on simple portfolios. After having
demonstrated the process of each of the internal and standardize approaches, the
applications showed a convergence between these two and highlighted the conditions that allow one method to be more restrictive than the other.
CVA risk adds a large weight to the capital requirement as expected, however
its computation depends highly on the risk type that we are handling and the effective maturity of the portfolios. As for the SA-CCR, our work showed a tendency to encourage banks into hedging techniques especially margin agreements
through reducing the capital charge amended when such practices are in place.
For the interest rate swap we deduct that the model chosen is less demanding
than the Basel approach: On a first hand, when no hedging techniques is there,
the model is representative at 80% for such maturities (up to 2.5 years). When
adding netting the percentage increases to 90%; therefore the recognition of the
netting effect is much more rewarded by Basel. On the second hand, when margin agreement is in place our model requests only 60% of Basel’s capital and
when netted is added the same effect as a non-margined portfolio. This is due to
the computation of the margined portfolio capital charge in the interest rate
bucket which includes decreasing the multiplier affecting the EAD resulting in
reducing the total charge.
As for the foreign exchange assets types, we have different behaviors depending on the presence of optionality or not. When not handling optionality (in
portfolio 2 with FX forwards), the internal model under no netting neither margin agreements represents 80% of the EAD under the SA-CCR. Netting added,
the internal model diverges from the standardized approach and requires 102%
of the SA-CCR capital charge. Again, with no netting however adding a collateral the ratio increases to 90% and finally when margin and netting are there the
IMM EAD represents 150% of the SA-CCR EAD due to the benefits added in the
Basel approach in order to reward netting and margining agreements (which is
not really “rewarded” in the Internal Model).
Handling the last portfolio, FX bucket under optionality, the conclusions differ a bit: In no netting no margin environment the IMM is a bit less demanding
than the SA-CCR (by 10%) of the EAD this is due to the volatility factor
amended by Basel (15%) which does not reflect the volatility of the FX currency
we considered (going from 14% up till 17% in GARCH approach volatility).
This is permitted for the standardized approach as it tries to cover all currencies therefore could not be more indulgent in terms of amended volatility however, this might be modified a little if Basel considered assigning different volatilities for different FX currency pairs in the options types. When netting, due to
the hypothesis of daily re-margin and the specificity in computing the EAD under the SA-CCR for optionality-included instruments, the equilibrium is not
bothered and the EAD under both methods remains 90%. Applying both tech32
M. Sayah
niques, once again Basel rewards the bank and reduces its capital requirement
making the ratio of the internally amended capital charge to the standardized
one equal to 118%. Again, this is another example on how the standardized approach is rooting for the margin and netting agreements.
A model based on experts’ opinion and future market estimations, even if calibrated on stressed historically observed data, showed as a differing capital
amendment than the one demanded by Basel. Logical interpretation could be
presented and reasonable choices could be made: Basel requires a standardized
figure not accounting for the currency of the instrument should be “generalized”
whereas our internal model is calibrated to the volatility, historical jumps, future
forecasting... of a given market therefore in some cases could be more beneficial
or more restrictive than the standardized EAD figure. In this paper examples on
EUR and USD instruments clarified the common and different points of the two
possible approaches to highlight this divergence or convergence between what
banks could choose to use. In parallel, the suggested models and calibrations are
a logical “mix” between the history and the future horizons trying to create a
complete figure of the market.
The last remark would be on the CVA capital charge, Basel is encouraging
banks to pass the deals to central clearing houses: in doing so no CVA capital
charge would be amended, after seeing the huge impact of the CVA capital
charge on the total counterparty capital charge we can deduct why banks are all
converging towards clearing their portfolios through trusted clearing houses, a
question on the stability and coherent risk management of these clearing houses
remain questionable in such cases.
This work aimed to offer a detailed view of the counterparty risk capital
charge handling in the banking sector through a description and interpretation
of the standardized amended methodologies and by presenting and contrasting
an internal model that is able to reflect both historical behaviors and future expert estimations. The internal approach is mostly less demanding to banks and
reflects in a better perspective their workflow however, we should note that our
results are highly depended of the portfolios we choose and the currency we
handled. This should be noted for further works. In addition, the CVA was
tackled without considering the wrong way risk (WWR) not to make the paper
any more computationally heavy, however the WWR which is the correlation
between the exposures and the probability of default of the counterparty, this
will have an important impact on the CVA capital charge computation and in
practice should not be neglected. Our next work will incorporate this variable
into the computation in order to measure its impact on the CVA capital charge.
Acknowledgements
This work is funded as part of my PhD thesis by the National Council for Scientific Research of Lebanon (CNRS-L) and Bank Audi s.a.l. However, the information and views set out in this article are those of the author and do not reflect the
official opinion of Bank Audi.
33
M. Sayah
References
[1]
Beier, N., Harreis, H., Poppensieker, T., Sojka, D. and Thaten, M. (2010) Getting to
Grips with Counterparty Risk. Mc Kinsey Working Papers on Risk, No. 20.
[2]
Ingves, S. (2013) Regulatory Reforms for OTC Derivatives: Past, Present and Future. Banque de France, Financial Stability Review, No. 17, 19-28.
[3]
Basel Committee on Banking Supervision (BCBS) (2010) Basel III: A Global Regulatory Framework for More Resilient Banks and Banking Systems.
[4]
CRDIV Framework, 2014, Credit Valuation Adjustment (CVA).
[5]
Basel Committee on Banking Supervision (BCBS) (2014) The Standardized Approach for Measuring Counterparty Credit Risk Exposures.
[6]
FEI A. (2014) Overview of Basel Committees Standardized Approach for Measuring
Derivatives Exposure.
[7]
Basel Committee on Banking Supervision (BCBS) (2014) Foundations of the Standardized Approach for Measuring Counterparty Credit Risk.
[8]
Basel Committee on Banking Supervision (BCBS) (2016) Reducing Variation in
Credit Risk-Weighted Assets: Constraints on the Use of Internal Model Approaches. Consultative Document, March 2016.
[9]
Pykhtin, M. and Zhu, S. (2007) A Guide to Modelling Counterparty Credit Risk.
Global Association of Risk Professionals, July/August 2007 Issue.
[10] Basel Committee on Banking Supervision (2015) Regulatory Consistency Assessment Program, Report on Risk-Weighted Assets for Counterparty Credit Risk.
[11] Gregory, J. (2015) Linking FRTB with CVA Capital. WBS FRTB Conference, London.
[12] Basel Committee on Banking Supervision (BCBS) (2015) Review of the Credit Valuation Adjustment Risk Framework. Consultative Document.
[13] Basel Committee on Banking Supervision, 2016, Instructions: CVA QIS.
[14] Basel Statistical Release (BIS) (2015) OTC Derivatives Statistics at End-June 2015.
Monetary and Economic Department, Basel.
[15] Nielsen, L. (1993) Understanding N (d1) and N (d2): Risk-Adjusted Probabilities in
the Black-Scholes Model. Finance, 14, 95-106.
[16] FOMC (2015) Federal Open Market Committee Economic Projections for December 2015. www.federalreserve.gov
[17] Planchet, F. and Karam, E. (2013) Estimation Errors and SCR Calculation. Bulletin
Français d’Actuariat, 13, 79-92.
[18] ISDA (2013) International Swaps and Derivatives Association, Standard Initial
Margin Model for Non-Cleared Derivatives.
34
M. Sayah
Appendix
Appendix 1: Supervisory Duration
In the Basel document, one component for determining the EAD of an interest
rate class instrument is the supervisory duration. In this computation we aim to
understand the hypothesis lying behind the choice of such factor.
The given formula is the following:
SD =
e −0.05 S − e −0.05 E
0.05
If we consider a bond with a starting date S and an ending date E , paying
coupons of rate α and having a yield to maturity YTM equal to α ; the valuation of this bond's duration in a continuous fashion will result in the following:
E −S
−α ( E − S )
∫ 0 α te dt + ( E − S ) e
=
Duration
E −S
−α ( E − S )
−α t
∫ 0 α e dt + e
−α t
× e −α S
Using an integration by parts process, the previous equation results in the following:
E −S
Duration =
−α t
 −te  0
− e −α t 
E −S
0
( − ( E − S ) e ( ) ) − α1 ( −e
−α E − S
Duration =
E −S
+ ∫ 0 eα t dt + ( E − S ) e
−α 0
+e
−α ( E − S )
−α ( E − S )
+e
−α ( E − S )
) + (E − S)e ( )
−α E − S
α eα S
Duration =
1− e
−α ( E − S )
α eα S
eα S − e −α E
Duration =
α
Replacing the α factor by 0.05 or 5% we obtain the supervisory duration
in Equation (3).
The duration is an indication of the instrument’s maturity because the maturity
is capped at one year, therefore the necessity of the incorporation of that factor.
Appendix 2: Data Used
Figure S1. Historical Euro swap rates for 1 m, 6 m, 1 y and 5 y.
35
M. Sayah
Figure S2. Historical USD swap rates for 1 m, 6 m, 1 y and 5 y.
Figure S3. Historical FX spot rate.
Appendix 3: Vasicek Model Implementation
The work on Vasicek model was based on the paper by Planchet and Karam
(2013):
Vasicek discretization formula:
(
)
rt +δ = rt e − kδ + θ 1 − e− kδ + σ
1 − e −2 kδ
k Estimating the parameters:
2k
( )
1
kˆ = − ln βˆ
δ
n∑ ri ri −1 −=
∑ i 1r=
i ∑ i 1ri −1
n
n
βˆ = =i 1
n
(
n∑ r − ∑ r
n 2
n
i −1
i 1 i −1
=i 1 =
(
(
n
∑ i=1 ri − βˆ ri−1
ˆ
θ=
n 1 − βˆ
36
)
)
)
2
M. Sayah
σˆ =
λ=
(
)
2
1 n 
r − βˆ ri −1 − θˆ 1 − βˆ 
∑
i =1  i

n
1 − e −2 kδ
2k

 σ 2


B ( 0, T ) + r0  B ( 0, T ) + ln ( P ( 0, T ) )  


2
σ    4k


 k
  θ − 2k 2  − 


−
B
T
T
0,
( )
 

 






σ
And getting the yield we apply the following:
R (t, T ) = −
ln ( P ( t , T ) )
T −t
P ( t , T ) = A ( t , T ) e{
− B( t ,T )r ( t )}

σλ σ 2 
σ2
2
A (t,=
T ) exp[ θ −
B (t, T )
− 2  ( B ( t , T ) − (T − t ) ) −
k
4k
2k 

B (t, T ) =
1− e
− k ( T −t )
k
Appendix 4: GARCH Model Parameters
Garch(1, 1) normal conditions:
Figure S4. GARCH for EUR/USD FX on the normal market conditions.
37
M. Sayah
Garch(1, 1) stressed conditions:
Figure S5. GARCH for EUR/USD FX on the stressed market conditions.
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38
DEGREE PROJECT IN MATHEMATICS,
SECOND CYCLE, 30 CREDITS
STOCKHOLM, SWEDEN 2019
Efficient Monte Carlo Simulation
for Counterparty Credit Risk
Modeling
SAM JOHANSSON
KTH ROYAL INSTITUTE OF TECHNOLOGY
SCHOOL OF ENGINEERING SCIENCES
Abstract
In this paper, Monte Carlo simulation for CCR (Counterparty Credit Risk) modeling is investigated. A jump-diffusion model, Bates’ model, is used to describe the price process of an
asset, and the counterparty default probability is described by a stochastic intensity model
with constant intensity. In combination with Monte Carlo simulation, the variance reduction
technique importance sampling is used in an attempt to make the simulations more efficient.
Importance sampling is used for simulation of both the asset price and, for CVA (Credit Valuation Adjustment) estimation, the default time. CVA is simulated for both European and
Bermudan options. It is shown that a significant variance reduction can be achieved by utilizing
importance sampling for asset price simulations. It is also shown that a significant variance
reduction for CVA simulation can be achieved for counterparties with small default probabilities by employing importance sampling for the default times. This holds for both European
and Bermudan options. Furthermore, the regression based method least squares Monte Carlo
is used to estimate the price of a Bermudan option, resulting in CVA estimates that lie within
an interval of feasible values. Finally, some topics of further research are suggested.
Keywords: CCR, OTC derivatives, European option, Bermudan option, CVA, jump-diffusion
model, stochastic intensity model, Monte Carlo, variance reduction, importance sampling, least
squares Monte Carlo
Contents
List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
III
IV
1 Introduction
1.1 Counterparty Credit Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Credit Valuation Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Purpose and Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1
1
2
2 Mathematical Background
2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Financial Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
4
11
3 Monte Carlo Pricing
3.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Least Squares Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Credit Valuation Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
13
14
15
4 Method and Models
4.1 Asset Price Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Default Time Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Price Process Importance Sampling . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 CVA and Default Time Importance Sampling . . . . . . . . . . . . . . . . . . .
4.5 Parameter Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
16
17
17
18
19
20
21
25
5 Results
5.1 Asset Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 CVA for a European Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 CVA for a European Option under a new Measure . . . . . . . . . . . . . . . .
5.4 CVA for a Bermudan Option . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 CVA for a Bermudan Option under a new Measure . . . . . . . . . . . . . . . .
27
27
30
32
33
36
6 Discussion and Conclusions
38
Bibliography
41
I
Chapter 1
Introduction
1.1
Counterparty Credit Risk
Operating in the financial markets is associated with risk. There are several different kinds of
financial risk, and they are connected to each other in different ways. This article focuses on
CCR (Counterparty Credit Risk). CCR is the risk of a counterparty defaulting before fulfilling
its contractual commitments. CCR is mainly related to both market risk and credit risk. These
can be described as follows:
Market risk is the risk associated with price movements that are affecting the performance of
the whole market. Market risk often arises from movements in underlying variables affecting
the prices of instruments, such as interest rates, foreign exchange rates, credit spreads and market volatility. Credit risk is the risk of losses arising from the possibility that a counterparty
might be unable to fulfill its contractual obligations. Associated with credit risk are both the
default of a counterparty and deterioration of a counterparty’s credit quality.
To handle CCR is a difficult task. It requires an understanding of both market risk and credit
risk, as well as the interactions between the two. Additionally, when dealing with CCR, one
must often deal with complex financial instruments. In particular, OTC derivatives are often
involved in CCR [1].
In recent times, CCR has been given increased attention. During the 2007-2009 financial crisis, banks suffered substantial CCR lossses on their OTC derivatives portfolios. Thus it was
evidenced at the time, that the regulations and practices for mitigating CCR were insufficient. Since then, efforts have been made to improve both regulations governing CCR and the
practices of banks related to CCR [2].
1.2
Credit Valuation Adjustment
Closely related to CCR is CVA (Credit Valuation Adjustment), which is defined as the market
value of the CCR losses incurred by a portfolio [3].
In connection with the larger focus placed on CCR after the 2007-2009 financial crisis, the
need for an increased use of CVA also came to light. At the time of the crisis, many firms were
1
CHAPTER 1. INTRODUCTION
operating under the Basel II framework. The conditions of this framework required the firms
to capitalise for default risk and migration risk. Therefore, the CCR management of firms were
mostly designed to protect them against losses incurred from defaults. However, the majority
of the losses banks suffered on their OTC derivatives portfolios during the crisis were not from
counterparty defaults, but from fair value adjustments on the derivatives. To account for the
large proportion of losses being due to CVA changes, regulations governing CVA have since
been created. Notably, the Basel III framework released in 2010 included a capital requirement
for CVA that must be calculated by banks operating under the framework [2].
As the banks themselves are responsible for calculating the CVA capital charge, it is common
for them to have desks set up solely for this purpose. While the banks are required to calculate
CVA once a month under the Basel III framework, some of them calculate it as frequently
as every day. It is common for the CVA calculations to involve large portfolios of complex
instruments, and they are therefore often carried out through Monte Carlo simulations. Consequently, these calculations are often very computationally expensive [4].
In general, CVA depends on several correlated market factors. These factors are dependent on
the portfolio, and could for instance be stock price, interest rate, volatility or default times.
A common approach to calculating CVA is to simulate the market factors over a discretized
time interval and use the simulated quantities to obtain a Monte Carlo estimate of CVA. In
order to conduct these simulations, model assumptions have to be made with regard to the
market factors. Usually, a market factor is assigned a probability distribution at each point of
calculation or its movement is assumed to be described by a stochastic process [5].
1.3
Purpose and Aim
Monte Carlo simulations are of large importance to CCR modeling in general as well as CVA
calculations in particular, with the objective being to achieve the desired accuracy while minimizing the computational time or the computational load. In order to achieve this objective,
several attempts have been made to improve Monte Carlo simulation techniques within CCR
modeling. For example, Glasserman and Li utilized the importance sampling technique for
Monte Carlo simulations to decrease the variance when simulating rare events of large losses
[6], and Antonov et.al. proposed a method of quickly calculating the portfolio exposure in order to speed up CVA calculations in a setting where the portfolio is priced using Monte Carlo
simulation [7].
For Monte Carlo simulations, the relative error ên is related to the sample standard deviation
Sn and the number of scenarios (or paths) n in the following way.
Sn
ên ∝ √ .
n
(1.1)
An efficient simulation method will have a small relative error. To decrease the relative error,
either the sample standard deviation (or equivalently the sample variance) must be decreased
or the number of paths must be increased. As an increase in the number of paths results in
both an increased computational time and an increased computational load, it is preferred
to reduce the variance. There exist several different variance reduction techniques that can
2
CHAPTER 1. INTRODUCTION
be used in the Monte Carlo setting. This paper focuses on the technique called importance
sampling. The idea behind importance sampling is to change the measure under which the
sampling is performed and adjust the resulting Monte Carlo estimate to account for the change
of measure. This paper also discusses the implementation of a regression based Monte Carlo
method, called least squares Monte Carlo, for the pricing of Bermudan options. The method
is later used to calculate CVA for Bermudan options.
The objectives of the paper are to investigate:
- How to decrease the variance of asset price simulation.
- How to estimate the price of a Bermudan option using regression based Monte Carlo
simulation.
- How to decrease the variance of CVA simulation for European and Bermudan options.
3
Chapter 2
Mathematical Background
This section presents the mathematical concepts that lay the foundation of the work performed
in the paper. If not stated otherwise, a probability space (Ω, F, Q) is assumed, where Q is a
risk neutral measure. Moreover, for any given stochastic process X, Xt is used to denote X(t).
2.1
Preliminaries
2.1.1
Wiener Process
The Wiener process is a continuous time stochastic process that can be seen as a generalization
of the random walk to continuous time, as the Wiener process is the limit of a random walk
when the size of the time increment approaches zero. In mathematical finance, the Wiener
process is often used to model the randomness of price processes. The Wiener process is
defined as follows:
Definition 2.1 A stochastic process W = {Wt | t ⩾ 0} is a Wiener process if the following
conditions hold.
1) W0 = 0
2) The sample paths t 7→ Wt are almost surely continuous.
3) {Wt | t ⩾ 0} has stationary and independent increments
4) Wt − Ws ∈ N (0, t − s) for t > s.
2.1.2
Poisson Process
To describe jumps in quantities related to financial mathematics, Poisson processes are often
used. A Poisson process is a stochastic point process that only takes non negative values and
is increasing. The value of a Poisson process at time t can be interpreted as the number of
occurances of some event on the time interval (0, t]. A Poisson process is defined as follows.
Definition 2.2 A stochastic process N = {Nt | t ⩾ 0} is a Poisson process if the following
conditions hold.
4
CHAPTER 2. MATHEMATICAL BACKGROUND
1) N0 = 0.
2) The increments Ntk − Ntk−1 are independent stochastic variables for
1 ⩽ k ⩽ n, 0 ⩽ t0 ⩽ t1 ⩽ · · · ⩽ tn−1 ⩽ tn and all n.
3) Nt − Ns ∈ Po(λ(t − s)) for t > s.
Furthermore, the times between jumps in a Poisson process are exponentially distributed with
rate parameter λ.
From the definition of a Poisson process, it follows that its mean is given by
E[Nt ] = λt.
(2.1)
A zero mean process called a compensated Poisson process can be constructed from a Poisson
process. A compensated Poisson process is defined as follows.
Definition 2.3 Let N = {Nt | t ⩾ 0} be a Poisson process. Then the stochastic process
process N̂ = {N̂t | t ⩾ 0}, where
N̂t = Nt − λt, t ⩾ 0,
is a compensated Poisson process.
The compensated Poisson process has the desirable property of being a martingale with respect
to its own filtration (Ft )t⩾0 .
2.1.3
Compound Poisson Process
The Poisson process has limited modeling capabilities in financial mathematics, as its jumps
are constant in size. For the purpose of modeling jumps that are random in size, a compound
Poisson process can be used. The compound Poisson process is defined as follows.
Definition 2.4 Let (Zk )k⩾1 denote an i.i.d. sequence of square-integrable random variables
and let N = {Nt | t ⩾ 0} be a Poisson process independent of the sequence (Zk )k⩾1 . Then the
process M = {Mt | t ⩾ 0}, where
Mt =
Nt
X
Zk , t ⩾ 0,
k=1
is a compound Poisson process.
The compound Poisson process has independent incremets Mtk − Mtk−1 , and its mean is given
by
E[Mt ] = λtE[Z1 ].
(2.2)
Similarly to the case with the compensated Poisson process, the compensated compound Poisson
process can be constructed using the compound Poisson process. The compensated compound
Poisson process is defined by
5
CHAPTER 2. MATHEMATICAL BACKGROUND
M̂ = {M̂t | t ⩾ 0},
where M̂t = Mt − λtE[Z1 ].
(2.3)
The compensated compound Poisson process is a martingale with respect to its own filtration.
2.1.4
Markov Processes
Markov Processes are a family of stochastic processes that are characterized by the future state
only depending on the present state. This property is called the Markov property. Formally, a
Markov process has the following definition.
Definition 2.5 A continuous time process X = {Xt | t > 0} is a Markov process on the state
space S if for any t ⩾ 0, ∆t ⩾ 0 and x ∈ S
P[Xt+∆t ⩽ x | Xs , s ⩽ t] = P[Xt+∆t ⩽ x | Xt ].
Markov processes are especially useful for the purpose of simulations, as the Markov property
allows for computationally efficient simulations.
2.1.5
Jump-Diffusion Processes
Jump-diffusion processes are used in mathematical finance to describe both the randomness and
the jumps of a price process. In general, a jump-diffusion process utilizes both a Wiener process
and a compound Poisson process, in addition to a drift component, to describe the dynamics
of the process. In the general case, a one-dimensional jump-diffusion process X = {Xt | t ⩾ 0}
can be described by the following SDE.
dXt = a(Xt , t)dt + b(Xt , t)dWt + c(Xt , Z, t)dN̂t ,
(2.4)
where Wt is a Wiener process and N̂t is a compensated Poisson process.
A process Yt on the form
dXt = a(Yt , t)dt + b(Yt , t)dWt ,
(2.5)
is called a diffusion-process.
From equations 2.4 and 2.5, it is apparent that jump-diffusion processes and diffusion processes in the general case are Markov processes. Therefore, these processes are well suited for
computationally heavy simulations.
2.1.6
Radon-Nikodym Derivative
In finance, it is often desirable to change from one probability measure to another. For example,
one may want to change from the risk neutral measure to the historical measure. The RadonNikodym derivative expresses a relation between two measures. Let (Ω, F, P) be a probability
space and let Z be a non-negative Borel function. Then, it holds that
6
CHAPTER 2. MATHEMATICAL BACKGROUND
Z
A∈F
Z(ω) dP(ω),
P̃(A) =
(2.6)
A
is a measure satisfying
P(A) = 0
⇒
P̃(A) = 0.
(2.7)
This is expressed as P̃ being absolutely continuous with regard to P and is written as P̃ P.
Furthermore, if EP [Z] = 1 then P̃(A) is a probability measure. The variable Z is called the
Radon-Nikodym derivative and is defined as follows.
Definition 2.6 Let P and P̃ be two measures on (Ω, F) and P σ-finite. If P̃ P, then there
exists a non-negative Borel function Z on Ω such that
Z
Z(ω) dP(ω), A ∈ F.
P̃(A) =
A
Furthermore, Z is almost everywhere unique. The function Z is called the Radon-Nikodym
derivative of P̃ with regard to P and is denoted by ddPP̃ .
2.1.7
The Girsanov Theorem
The Girsanov theorem describes the change in behaviour of stochastic processes when there is
a change of measure. For diffusion processes, an additional theorem called Novikov’s condition
is useful. Novikov’s condition is given by the following.
Theorem 2.1 Let Wt be a Wiener process defined on the filtered probability space (Ω, Ft , P, (Ft )t∈[0,∞] )
and let θt , t ⩾ 0 be an adapted process. Define
Z t
Z t
θs dWs −
Zt = exp
0
θs2 ds
.
0
Then, if for each t ⩾ 0
Z t
1
2
E exp
θ dWs
< ∞,
2 0 s
P
then for each t ⩾ 0
EP [Zt ] = 1.
If this is the case, then the process (Zt )t⩾0 is a positive martingale.
Novikov’s condition can be utilized to state Girsanov’s theorem for diffusion processes, which
is given below.
Theorem 2.2 Let Wt be Wiener process defined on the filtered probability space (Ω, Ft , P, (Ft )t∈[0,T ] )
and let θt , t ⩾ 0 an adapted process. Define
7
CHAPTER 2. MATHEMATICAL BACKGROUND
Z t
Z t
θs dWs −
Zt = exp
θs2 ds
,
(2.8)
0
0
Z t
W̃t = Wt −
θs ds.
(2.9)
0
If θt , t ⩾ 0 fulfills Novikov’s condition, then the stochastic process (W̃t )0⩽t⩽T is a Wiener
process under the probability measure P̃ given by
Z
Z(ω) dP(ω), A ∈ F.
P̃(A) =
A
2.1.8
Monte Carlo Estimators
In the Monte Carlo simulation framework, a large number of simulations of a quantity are
made in order to obtain an estimate of that quantity. Suppose that X is a random variable
and that E[f (X)] is to be estimated. The standard Monte Carlo estimatior of E[f (X)] is given
by the sample average of n independently simulated copies of f (x).
n
1X
µn =
f (Xi ).
n
(2.10)
i=1
By the law of large numbers, the standard Monte Carlo estimator µn will converge to E[f (X)]
as n → ∞. By the central limit theorem, it holds that
√
n(µn − E[f (X)])
→ N (0, 1),
(2.11)
σ
where σ 2 = Var[f (X)]. An unbiased estimate of σ is given by the sample standard deviation
Sn ,
n
Sn2 =
1 X
(f (Xi ) − µn )2 .
n−1
(2.12)
i=1
From equations 2.10, 2.11 and 2.12, an expression of a confidence interval of E[f (X)] can be
obtained. Given significance level p, the confidence interval is given by
Sn −1
Sn −1
µn − √ Φ (1 − p/2), µn + √ Φ (1 − p/2) .
(2.13)
n
n
One measure of the performance of a Monte Carlo estimator µn is the relative error ên , which
is defined as
ên =
Sn
√ .
µn n
8
(2.14)
CHAPTER 2. MATHEMATICAL BACKGROUND
2.1.9
Importance Sampling
The confidence interval of E[f (X)], as well as the relative error, can be made smaller by increasing the sample size or by reducing the sample standard deviation (or equivalently reducing
the sample variance). To reduce the computational load, it is therefore desirable to reduce the
sample standard deviation. This can be achieved through several different variance reduction
techniques. In this paper, the variance reduction technique called importance sampling is considered.
The idea behind importance sampling is to change the probability measure that is sampled
under in order to achieve a smaller variance. Consider the continuous random variable X, the
function f (X) and two different probability measures P and P̃. The following holds for the
expected value of f (X).
Z
Z
dP
dP
P
P̃
E [f (X)] =
f (X) dP =
f (X)
dP̃ = E f (x)
.
(2.15)
dP̃
dP̃
Ω
Ω
The Monte Carlo estimator when using importance sampling can be formulated as
n
1X
dP
µn =
f (Xi ) (Xi ),
n
dP̃
(2.16)
i=1
where (Xi )1⩽i⩽n are sampled under P̃. The variance of the estimator is given by
"
2 # dP
dP 2
2 dP
P̃
P̃
P̃
Var f (X)
= E f (X)
− E f (X)
dP̃
dP̃
dP̃
2
dP
= EP f (X)2
− EP [f (X)] .
dP̃
In order to minimize the variance, the change of measure should be chosen so that
dP
EP [f (X)]
=
.
f (X)
dP̃
(2.17)
(2.18)
This is however impossible, as EP [f (X)] is the quantity that is to be estimated. Thus, alternative methods must be used in order to find changes of measure that are close to optimal.
The change of measure is however not always derived with the explicit goal of minimizing the
variance. Depending on the application, importance sampling can be used to give the new
probability measure desirable properties that in turn lead to a reduced variance. For example,
in the context of mathematical finance, importance sampling can be used to increase the probability of a rare event occurring or to drive the value of a process up or down.
To perform Monte Carlo simulations without any variance reduction techniques is often referred
to as naive Monte Carlo simulation.
2.1.10
Importance Sampling for Diffusion Processes
One method of finding a close to optimal change of measure for diffusion processes is outlined
by Nykvist [8]. The aim of the method is to find a close to optimal parameter θ for the change
of measure given by Girsanov’s theorem,
9
CHAPTER 2. MATHEMATICAL BACKGROUND
dP̃
= exp
dP
Z t
Z t
θs dWs −
0
θs2 ds
.
(2.19)
0
Consider a general diffusion process, with dynamics given by
dXt = a(Xt )dt + b(Xt )dWt ,
(2.20)
X0 = x0 .
(2.21)
The dynamics of the process are obtained by inserting 2.9 into 2.20.
dXt = (a(Xt ) + b(Xt )θ(Xt , t))dt + b(Xt )dW̃t ,
(2.22)
X0 = x0 .
(2.23)
The method involves constructing classical subsolutions to a Hamilton-Jacobi type of PDE.
The solutions are constructed from the Mané potential. With c, x, y ∈ R, the Mané potential
at level c is given by
Z τ n
S (x, y) = inf
c + L(ψ(s), ψ̇(s)) ds, ψ ∈ AC([0, ∞); R ), ψ(0) = x, ψ(τ ) = y, τ > 0 ,
c
(2.24)
t
where AC is the set of all absolutely continuous functions ψ : [0, T ] 7→ R and L is the local rate
function given by
2
1 −1
b (x)(v − a(x)) .
(2.25)
2
If the Mané potential is finite, a viscosity sub-solution to the stationary Hamilton-Jacobi equation
L(x, v) =
H(y, ∇S c (x, y)) = c,
y∈R
(2.26)
is given by
y 7→ S c (x, y).
(2.27)
An asymptotically optimal change of measure is given by the Radon-Nikodym derivative with
parameter
θ(t, x) = b(x)∇S c (x0 , x).
(2.28)
The Hamiltonian associated with the process 2.20 is given by
1
H(x, p) = a(x)∇S c (x0 , x) + (σ(x)∇S c (x0 , x))2 .
2
The stationary Hamilton-Jacobi equation 2.26 then becomes
1
a(x)∇S c (x0 , x) + (σ(x)∇S c (x0 , x))2 = c.
2
This equation has the solution
10
(2.29)
(2.30)
CHAPTER 2. MATHEMATICAL BACKGROUND
a(x)
∇S (x0 , x) = −
±
b(x)2
c
p
a(x)2 + 2cb(x)2
,
b(x)2
x 6= x0 .
(2.31)
From equation 2.28, it follows that an asymptotically optimal change of measure is given by
the Radon-Nikodym derivative with parameter
p
a(x)2 + 2cb(x)2
a(x)
±
, x 6= x0 .
(2.32)
θ(t, x) = −
b(x)
b(x)
2.2
Financial Pricing
2.2.1
Types of Options
The most common types of options are European and American options. A European option
gives the buyer the right to exercise the option at the expiration date, while an American
option gives the buyer the right to exercise the option at the expiration date as well as any
date between acquiring the option and the expiration date. European and American options
have the same payoff function, which is given by
Payoff = max(S − K, 0),
for call options,
(2.33)
Payoff = max(K − S, 0),
for put options,
(2.34)
where S is the spot price of the underlying asset and K is the strike price. While there exist
formulas for pricing European options, it is considerably harder to price American options.
This is because the possibility of early exercise has to be taken into account at each date.
American options are in general priced higher than European options because the buyer of an
American option has the additional right of early exercise.
Options with other exercise rights or payoff structures are called exotic options. There exist
many types of exotic options, but in this paper only Bermudan options are considered. Bermudan options have the same payoff function as American and European options, but give the
buyer the right to exercise the option only at certain specified dates. The American option
can therefore be seen as a specific case of the Bermudan option, where all dates are eligible for
early exercise.
2.2.2
Credit Valuation Adjustment
Assume a complete and arbitrage-free market. Let (Ω, Ft , Q) be a filtered probability space.
Ft is the filtration modeling market information up to time t and Q is the risk neutral measure.
From here on, E[· | Ft ] is denoted by Et [·].
Suppose a portfolio is held at time t and consists of OTC derivative contracts with a common
expiration time T . Also suppose that the counterparty has a risk of defaulting and that τ is the
stochastic default time of the counterparty. In this paper, only unilateral CVA is considered,
meaning that the investor is assumed to have default probability zero. As previously mentioned,
11
CHAPTER 2. MATHEMATICAL BACKGROUND
CVA is the market value of the CCR losses incurred by a portfolio. Using this definition, CVA
can be rewritten as
CVAt = EQ
t [1{τ ⩽ T }Lτ D(t, τ )],
(2.35)
where Lτ is the portfolio exposure at time τ and D(t, τ ) is the discount factor, based on the
risk free rate, between times t and τ .
To be able to calculate CVA, it is required to calculate the exposure of the portfolio. For OTC
derivatives, the exposure depends on the value of the contract. If the value of the contract is
positive from the investor’s perspective and the counterparty defaults, the investor will only
receive a fraction R of the agreed upon payments. On the other hand, if the value of the
contract is negative from the investor’s perspective and the counterparty defaults, the investor
is still obliged to pay the full amount on the remaining payment. Thus, given N different
contracts in the portfolio, no netting agreements and no margin agreements, the exposure of
the portfolio at time t is given by
Lt = (1 − R)
N
X
max Vti , 0 ,
(2.36)
i=1
where Vti is the value of derivative contract i at time t. In this paper, it is assumed that R = 0.
The exposure of the portfolio at time t is then given by
Lt =
N
X
max Vti , 0 .
(2.37)
i=1
Furthermore, assuming that default probability, credit exposure and discount rate are independent of each other, the expression 2.35 can be rewritten in the following way.
CVAt = EQ
t [1{τ ⩽ T }Lτ D(t, τ )] =
Z T
t
EQ
t [Ls ]D(t, s) dP (s),
where P is the distribution of τ .
Henceforth, if nothing else is specified, CVA refers to CVA0 .
12
(2.38)
Chapter 3
Monte Carlo Pricing
3.1
Options
In the Monte Carlo setting, options are generally priced by discretizing the time interval until
expiration and then completing the following steps.
• Simulate a large number of paths for the price of the underlying asset.
• Calculate the option value at each time point for each path.
• Obtain the Monte Carlo estimate of the option value using the simulated option values,
i.e.
n
1X i
V̂t =
Vt ,
n
(3.1)
i=1
where Vti is the value of the option for path i at time t.
It is the second step of the procedure that varies when pricing different types of options. For
European options, it is straightforward to calculate the option value. At expiration, the payoff
is known. The values at remaining times are acquired by discounting the payoff at expiration.
Assume a discretized time interval t1 , . . . , tm , where tm = T . For a European call option, the
option values of path i are given by
VTi = max(STi − K, 0)
Vtij = Dtj ,T VTi ,
j = 1, . . . , m − 1,
(3.2)
where STi is the asset spot price for path i at time T and Dtj ,T is the discount factor between
times tj and T . In order to pathwise obtain the values of a European put option, the payoff
function of a European put option is instead used.
When evaluating an American option in the Monte Carlo setting, the time discretization only
allows for a finite number of exercise dates. This gives an error when calculating the value of
an American option. It also means that an American option is treated as a Bermudan option
when performing Monte Carlo simulations. The values of a Bermudan call option for path i
are obtained in the following way.
13
CHAPTER 3. MONTE CARLO PRICING
•
VTi = max(STi − K, 0)
•
for j = m − 1, . . . , 1
Vtij = max(Stij − K, Ctij ),
Vtij = Dtj ,tj+1 Vtij+1 ,
if tj is an early exercise date,
(3.3)
else,
where Ctij is the value of the option at path i conditional on not exercising at time tj . Ctij is
called the continuation value at time tj and path i. A possible way to calculate the continuation
value is to for each path set the continuation value at time tj and path i to
Ctij = Dtj ,tj+1 Vtij+1 .
(3.4)
This approach, however, uses future market information to assess the continuation value and
determine the optimal exercise strategy, and will therefore overestimate the option value. There
are several approaches to estimating the continuation value in the Monte Carlo setting. One
of these is to use regression based Monte Carlo methods [9].
3.2
Least Squares Monte Carlo
Least Squares Monte Carlo is a method for valuation of American and Bermudan options that
was first introduced by Longstaff and Schwartz [10]. Least squares Monte Carlo estimates by
regression the continuation value of an option.
Let (Ω, Ft , Q) be a filtered probability space. Ft is the filtration modeling market information
up to time t and Q is the risk neutral measure. Let F (ω, s; t, T ) denote the cash flow of the
option conditional on the option not being exercised prior to time t and the optimal exercise
strategy being followed between times t and s. Here, t < s ⩽ T . Let tm = T . The continuation
value at time tk is given by


m
X

Dtk ,tj F (ω, tj ; tk , T ) .
C(ω; tk ) = EQ
(3.5)
tk
j=k+1
To implement the least squares Monte Carlo method, C(ω; tm−1 ) is estimated by least squares
regression of the discounted values of F (ω, tm ; tk , T ) onto a basis Φtm−1 consisting of functions
of the underlying asset’s price at time tm−1 . The option value at time tm−1 can then be estimated by taking the maximum of the immediate exercise value at time tm−1 and the estimated
continuation value. Then C(ω; tm−2 ) is estimated by least squares regression of the discounted
values of F (ω, tm−1 ; tk , T ) onto the basis Φtm−2 , and the option value at tm−2 is estimated by
taking the maximum of the immediate exercise value at time tm−2 and the estimated continuation value. By recursion, the option value can be estimated at each time point until t1 . Only
in the money paths are used for the regression, as out of the money paths will never be exercised.
In a Monte Carlo setting with n paths and m time points, the least squares Monte Carlo
method is implemented by the following. Let Ctij denote the continuation value for path i at
time tj conditional on the estimated option value Vtij+1 at time tj+1 and path i, given by
14
CHAPTER 3. MONTE CARLO PRICING
Ctij = Dtj ,tj+1 Vtij+1 .
(3.6)
Let Ĉtij denote the estimated continuation value of path i at time tj . Furthermore, let
{φ1 (·), . . . φM (·)} denote the basis functions used for regression and Stij the spot price of the
underlying asset at path i and time tj . The estimated continuation value for an in the money
path i at time tj is given by
Ĉtij =
M
X
β̂k φk (Stij ),
(3.7)
k=1
where β̂ is given by
0
β̂ = min
n
X
β∈RM
Ctlj −
l=1
M
X
!2
βk φk (Stlj )
,
(3.8)
k=1
and l = 1, . . . , n0 denote the indices of the in the money paths. The values of a Bermudan call
option at path i are estimated in the following way.
•
VTi = max(STi − K, 0)
•
for j = m − 1, . . . , 1
Vtij = max(Stij − K, Ĉtij ),
Vtij = Dtj ,tj+1 Vtij+1 ,
if tj is an early exercise date and Stij > K,
(3.9)
else.
Bermudan put options are valued by using the payoff function of a put option and the criteria
Stij < K for determining whether path i is in the money at time tj .
3.3
Credit Valuation Adjustment
When constructing a Monte Carlo estimator of CVA it is utilized that CVAt can be expressed
in the following way
CVAt = EQ
t [f (L, τ )],
(3.10)
f (L, τ ) = 1{τ ⩽ T }Lτ Dt,τ .
(3.11)
where
Thus, a Monte Carlo estimator of CVAt can be constructed as follows
[t = 1
CVA
n
n
X
i=1
n
f (Li , τ i ) =
1X
1{τ i ⩽ T }Liτ Dt,τ i .
n
(3.12)
i=1
To obtain this Monte Carlo estimator, the default time as well as the portfolio exposure must
be pathwise simulated.
15
Chapter 4
Method and Models
4.1
Asset Price Model
Within mathematical finance, there exist several different formulations of jump-diffusion processes. Most of these are based on Merton’s model [11]. Merton’s model is described by the
SDE
dXt
= µdt + σdWt + M̂t ,
Xt
(4.1)
where M̂ = {M̂t | t ⩾ 0} is a compensated compound Poisson process with the jumps being
described by the random variable (Jt − 1)t⩾t1 , where (Jt )t⩾t1 are i.i.d. log-normal distributed
random variables. µ is the instantaneous expected return on Xt and σ is the volatility of Xt .
In Merton’s model, both µ and σ are constant. A common way to present the SDE of Merton’s
model is to move the compensation of the Poisson process into the drift. Equation 4.1 then
becomes
dXt
= (µ − λs E[Jt1 − 1])dt + σdWt + (Jt − 1)dNt .
Xt
(4.2)
Here, N = {Nt | t ⩾ 0} is a Poisson process with intensity λs . Extensions of Merton’s model
exist, where for example stochastic volatility is used or a different jump size distribution is
considered. One of these extensions is Bates’ model [12]. Bates’ model has stochastic volatility,
but is otherwise equivalent to Merton’s model. The SDE of Bates’ model can be written as
follows.
p
dXt
= (µ − λs E[Jt1 − 1])dt + Vt dWt + (Jt − 1)dNt ,
Xt
p
dVt = κ(θ − Vt )dt + σv Vt dWt0 ,
(4.3)
corr(Wt , Wt0 ) = ρdt,
where Vt is the variance of the diffusion component of Xt at time t, σv is the volatility of Vt and
W 0 = {Wt0 | t ⩾ 0} is a Wiener process. V = {Vt | t ⩾ 0} follows a mean reverting process with
drift θ and mean reversion rate κ. (Jt )t⩾t1 are i.i.d. log-normal distributed random variables.
In this paper, Bates’ model with uncorrelated Wiener processes are used. Thus, the model
given in equation 4.3 becomes
16
CHAPTER 4. METHOD AND MODELS
p
dXt
= (µ − λs E[Jt1 − 1])dt + Vt dWt + (Jt − 1)dNt ,
Xt
p
dVt = κ(θ − Vt )dt + σv Vt dWt0 ,
(4.4)
where Wt0 is an independent copy of Wt .
4.2
Default Time Model
A common family of models for counterparty default is the family of stochastic intensity models.
A stochastic intensity model is characterized by the stochastic intensity process
λτt ,
λτt ⩾ 0 for all t ⩾ 0.
(4.5)
Under a stochastic intensity model, the probability of default is given by
Z t
τ
λu du .
P(τ ⩽ t) = 1 − exp −
(4.6)
0
From equation 4.6, it is evident that the default probability is an increasing function of the
default intensity λτ .
For further reading on how stochastic intensity models can be used for CVA calculations, see
for example the works of Crépey and Rahal [13], or Brigo and Vrins [14].
In this paper, a constant default intensity λτ is used. The expression of the default probability
in equation 4.6 can then be simplified to
τ
P(τ ⩽ t) = 1 − e−λ t .
(4.7)
Thus for a constant default intensity λτ , the occurrence of a default event is described by the
first jump of a Poisson process with intensity λτ . Hence, for a constant intensity λτ , the default
time τ is exponentially distributed with rate parameter λτ ,
τ ∈ Exp(λτ ).
4.3
(4.8)
Price Process Importance Sampling
When employing importance sampling on the asset price process, the computations can be
simplified by handling the jump component and the diffusion component separately.
The diffusion component of the SDE driving Bates’ model is given by
(µ − λs E[Jt1 − 1])dt +
p
Vt dWt .
(4.9)
With the notation of a general diffusion process given in equation 2.5, the coefficients of Bates’
model are given by
17
CHAPTER 4. METHOD AND MODELS
a(x, t) = x(µ − λs E[Jt1 − 1]),
p
b(x, t) = x Vt .
(4.10)
(4.11)
These coefficients can be used in the method described in section 2.1.10 to obtain the optimal
change of measure parameter at level c,
p
a(x, t)2 + 2cb(x, t)2
a(x, t)
θ(x, t) = −
±
b(x, t)
b(x, t)
(4.12)
p
s
(µ − λs E[Jt1 − 1])2 + 2cVt
µ − λ E[Jt1 − 1]
√
√
=
±
.
Vt
Vt
It is clear that two asymptotically optimal changes of measure can be chosen from equation
4.12 depending on the sign. In this paper, the choice was made to take the parameter
p
(µ − λs E[Jt1 − 1])2 + 2cVt
µ − λs E[Jt1 − 1]
√
√
θ(x, t) =
+
.
(4.13)
Vt
Vt
The change of measure for the diffusion process is then given by
dP̃
= exp
dP
4.4
Z t
Z t
θ(Xs , s) dWs −
0
θ(Xs , s)2 ds .
(4.14)
0
CVA and Default Time Importance Sampling
The importance sampling of the default time is based on a method described by Joshi and and
Leung [15]. The idea behind the method is to sample only from relevant areas. In the context
of CVA calculations, it is of interest to sample the default time such that the counterparty
defaults before an option expires. This is especially effective if the default probability is very
low, as naive Monte Carlo simulation would result in few defaults before option expiration
and therefore few non-zero values to be used for estimating CVA. To motivate this sampling
method, the Monte Carlo estimator of CVA given by equation 3.12 is rewritten.
n0
n
1X
1X j
1{τ i ⩽ T }Liτ Dt,τ i =
Lτ Dt,τ j ,
n
n
i=1
(4.15)
j
where j = 1, . . . , n0 denote the indices of the paths where τ j ⩽ T . The expression 4.15 can be
further rewritten as
0
n
1X
n
j

Ljτ Dt,τ j = 
0
n
1 X
n0
n0
j

Ljτ Dt,τ j 
n0
.
n
(4.16)
It is noted that n is a Monte Carlo estimator of the probability P(τ ⩽ T ) of a counterparty
default occuring before expiration. Thus, the following Monte Carlo estimator of CVA is
obtained.
18
CHAPTER 4. METHOD AND MODELS

[t = 
CVA

0
n
1 X
n0
Ljτ Dt,τ j  P(τ ⩽ T ).
(4.17)
j
The algorithm for estimating CVAt becomes:
•
Simulate n paths of exposures (Lit )i=1,...,n
•
Simulate n default times, τ̄ i , that occur before time of expiration.
!
n
X
1
[t =
Liτ̄ i Dt,τ̄ i P(τ ⩽ T )
Calculate the Monte Carlo estimate CVA
n
•
(4.18)
i
In order to perform the steps in the above algorithm, the probability P(τ ⩽ T ) must be
calculated and the default times before expiration must be sampled. Let the investor hold a
derivative asset at time t with no counterparty default having occured before time t. For a
constant default intensity λ, the probability of a counterparty default event before expiration
is given by
τ
P(τ ⩽ T ) = 1 − e−λ (T −t) .
(4.19)
Given a constant default intensity λτ , the default time is described by
τ = t + ∆t,
∆t ∈ Exp(λτ ).
(4.20)
To sample a default time, inverse transform sampling can be used. A random sample of τ is
given by
1−u
τ i = t − log
, u ∈ U (0, 1).
(4.21)
λτ
To exclude default times that are after expiration, let u ∈ U (0, P(τ ⩽ T )) when performing
inverse transform sampling. Thus, a sampled default time before expiration is acquired by
1−u
i
, u ∈ U (0, P(τ ⩽ T )).
(4.22)
τ̄ = t − log
λτ
For the purpose of calculating CVA, it is difficult to use importance sampling of asset prices.
The difficulty lies in finding the factor ddPP̃ , which is needed to adjust the Monte Carlo estimate
of CVA under the new measure in order to obtain the estimate under the original measure.
Finding this factor is outside the scope of this paper. However, CVA will be estimated under the
new measure given by the optimal parameter θ(x, t) for asset price simulation. This estimate
is expected to differ from the estimate of CVA under the original measure.
4.5
Parameter Selection
The choice of parameters in both the asset price model and the default time model is highly
dependent on the counterparties and the economy involved. It is outside the scope of this paper
to calibrate the parameters to specific counterparties and economies, and the focus is instead
19
CHAPTER 4. METHOD AND MODELS
on the simulation methods.
The parameters chosen for Bates’ model, which was used for the asset price simulation, were
κ = 2,
s
λ = 2,
θ = 0.04,
µ = 0.02,
ρ = 0,
V0 = 0.04
J0 ∈ lognorm(−0.2, 0.2).
(4.23)
The portfolio for CVA calculation was chosen to consist of one call option with parameters
S0 = 100,
K = 100,
T = 1.
(4.24)
The Bermudan option was chosen to have 9 equidistant early exercise dates,
T
.
(4.25)
10
The discount factor used for calculations was obtained by using continuous compounding with
the risk free interest rate r = 0.02,
t0 ∈ {∆t, . . . , T − ∆t},
∆t =
Ds,t = er(t−s) = e0.02(t−s) .
(4.26)
To minimize the variance of the simulated asset price, it is essential to determine a close to
optimal level c for the change of measure. This was done by performing a grid search over a
range of levels c and choosing the value that minimized the relative error.
Similarly, a suitable basis should be chosen for the least squares Monte Carlo method used
for Bermudan option valuation. This was done by simulating a sample of several Monte Carlo
estimates of CVA for the Bermudan option for different sets of basis functions. The most
suitable basis was then chosen based on the sample average Monte Carlo estimate, the sample
relative error of the Monte Carlo estimate and simplicity of the basis. The considered bases
were the following.
{1}, {1, S}, {1, S, S 2 }, {1, S, S 2 , S 3 }
{1, P1 (S)}, {1, P1 (S), P2 (S)}, {1, P1 (S), P2 (S), P3 (S)},
(4.27)
where Pi (·) is the ith Legendre polynomial. In particular
P1 (x) = x,
4.6
P2 (x) =
3x2 − 1
,
2
P3 (x) =
5x3 − 3x
.
2
(4.28)
Performance Evaluation
The performance evaluation of the importance sampling method for asset prices takes the following into account: the estimated asset price at all time points should be similar to that of
naive Monte Carlo and the variance should be as low as possible.
For CVA calculations, the estimated CVA of naive Monte Carlo and of the method using importance sampling should be similar. For CVA, as opposed to the asset price, the sample
20
CHAPTER 4. METHOD AND MODELS
variance of one run of simulations does not always give a good reflection of the performance of
the method. Because CVA for a path is zero if the simulated default time is after expiration,
the CVA sample variance of one run of simulations is bound to be very large if there is a
probability of default after expiration. Therefore when dealing with CVA simulations without
importance sampling for the default times, the sample variance of Monte Carlo estimates of
CVA for different runs of simulations is used to evaluate the performance of the method. This
variance should be as low as possible. Furthermore, the estimated CVA of a Bermudan option
should be higher than the estimated CVA of a European option with the same parameters
where applicable, and lower than the estimated CVA using the optimal exercise strategy conditional on all market information up to expiration.
To determine whether there is a significant difference in variance between different runs of
Monte Carlo simulations, Levene’s test can be used. Levene’s test is a statistical test that
assesses the null hypothesis that the variances of two or more populations are equal. Thus, a low
p-value implies that the variances of the populations are not equal. Levene’s test is well suited to
non-normal distributed populations and approximately normal distributed populations. Thus,
Levene’s test can be used on two populations of simulated quantities from two different Monte
Carlo methods in order to assess differences in variance of the two methods. It can also be used
on two samples of Monte Carlo estimates obtained from two different Monte Carlo methods in
order to assess differences in the variance of the Monte Carlo estimates of the two methods.
For details about Levene’s test as well as discussions of its usage, the reader is referred to the
work of Gastwirth et.al. [16]. Unless stated otherwise, in this paper, a significant difference in
variance between two populations refers to a difference in variance between the populations at
the significance level 0.05.
4.7
Algorithms
The simulations are performed by computations at each time step of a discretized time interval.
The time interval [0, T ] is discretized into m equidistant time steps, i.e.
T
, tj = (j − 1)∆t, j = 1, . . . , m.
(4.29)
m−1
The asset price simulation without importance sampling is performed according to the following algorithm.
∆t =
Algorithm 1: simulateBatesModel
Result: Returns asset spot price and variance at all m time points for all n paths.
1 for each i ∈ {1, . . . , n} do
2
S1i = s0
3
V1i = v0
4
for each j ∈ {1, . . . , m − 1} do
i
i
5
Use Sji and Vji to calculate Sj+1
and Vj+1
according to Bates’ model.
6
end
7 end
8 return
21
CHAPTER 4. METHOD AND MODELS
With importance sampling, the asset price simulation algorithm becomes.
Algorithm 2: simulateBatesModel importanceSampling
Result: Returns asset spot price and variance at all m time points for all n paths.
1 for each i ∈ {1, . . . , n} do
2
S1i = s0
3
V1i = v0
4
for each j ∈ {1, . . . , m − 1} do
5
Calculate the optimal change of measure parameter θji
i
6
Calculate the change of measure dP
dP̃
j
7
8
i
i
Use Sji and Vji to calculate Sj+1
and Vj+1
under the new measure.
Multiply the asset price with the importance sampling weight:
i
dP
i
i
.
Sj+1
= Sj+1
dP̃
j
end
10 end
11 return
9
To calculate CVA for an option, the default time needs to be simulated and the option exposure
must be estimated. In the case of the Bermudan option, the option exposure is estimated using
least squares Monte Carlo. The following algorithm describes how to evaluate a Bermudan
option and calculate its exposure using least squares Monte Carlo.
22
CHAPTER 4. METHOD AND MODELS
Algorithm 3: exposureBermudan
Result: Returns exposure Lij at all m time points for all n paths.
Data: Asset spot price Sji at all m time points for all n paths.
1 Choose a set of basis functions {φ1 (·), . . . , φM (·)}
2 for each i ∈ {1, . . . , n} do
// Calculate exposure at expiration
i , K)
3
Vmi = Payoff(Sm
4
Lim = max(Vmi , 0)
5
6
7
8
9
10
// Compute option values using regression
for each j ∈ {m − 1, . . . , 1} do
if j is an early exercise index then
Obtain in the money indices {k1 , . . . , km0 }
km0
k1
by regressing (Dtj ,tj+1 Vj+1
Obtain Ĉjk
, . . . , Dtj ,tj+1 Vj+1
) on
k∈{k1 ,...,km0 }


φ1 (Sjk1 ) · · · φM (Sjk1 )


..
..


.
·
·
·
.


k 0
k 0
φ1 (Sj m ) · · · φM (Sj m )
// Compute option value for in the money paths
for each k ∈ {k
1 , . . . , km0 } do V̂jk = max Payoff(Sjk , K), Ĉjk
end
// Compute option value for out of the money paths
12
for each l ∈ {1, . . . , n} \ {k1 , . . . , km0 } do
l
13
V̂jl = Dtj ,tj+1 V̂j+1
14
end
15
else
16
for each i ∈ {1, . . . , n} do
i
17
V̂ji = Dtj ,tj+1 V̂j+1
18
end
19
end
20
Lij = max(V̂ji , 0)
21
end
22 end
11
The following algorithm describes how to calculate the exposure of a European option.
23
CHAPTER 4. METHOD AND MODELS
Algorithm 4: exposureEuropean
Result: Returns exposure Lij at all m time points for all n paths.
Data: Asset spot price Sji at all m time points for all n paths.
1 for each i ∈ {1, . . . n} do
// Calculate exposure at expiration
i , K)
2
Vmi = Payoff(Sm
i
i
3
Lm = max(Vm , 0)
4
for each j ∈ {m − 1, . . . , 1} do
i
5
Vji = Dtj ,tj+1 Vj+1
6
end
7
Lij = max(Vji , 0)
8 end
The CVA calculations without importance sampling of the default time are carried out in the
following way.
Algorithm 5: calculateCVA
Result: Returns CVA estimates for all n paths.
Data: Asset spot price Sji at all m time points for all n paths.
1 Simulate n default times (τ i )i=1,...,n
2 Estimate the exposures {Lij } by exposureBermudan or exposureEuropean
3 for each i ∈ {1, . . . , n} do
4
CVAi = Liτ i D0,τ i 1{τ i ⩽ T }.
5 end
6 return
With importance sampling of the default time, the CVA calculation algorithm becomes
Algorithm 6: calculateCVA importanceSampling
Result: Returns CVA estimates for all n paths.
Data: Asset spot price Sji at all m time points for all n paths.
1 Calculate probability of default before exposure, P (τ ⩽ T )
2 Simulate n default times (τ i )i=1,...,n before expiration
3 Estimate the exposures {Lij } by exposureBermudan or exposureEuropean
4 for each i ∈ {1, . . . , n} do
5
CVAi = Liτ i D0,τ i
6
Multiply with the importance sampling weight: CVAi = CVAi P (τ ⩽ T )
7 end
8 return
24
CHAPTER 4. METHOD AND MODELS
4.8
Simulations
This section describes the simulations performed in order to evaluate the performance of the
employed methods. All simulations were performed on a time interval discretized into m = 101
equidistant time points and the parameter values specified in section 4.5 were used.
4.8.1
Asset Price
To evaluate the effectiveness of the importance sampling method used for the asset price, the
optimal energy level was first found. This was done through a grid search where the mean
relative error taken over all time points was plotted against the energy level c. The relative
error was based on n = 20000 paths.
Simulations of the asset price for n = 100000 paths were performed in order to investigate the
performance of the importance sampling method. The simulation was performed both with
importance sampling and with naive Monte Carlo. For the importance sampling method, the
optimal energy level c was used. The asset prices obtained from these simulations were used
to compute the Monte Carlo estimate of the asset price at each time point for both methods.
Through these quantities, a two sided confidence interval of the Monte Carlo estimate could
be calculated at a 95% confidence level .
4.8.2
CVA of a European Option
For estimation of CVA for the European option, the price paths were simulated without importance sampling. 10 different runs of simulations were performed with n = 100000 paths
for each of the default intensities λτ ∈ {0.01, 1, 10}, resulting in 10 different sets of asset price
paths and default time paths. The default time paths were calculated both with naive Monte
Carlo and with importance sampling. With these values, a sample of 10 CVA Monte Carlo
estimates could be computed for each default intensity, both for naive Monte Carlo and for the
method utilizing importance sampling of the default times. The mean, variance and relative
error of these samples could then be calculated.
Simulations of n = 100000 paths were performed in order to investigate the variance of CVA
under the the optimal measure for the asset price. For the new measure given by equation 4.13,
the optimal energy level c found as described above was used. Under the new measure, a Monte
Carlo estimate of CVA, an estimate of the variance of CVA and a two sided confidence interval
of the CVA estimate at a 95% confidence level were calculated using importance sampling of
the default time. The default intensity λτ = 1 was used. Simulations of n = 100000 paths were
also performed under the original measure for the asset price. Importance sampling was used
for the default times. Using the simulated asset prices and default times, an estimate of CVA,
an estimate of the variance of CVA and a 95% confidence interval of the CVA estimate were
computed.
25
CHAPTER 4. METHOD AND MODELS
4.8.3
CVA of a Bermudan Option
In order to determine an appropriate basis for CVA calculations, a grid search was performed
over different sets of basis functions, for which 10 runs of Monte Carlo simulations were performed, yielding 10 different Monte Carlo estimates of CVA of the Bermudan option. The
number of paths per run of simulations was n = 10000. The most suitable basis was chosen
based on sample average Monte Carlo estimate, sample relative error of the Monte Carlo estimate and simplicity of the basis.
Similarly to the case with the European option, the asset price paths were calculated without
importance sampling. 10 different sets of n = 100000 asset price paths were simulated for
default intensities λτ ∈ {0.01, 1, 10}. 10 different sets of n = 100000 default times were simulated both with naive Monte Carlo and importance sampling. With these values, a sample
of 10 CVA Monte Carlo estimates could be computed for each default intensity and for both
methods. For these calculations, the most suitable basis obtained as descried above was used.
The mean, variance and relative errors of these samples were calculated.
Simulations with n = 100000 paths were also performed under the optimal measure for the
asset price given by equation 4.13. For these simulations, the optimal energy level c found as
described above was used, and the default intensity was λτ = 1. Under the new measure, the
Monte Carlo estimate of CVA, the estimate of the variance of CVA and a two sided confidence
interval of the CVA estimate at a 95% confidence level were calculated using importance sampling of the default time. Additionally, simulations of n = 100000 paths were performed under
the original measure for the asset price, with importance sampling being used for the default
times. Using the simulated asset prices and default times, an estimate of CVA, an estimate of
the variance of CVA and a 95% confidence interval of the CVA estimate were computed.
26
Chapter 5
Results
The simulations from which the results in this chapter were obtained were all performed on
a time interval discretized into m = 101 equidistant time points. All simulations used the
parameter values specified in section 4.5.
5.1
Asset Price
The mean relative error taken over all time points is plotted against energy level c in figure
5.1. The relative errors were calculated using n = 20000 asset price paths.
Figure 5.1: Relative error plotted against energy level c.
The energy level minimizing the relative error is c = 0.37. Hence, c = 0.37 was chosen as the
optimal energy level.
27
CHAPTER 5. RESULTS
In figure 5.2, the first 20 paths of the asset price as well as the volatility are plotted. These
values were obtained by simulation with naive Monte Carlo.
Figure 5.2: Plots of first 20 paths of asset price (left) and volatility of asset price (right) against
the indices of the time points.
In figure 5.3, the Monte Carlo estimate of the asset price with naive Monte Carlo, as well as
the difference between the Monte Carlo estimate of the asset price with importance sampling
and with naive Monte Carlo, ŜnIS − Ŝn , are plotted against the indices of the time points. The
Monte Carlo estimates were computed from n = 100000 paths.
Figure 5.3: Plot of the asset price Monte Carlo estimate with naive Monte Carlo against the
indices of the time points (left). Plot of the difference between the asset price Monte Carlo
estimate with importance sampling and with naive Monte Carlo against the indices of the time
points (right).
Figure 5.3 shows an increasing trend of the asset price Monte Carlo estimate with time. This
is consistent with the fact that the drift of the asset price model was set to r = 0.02. The plot
28
CHAPTER 5. RESULTS
of the difference in Monte Carlo estimate between the case with importance sampling and the
case with naive Monte Carlo indicates that the two Monte Carlo estimates are similar. There
is also no clear sign of overestimation or underestimation of the asset price by the importance
sampling method compared to the naive Monte Carlo method.
In figure 5.4, the Monte Carlo asset price variance estimates are plotted at all time points. The
variance was calculated over n = 100000 simulated paths.
Figure 5.4: Plots of the Monte Carlo estimate of asset price variance against the indices of the
time points. To the left is the variance for naive Monte Carlo and to the right is the variance
for the method using importance sampling.
It is seen in figure 5.4 that the Monte Carlo estimate of the variance of the asset price for both
naive Monte Carlo and importance sampling are approximately linear functions of time. It is
also seen that the variance is consistently smaller for the estimate obtained using importance
sampling. The average relative decrease in variance calculated over all time points was 0.2761.
This is a substantial decrease in variance. Levene’s test on the populations of asset prices at
expiration of all paths, for important sampling and naive Monte Carlo, returned a p-value of
0. This indicates a significant difference in variance between the two populations.
In figure 5.5, the asset price Monte Carlo estimate at expiration together with a two sided 95%
confidence interval is plotted against the number of paths, both for the case with naive Monte
Carlo and the case with importance sampling. The results were based on n = 100000 paths.
29
CHAPTER 5. RESULTS
Figure 5.5: Plots of asset price Monte Carlo estimate at expiration together with a two sided
95% confidence interval against the number of paths. For the case with naive Monte Carlo
(left) and for the case with importance sampling (right).
Notably, by inspection of figure 5.5, the variance reduction of the method using importance
sampling is not discernible. Moreover, for this run of simulations, the importance sampling
method underestimates both the upper and the lower confidence interval limits of the asset
price at expiration, compared to naive Monte Carlo. However, the asset price estimate at
expiration is similar for both methods, which is consistent with the differences in the estimate
plotted in figure 5.3.
5.2
CVA for a European Option
The Monte Carlo estimates of the exposure of one European call option are plotted against the
indices of the time points in figure 5.6. Note that the option value at all times is positive and
the exposure is therefore equal to the option value. The Monte Carlo estimates were based on
100000 asset price paths.
30
CHAPTER 5. RESULTS
Figure 5.6: Monte Carlo estimate of the exposure of one European call option plotted against
the indices of the time points.
As expected, the estimated exposure of the European option plotted in figure 5.6 is an increasing function of the time indices. The positive slope is caused by the discounting of the payoff
at expiration.
In table 5.1, Monte Carlo estimates of CVA, both with naive Monte Carlo and with importance
sampling are shown for one European call option. The estimates were based on 10 different
runs of simulations with n = 100000 paths and were computed for the default intensities
λτ ∈ {0.01, 0.1, 10}.
λτ = 0.01
λτ = 1
λτ = 10
0.1671
11.0005
17.3317
λτ = 0.01
λτ = 1
λτ = 10
0.1716
10.9367
17.3309
CVA Monte Carlo Estimates Naive
0.1623
0.1573
0.1834
0.1784
0.1562
0.1727
10.8820 10.9226 10.9583 10.9182 10.9906 10.8831
17.4628 17.3168 17.2975 17.3049 17.3571 17.1947
CVA Monte Carlo Estimates Importance Sampling
0.1727
0.1725
0.1717
0.1730
0.1719
0.1722
0.1734
10.9592 10.9590 10.9499 10.9153 10.8990 10.9701 10.9317
17.4472 17.4624 17.3165 17.2973 17.3041 17.3570 17.1940
0.1845
10.9300
17.4479
0.1630
11.0059
17.3371
0.1705
10.8662
17.4096
0.1725
10.9851
17.3369
0.1717
10.9172
17.4103
Table 5.1: Monte Carlo estimates of CVA for a European call option for 10 different runs of
simulations, for both naive Monte Carlo and Monte Carlo with importance sampling.
The mean, variance and relative error for the samples of Monte Carlo estimates shown in table
5.1 are displayed in table 5.2.
31
CHAPTER 5. RESULTS
λτ = 0.01
λτ = 1
λτ = 10
Mean
0.1744
10.9414
17.3460
Mean IS
0.1720
10.9313
17.3457
Var
1.1860 · 10−4
0.0058
0.0063
Var IS
3.0008 · 10−7
0.0028
0.0063
Relative Error
0.0197
0.0058
0.0014
Relative Error IS
0.0010
0.0028
0.0014
Table 5.2: Mean, variance and relative error for the samples of Monte Carlo estimates of CVA.
The estimates were computed for 10 different runs of simulations, both with naive Monte Carlo
and Monte Carlo with importance sampling.
In table 5.3, the p-values of Levene’s test on the populations of pathwise simulated CVA values
with naive Monte Carlo and with importance sampling are displayed.
p-value
λτ = 0.01
1.2749 · 10−4
λτ = 1
0.0373
λτ = 10
0.9939
Table 5.3: p-values for Levene’s test on the populations of CVA estimates for a European
option, with importance sampling and with naive Monte Carlo.
Tables 5.1 and 5.2 show that the Monte Carlo estimates of CVA are similar for both methods.
The CVA estimate increases with the default intensity. This is in line with expectations, as a
high default intensity implies a high default probability, which in turn means that the counterparty has a high probability of being unable to fulfil its contractual obligations as a result
of a default.
The variance is significantly lower when using importance sampling compared to naive Monte
Carlo for λτ = 0.01, which is confirmed by the small p-value of Levene’s test of 1.2749 · 10−4
(see table 5.3). This is expected, as few paths with a counterparty default will be simulated
using naive Monte Carlo for such a small default probability. The variance reduction is smaller
for λτ = 1, and the p-value of Levene’s test of 0.0373 indicates a significant variance reduction.
For λτ = 10, the obtained variances of the two methods are identical, and the high p-value
of Levene’s test of 0.9939 indicates no significant difference in variance between the methods.
Because the default probability is so high, a large portion of the paths is expected to have a
counterparty default before expiration. The number of paths with nonzero CVA contribution
are therefore expected to be similar for naive Monte Carlo and importance sampling. The
observed relative error follows a similar pattern as the variance. The relative error is much
smaller for the method with importance sampling when λτ = 0.01. The difference is smaller
for λτ = 1 and the relative errors of the two methods are equal for λτ = 10.
5.3
CVA for a European Option under a new Measure
The Monte Carlo estimate of CVA, the estimated variance and the relative error of the estimate
for one European call option, under the original measure and the optimal measure for asset price
simulation, are displayed in table 5.4. The estimates were both calculated using importance
sampling of the default time. The default intensity was set to λτ = 1 and n = 100000 paths
were simulated.
32
CHAPTER 5. RESULTS
Original Measure
New Measure
CVA Estimate
10.9154
12.6296
Variance
279.1447
334.7185
Relative Error
1.5306
1.4486
Table 5.4: CVA Monte Carlo estimate, estimated variance and relative error for a European
call option, under the original measure and the new measure.
From table 5.4, it can be seen that the CVA estimate is larger under the new measure. The variance is also larger under the new measure, while the relative error is slightly smaller. Levene’s
test on the populations of simulated CVA values under the old and the new measure resulted
in a p-value of 1.4050 · 10−168 , which implies a significant difference in variance between the
populations.
In figure 5.7, the CVA Monte Carlo estimate together with a two sided 95% confidence interval
is plotted against the number of paths, under both the original measure and the new measure.
The results were based on n = 100000 paths.
Figure 5.7: Plots of CVA Monte Carlo estimate for a European call option together with a two
sided 95% confidence interval against the number of paths, under the original measure (left)
and the new measure (right).
Figure 5.7 shows that both the CVA Monte Carlo estimate and the estimated variance are
consistently larger under the new measure. This is consistent with the previous observations
in this section.
5.4
CVA for a Bermudan Option
In table 5.5, the Monte Carlo estimates of CVA of a Bermudan call option for 10 different runs
of simulations of n = 10000 paths are displayed. The option has 9 equidistant exercise dates.
The default intensity was set to λτ = 1. Table 5.6 shows the mean, variance and relative error
of the sample of Monte Carlo estimates. The estimates were computed for the bases
33
CHAPTER 5. RESULTS
{1}, {1, S}, {1, S, S 2 }, {1, S, S 2 , S 3 }
{1, P1 (S)}, {1, P1 (S), P2 (S)}, {1, P1 (S), P2 (S), P3 (S)},
(5.1)
where Pi (·) is the ith Legendre polynomial. The estimates were also computed for the optimal
exercise strategy conditional on all market information up to time T .
Basis
{1}
{1, S}
{1, S, S 2 }
{1, S 2 , S 3 )}
{1, P1 (S)}
{1, P1 (S), P2 (S)}
{1, P1 (S), P2 (S), P3 (S)}
Optimal
17.2195
11.0314
11.0121
11.0158
11.0314
11.0121
11.0158
15.2022
17.6302
11.3281
11.3059
11.3073
11.3281
11.3059
11.3073
15.4870
17.6523
11.1585
11.1213
11.1219
11.1585
11.1213
11.1219
15.7086
CVA Monte Carlo Estimates
17.3946 17.4047 17.0113 17.1123
10.9255 11.1461 10.9043 10.8645
10.9113 11.1336 10.8789 10.8406
10.9164 11.1338 10.8587 10.8308
10.9255 11.1461 10.9043 10.8645
10.9113 11.1336 10.8789 10.8406
10.9164 11.1338 10.8587 10.8308
15.0774 15.4416 15.0319 14.9988
17.1144
10.8032
10.7969
10.8070
10.8032
10.7969
10.8070
15.0816
17.3903
11.0552
11.0362
11.0451
11.0522
11.0362
11.0451
15.2272
17.0226
10.8509
10.8248
10.8403
10.8509
10.8248
10.8403
15.0901
Table 5.5: Monte Carlo estimates of the value of a Bermudan call option for 10 different runs
of simulations and for different sets of regression basis functions.
Basis
{1}
{1, S}
{1, S, S 2 }
{1, S 2 , S 3 )}
{1, P1 (S)}
{1, P1 (S), P2 (S)}
{1, P1 (S), P2 (S), P3 (S)}
Optimal
Mean
17.2952
11.0068
10.9862
10.9877
11.0068
10.9862
10.9877
15.2346
Variance
0.0553
0.0280
0.0273
0.0274
0.0280
0.0273
0.0274
0.0553
Relative Error
0.0043
0.0048
0.0048
0.0048
0.0048
0.0048
0.0048
0.0049
Table 5.6: Mean, variance and relative error for the samples of Monte Carlo estimates of CVA
of a Bermudan call option, for 10 different runs of simulations and for different sets of regression
basis functions.
The results in tables 5.5 and 5.6 indicate that the basis {1} considerably overestimates the
option value. The estimated values of CVA for this basis are even larger than the estimates of
CVA obtained when following the optimal exercise strategy conditional on all market information up to expiration, which is known to overestimate the option value. However, for the rest
of the bases, both the CVA estimates and the relative error are very similar. Therefore, the
most simple basis, {1, S} was chosen as the most suitable basis.
The Monte Carlo estimate of the exposure of one Bermudan call option with 9 equidistant
early exercise dates is plotted against the indices of the time points in figure 5.8. Note that
the option value at all times is positive and the exposure is therefore equal to the option value.
The regression basis functions {1, S} were used and the estimates were based on n = 100000
asset price paths.
34
CHAPTER 5. RESULTS
Figure 5.8: Monte Carlo estimate of the exposure of one Bermudan call option plotted against
the indices of the time points.
Compared to the plot of the estimated value of a European call option (see figure 5.6), the
estimated value of the Bermudan option has a similar increasing trend. However, there are
jumps in the estimated option value. These are explained by the possibility of early exercise
at the time indices of the jumps.
In table 5.7, Monte Carlo estimates of CVA, both with naive Monte Carlo and with importance
sampling, for one Bermudan call option and for 10 different runs of simulations with n = 100000
paths are shown. The simulations were performed for the default intensities λτ ∈ {0.01, 1, 10}.
λτ = 0.01
λτ = 1
λτ = 10
0.1777
10.8698
17.4514
λτ = 0.01
λτ = 1
λτ = 10
0.1715
10.9106
17.4435
CVA Monte Carlo Estimates Naive
0.1593
0.1794
0.1689
0.1629
0.1689
0.1749
10.9813 10.8691 10.8822 11.1821 11.0610 10.9184
17.4619 17.4885 17.2837 17.3064 17.4660 17.3850
CVA Monte Carlo Estimates Importance Sampling
0.1716
0.1735
0.1721
0.1719
0.1715
0.1740
0.1724
10.9055 11.0304 10.9267 10.9144 11.1086 11.0346 10.9612
17.3523 17.4244 17.4959 17.2852 17.3175 17.4422 17.3739
0.1679
10.9659
17.3587
0.1775
10.9700
17.2395
0.1704
11.0004
17.3584
0.1728
10.9610
17.2398
0.1730
11.0160
17.3252
Table 5.7: Monte Carlo estimates of CVA for a Bermudan call option for 10 different runs of
simulations, for both naive Monte Carlo and Monte Carlo with importance sampling.
The mean, variance and relative error for the sample of Monte Carlo estimates shown in table
5.7 are displayed in table 5.8.
35
CHAPTER 5. RESULTS
λτ = 0.01
λτ = 1
λτ = 10
Mean
0.1708
10.9704
17.3800
Mean IS
0.1724
10.9766
17.3700
Var
4.3660 · 10−5
0.0095
0.0074
Var IS
7.6179 · 10−7
0.0047
0.0065
Relative Error
0.0122
0.0028
0.0016
Relative Error IS
0.0016
0.0020
0.0015
Table 5.8: Mean, variance and relative error for the sample of Monte Carlo estimates of CVA for
10 different runs of simulations, for both naive Monte Carlo and Monte Carlo with importance
sampling.
In table 5.9, the p-values of Levene’s test on the populations of simulated CVA values for all
paths, with naive Monte Carlo and with importance sampling, are displayed.
p-value
λτ = 0.01
9.2877 · 10−4
λτ = 1
0.5821
λτ = 10
0.8080
Table 5.9: p-values of Levene’s test on the populations of simulated CVA values for a Bermudan
option, with importance sampling and with naive Monte Carlo.
The displayed values in tables 5.8 and 5.2 (the corresponding table for the European option)
show similar patterns for the CVA estimates. The sample means of the estimates are similar for
both methods across the three different default intensities. The relative error and the variance
are much smaller for the method with importance sampling for λτ = 0.01. This variance
reduction is confirmed by the p-value of Levene’s test of 9.2877 · 10−4 (see table 5.9). The
method using importance sampling has smaller variance and relative error for λτ = 1 compared
to naive Monte Carlo as well. However, the difference is smaller than for λτ = 0.01. The pvalue of Levene’s test of 0.5821 indicates that no significant variance reduction is achieved by
using importance sampling for λτ = 1, as opposed to the case with the European option where
a significant difference in variance was observed. The variances and relative errors for naive
Monte Carlo and importance sampling are similar for λτ = 10. However, both the relative error
and the variance are slightly smaller for the method utilizing importance sampling, which is not
the case for the European option. Levene’s test indicates no significant difference in variance
between the two methods, with a p-value of 0.8080. The relative error for the Bermudan option
is similar to that for the European option for all considered default intensities. Notably, the
relative error of naive Monte Carlo for λτ = 1 is considerably lower for the Bermudan option
than for the European option, 0.0028 compared to 0.0058. It is also notable that the CVA
estimate is consistently slightly higher for the Bermudan option compared to the European
option. This is expected, as a Bermudan option has a higher value than a European option
with the same parameters where applicable.
5.5
CVA for a Bermudan Option under a new Measure
The Monte Carlo estimate of CVA, the estimated variance and the relative error of the estimate
of one Bermudan call option, under the original measure and the optimal measure for asset
price simulation, are displayed in table 5.10. Both of the estimates were calculated by using
importance sampling of the default time. The option has 9 equidistant exercise dates. The
default intensity was set to λτ = 1 and n = 100000 paths were simulated.
36
CHAPTER 5. RESULTS
Original Measure
New Measure
CVA Estimate
11.0364
12.7293
Variance
117.9449
140.7910
Relative Error
0.9842
0.9321
Table 5.10: CVA Monte Carlo estimate, estimated variance and relative error for a Bermudan
call option, under the original measure and the new measure.
From table 5.10, it can be seen that the CVA estimate is larger under the new measure. The
estimated variance is also larger under the new measure, while the relative error is slightly
lower under the new measure. These results are similar to those of the European option. Levene’s test on the populations of simulated CVA values under the original measure and the
new measure resulted in a p-value of 4.6027 · 10−110 , which implies a significant difference in
variance between the populations. Notably, the estimated variance and the relative error are
considerably smaller for the Bermudan option compared to the European option, both under
the original measure and the new measure.
In figure 5.9, the CVA Monte Carlo estimate together with a two sided 95% confidence interval
is plotted against the number of paths, under both the original measure and the new measure.
The results were based on n = 100000 paths.
Figure 5.9: Plots of CVA Monte Carlo estimates for a Bermudan call option together with
a two sided 95% confidence interval against the number of paths, under the original measure
(left) and the new measure (right).
Figure 5.9 shows that both the CVA Monte Carlo estimate and the estimated variance are
consistently larger under the new measure. This is consistent with the previous observations
in this section.
37
Chapter 6
Discussion and Conclusions
The first objective of this paper was to investigate how to decrease the variance of asset price
simulation. By using a Monte Carlo importance sampling method with an optimal change of
measure based on the diffusion component of the price process, a significant variance reduction
was achieved compared to naive Monte Carlo. Because the importance sampling employed
in the simulation only takes the diffusion part of the price process into account, it might be
possible to reduce the variance further by using an importance sampling algorithm that also
takes the jumps into account when changing the measure. An area of further research is to
investigate if the variance of the simulation of an asset price following a jump-diffusion process
can be further reduced by employing an importance sampling algorithm that takes both the
jump and the diffusion components into account.
The second objective of the paper was to investigate how the price of a Bermudan option can
be estimated using regression based Monte Carlo simulation. By using least squares Monte
Carlo, the asset price of a Bermudan option could be estimated and later used for CVA calculations. It is however hard to evaluate how good the estimate is, as it is difficult to find a
baseline Monte Carlo estimate to compare the obtained estimate with. The estimated prices
were deemed reasonable, as the estimated CVA of the Bermudan option was larger than the
estimated CVA of a European call option with the same parameters where applicable and
smaller than the CVA estimate obtained by using the optimal exercise strategy conditional on
all market information up to expiration. This is a large interval, and it is of interest to find
a more accurate way of evaluating the estimated price of a Bermudan option. A suggestion
for further work is to investigate methods of improving the evaluation of the estimated option
price. Additional research could also be made on other regression based methods for Bermudan
option pricing.
The third objective of the paper was to investigate how to decrease the variance of CVA simulation for European and Bermudan options. For a European option, it was shown that a variance
reduction compared to naive Monte Carlo could be achieved by using a Monte Carlo method
based on importance sampling of the default time. The variance reduction was significant for
the default intensities λτ = 0.01 and λτ = 1, while the variances of the two methods were not
significantly different for λτ = 10. This was consistent with the expectation that the variance
reduction should be large for small default probabilities and small for large default probabilities. For a Bermudan option, similar results were obtained when comparing simulations of
38
CHAPTER 6. DISCUSSION AND CONCLUSIONS
CVA using naive Monte Carlo and least squares Monte Carlo to simulations of CVA using importance sampling of the default time and least squares Monte Carlo. However, for Bermudan
options, the variance reduction was only significant for λτ = 0.01, while the variances were
not significantly different for λτ = 1 or λτ = 10. This was, again, consistent with the results
expected from theory. As previously discussed, there was no baseline naive Monte Carlo estimate to compare the simulated CVA values to. The comparison was instead made between
two methods using least squares Monte Carlo, one of them using importance sampling of the
default time and one of them not using importance sampling. Thus for the Bermudan option, it
was shown that a significant variance reduction was achieved in the least squares Monte Carlo
setting by using importance sampling of the default time. In future work, one could investigate
whether the employed importance sampling method achieves variance reduction for alternative ways of pricing Bermudan options. It is also noted that the used importance sampling
method only gives a significant variance reduction for sufficiently small default probabilities
and is therefore particularly useful for counterparties with high credit ratings. The method is
therefore not as useful for counterparties with large default probabilities. A topic of further
research is to devise importance sampling methods that also significantly reduce the variance
for large counterparty default probabilities.
The asset price importance sampling technique could not be applied on CVA calculations, as
the factor associated with the change of measure could not be found. The Monte Carlo estimate
under the new measure could therefore not be adjusted in order to obtain the estimate under
the original measure. CVA was instead simulated under the optimal measure for asset price
importance sampling, without multiplication of this factor. As was expected from theory, the
CVA estimate under the new measure was different from the CVA estimate under the original
measure. The CVA estimate as well as the estimated variance of CVA was larger under the
new measure, for both the European option and the Bermudan option. However, the relative
error was smaller under the new measure for both options. It is therefore possible that the
larger variance under the new measure is in part explained by the larger estimate of CVA under
the new measure. This motivates attempts to find ways of employing asset price importance
sampling for CVA simulations. To build upon the findings of this paper, one could try to
find the factor associated with the change of measure, that is necessary in order to obtain an
estimate of CVA under the original measure by using asset price importance sampling.
Furthermore, the importance sampling method employed for the asset price process was a
general one, designed to reduce the variance of the simulation as much as possible. For CVA
simulation, or other applications, however, the optimal change of measure might depend on
other factors as well. For instance, the CVA contribution will be zero if the path is out of
the money at the time of default, which might motivate a change of measure that drives the
asset price to the region that puts the option in the money. By further investigating changes
of measure based on specific applications, convergence results might be improved. It is also
noted that the model used for the default time was quite simple, and the c.d.f of the default
time could be computed analytically. To further build upon the findings of this paper, similar
importance sampling methods could be investigated for other stochastic intensity models. In
particular, it would be of interest to find a method of performing importance sampling when
the c.d.f of the default time cannot be computed analytically.
39
CHAPTER 6. DISCUSSION AND CONCLUSIONS
Moreover, the findings of this paper are for asset prices following a jump-diffusion process.
It would be interesting to further investigate how similar methods could be used for different
types of asset price processes. Finally, in this paper, unilateral CVA was considered and
the exposure was assumed to be independent of the default probability. A further topic of
research is to adapt the methods in this paper to bilateral CVA, where both the investor and
the counterparty run the risk of defaulting. Furthermore, one could also consider the case
when the default probabilities of both the investor and the counterparty are correlated to the
exposure.
40
No. 581
Martin D. Gould, Nikolaus Hautsch, Sam D. Howison,
and Mason A. Porter
Counterparty Credit Limits: An
Effective Tool for Mitigating
Counterparty Risk?
Electronic copy available at: https://ssrn.com/abstract=3043112
Counterparty Credit Limits: An Effective Tool for Mitigating
Counterparty Risk?
Martin D. Gould∗ †1 , Nikolaus Hautsch2 , Sam D. Howison3 , and Mason A. Porter3,4,5
1
CFM–Imperial Institute of Quantitative Finance, Department of Mathematics,
Imperial College, London SW7 2AZ, UK
2
Department of Statistics and Operations Research, University of Vienna, Vienna
A-1090, Austria
3
Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
4
CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, UK
5
Department of Mathematics, University of California, Los Angeles, CA 90095, USA
Abstract
A counterparty credit limit (CCL) is a limit imposed by a financial institution to
cap its maximum possible exposure to a specified counterparty. Although CCLs are
designed to help institutions mitigate counterparty risk by selective diversification of their
exposures, their implementation restricts the liquidity that institutions can access in an
otherwise centralized pool. We address the question of how this mechanism impacts trade
prices and volatility, both empirically and via a new model of trading with CCLs. We
find empirically that CCLs cause little impact on trade. However, our model highlights
that in extreme situations, CCLs could serve to destabilize prices and thereby influence
systemic risk.
Keywords: Counterparty credit limits; counterparty risk; price formation; market design; systemic risk.
1
Introduction
The recent international financial crisis has underlined the vital importance of understanding
counterparty risk. As exemplified by the collapse of Lehman Brothers and the ensuing
defaults and near-defaults by AIG, Bear Stearns, Fannie Mae, Freddie Mac, Merrill Lynch,
the Icelandic banks, and the Royal Bank of Scotland, the complex and highly interconnected
nature of the modern financial ecosystem can cause counterparty failures to propagate rapidly
between institutions and can thereby amplify their severity [May et al., 2008]. Consequently,
assessing and implementing measures to mitigate the risk of default contagion remains a task
of primary importance.
One possible mitigation measure, currently implemented by several multi-institution
trading platforms in the foreign exchange (FX) spot market, is the application of counterparty credit limits (CCLs). A CCL is a limit imposed by a financial institution to cap its
∗
Corresponding author. Email: m.gould@imperial.ac.uk.
Martin D. Gould completed part of this work while at the University of Oxford and as an academic visitor
at the Humboldt-Universität zu Berlin.
†
1
maximum possible exposure to a specified counterparty. CCLs are designed to complement
existing risk-based capital requirements by protecting financial institutions from the large
losses that can result from sudden counterparty defaults, such as those that occurred with
the failure of Lehman Brothers in 2008.
Despite this clear benefit, the application of CCLs also entails an important drawback.
With CCLs in place, institutions can only access the trading opportunities offered by counterparties with whom they possess sufficient bilateral credit. Therefore, CCLs cause otherwise
centralized liquidity to fracture into localized liquidity pools, such that different institutions
have access to different trading opportunities at the same time. Because it limits individual
institutions’ access to liquidity, this process could severely destabilize prices, and may therefore influence systemic risk. Indeed, several prominent market commentators1 made a similar
argument in opposition to the proposed introduction of mandatory credit exposure limits
between large financial institutions (see Basel Committee on Banking Supervision [2014] and
Scott [2014]).
The aim of the present paper is to assess how the implementation of CCLs affects liquidity
and trade in financial markets. To address this question, we utilize an unusually rich data
set from Hotspot FX, which is a large electronic trading platform that enables institutions
to apply CCLs to their trading counterparties. Crucially, this data enables us to quantify
how CCLs affect both the liquidity available to given institutions and the prices at which
they consequently trade.
Our empirical investigation focuses on two main questions. First, how do CCLs impact
the prices that individual institutions pay for their trades? To address this question, we
introduce the notion of the “skipping cost” of a trade to measure the additional cost borne by
an institution due to the liquidity restrictions imposed by its CCLs. Second, to what extent
do these liquidity restrictions influence volatility? We address this question by comparing the
realized volatility of trade prices with the corresponding realized volatility in the platformwide best quotes from all institutions, irrespective of their CCLs. Our work is the first study
to address these questions.
We find that more than half of all the trades in our data set have a skipping cost of 0
and that the mean additional cost caused by CCLs is less than half a basis point. Although
we identify a handful of trades with large skipping costs, we argue that the existence of such
trades is a natural consequence of the substantial heterogeneity in the types and sizes of
institutions that trade in the FX spot market. We also find that the realized volatility of
trade prices is very similar to the corresponding realized volatility in the platform-wide best
quotes.
These empirical results all suggest that CCLs have very little impact on trading on
Hotspot FX. However, examining how CCLs impact trade on a specific platform is only
one aspect of understanding how they might affect financial markets more generally. In
particular, empirical study of historical data does not provide insight into how these results
might change if institutions were to make substantial modifications to their CCLs. Therefore,
we complement our empirical analysis with an investigation of a third question: how does the
structure of the underlying CCL network influence skipping costs and trade-price volatility?
To address this question, we introduce a model of trade in which institutions assign CCLs
to their trading counterparties. In contrast to our empirical analysis, in which the CCL
network is fixed and unobservable to us, this approach makes it possible to investigate how
varying a market’s CCL network affects trade in our model.
1
See, e.g., Goldman Sachs [2012] and J.P. Morgan [2012], and “Banks urge Fed retreat on credit exposure”,
Financial Times, 15 April 2012.
2
Simulations of our model provide valuable insights into the possible impact of CCLs. For
example, when the CCL network is dense (in the sense that most institutions can access
most trading opportunities), we find that the application of CCLs has very little impact on
trade prices and volatility. However, as the CCL network’s edge density falls, we find that
the skipping costs of trades and the corresponding trade-price volatility both rise sharply.
These sharp rises are not accompanied by a corresponding rise in quote-price volatility, which
remains approximately constant. This result indicates that when CCLs progressively restrict
institutions’ access to liquidity, their impact on trade escalates considerably. This finding is
consistent with concerns regarding the possible dangers of CCLs in situations where liquidity
is scarce. We also find that the CCL network’s topology can strongly influence both trade
prices and volatility. This result raises important questions regarding regulators’ abilities to
monitor the impact of CCLs among the large and heterogeneous populations of institutions
in real markets.
Together, our results paint an interesting and complex picture regarding the impact
of CCLs in financial markets. They also raise several important issues for regulators and
policy makers. Both our empirical investigation and our model simulations suggest that
when liquidity is plentiful, CCLs may indeed be an effective tool for mitigating counterparty
risk. However, our model also illustrates how an aggressive application of CCLs can create
large jumps in the trade-price series, even when the quote-price series remain relatively
stable. We therefore argue that understanding and monitoring how institutions set and
adjust their CCLs is a vital step for regulators in assessing how their implementation might
impact market stability and, ultimately, whether they constitute a benefit or a hindrance in
combating systemic risk.
Our work contributes to the rapidly growing literature that addresses effective ways to
mitigate counterparty risk. We discuss several such publications, and highlight how CCLs
differ from other possible approaches to this problem in Section 2.2. More generally, we also
contribute to the literature about the causes and consequences of counterparty risk. Jarrow and Yu [2001] noted that market-wide risk factors and institution-specific counterparty
risks can interact to generate highly correlated failure probabilities for different institutions.
Giesecke and Weber [2004] illustrated how the strength of default-contagion effects depend
heavily on the specific counterparty network between different institutions. Jorion and Zhang
[2009] noted that counterparty risk contagion could explain the strongly clustered nature of
defaults over time, and thus conjectured that a fear of counterparty failures could explain
the sudden worsening of the international credit crisis after the collapse of Lehman in 2008.
Our paper adds a specific focus on how CCLs feature in this discussion.
Our model contributes to the literature on price formation in non-centralized liquidity
pools. Perraudin and Vitale [1996] studied price formation in a model of trade in a decentralized market in which designated market makers attempt to infer information based on
the order flow that they experience from dealers. Our paper incorporates a similar framework in which individual institutions trade bilaterally. In contrast to Perraudin and Vitale
[1996], our core focus is the relationship between the institutions’ interaction topology and
the consequent impact on trade prices.
The paper proceeds as follows. In Section 2.3, we provide an introduction to counterparty
risk, describe the CCL mechanism in detail, and discuss how CCLs are currently implemented
by several large electronic trading platforms in the FX spot market. In Section 3, we describe
the data that forms the basis of our empirical study. We present our empirical results in
Section 4. In Section 5, we introduce and study our model of how CCLs affect trade. We
conclude in Section 6.
3
2
Counterparty Risk and Counterparty Credit Limits
2.1
Counterparty Risk
Counterparty risk is the risk that one or more of a financial institution’s counterparties
will default on their agreed obligations (see Gregory [2010]). Counterparty defaults can
occur for a wide variety of reasons, ranging from technical issues, such as computer system
malfunctions, to serious financial difficulties, such as insolvency. Irrespective of their cause,
counterparty defaults can cause significant financial distress and can push other institutions
towards their own defaults. This, in turn, can create a cascade of rapidly propagating
institutional failures. Therefore, counterparty risk is a key factor in determining whether
and with what speed localized shocks escalate to systemic events that impact the global
economy [The Counterparty Risk Management Policy Group, 2005].
To date, the vast majority of work on counterparty risk has focused on the counterparty
credit risk arising from the possibility that a counterparty defaults on its payment obligations
from a derivative contract (see, e.g., Brigo et al. [2013] for a detailed survey). Despite the
dominance of counterparty credit risk in the existing literature, financial institutions also face
several other important types of counterparty risks [Gregory, 2010]. Prominent examples
include liquidity risk, which is the risk of a liquidity shortage arising from a counterparty
default, and settlement risk, which is the risk of suffering losses by delivering cash or assets
to a counterparty that fails to settle the opposite leg of an agreement. Several historical
events, such as the near-catastrophic domino-effect defaults caused by the failure of Bankhaus
Herstatt in 1974 [Bank for International Settlements, 2002], underline the severity of these
forms of counterparty risk and provide strong motivation for exploring safeguards against
them.
2.2
Approaches to Mitigating Counterparty Risk
There are several possible approaches to mitigating counterparty risk, among which two have
received particular attention. The first is that of trade novation via a central counterparty
(CCP); see Norman [2011] and Rehlon and Nixon [2013] for detailed discussions. The role
of a CCP is to guarantee the obligations arising from all contracts agreed between two counterparties. If one counterparty fails, then the other is protected via the default-management
procedures and resources of the CCP. During the past decade, several prominent regulatory
bodies2 have argued that CCPs are an effective tool for mitigating counterparty risk.
The second approach is that of applying a credit valuation adjustment (CVA); see Brigo
et al. [2013] and Gregory [2010] for detailed discussions. In this framework, an institution
adjusts the price that it offers another institution to account for the risk of trading with
it. In other words, an institution may offer each other institution a different price for the
same transaction to account for its perceived risk of counterparty failure. In principle, an
institution can use the additional revenue generated by a CVA to construct a contingent claim
whose payoff is triggered by the default of the given counterparty, such that the resulting
net loss is zero.
Despite their clear benefits, these approaches to mitigating counterparty risk also suffer from important drawbacks. Koeppl [2013] noted that CCPs generate moral hazard by
removing the incentive for individual institutions to assess the creditworthiness of their trading counterparties. Pirrong [2012] argued that CCP novation does not reduce the aggregate
2
See, e.g., The Basel Committee on Banking Supervision [2013] and The Counterparty Risk Management
Policy Group [2005].
4
counterparty risk across all institutions, but rather concentrates all such risk into the CCP,
which thus becomes a single point of failure with systemic importance. Biais et al. [2012]
noted that although CCPs allow mutualization of the idiosyncratic risk faced by individual institutions, they cannot provide protection against the aggregate risk that affects all
institutions together. Menkveld [2015] showed that standard methodologies for calculating
default probabilities can greatly underestimate the probability of clustered defaults, which
place severe stress on a CCP. Given the historical failures of several CCPs in a wide variety
of asset classes — including FX, equities, and futures [Gregory, 2010] — concerns about
whether CCPs really mitigate risk, or simply repackage it, seem to be well-founded.
CVA also suffers from important drawbacks. Calculating a CVA requires each institution to estimate a time-varying risk premium for each of its trading counterparties. This
risk premium depends heavily on the counterparty’s default probability, which is extremely
difficult to estimate in practice. Cesari et al. [2010] noted that even if an institution is able
to estimate a risk premium for a given counterparty, performing this estimation does not
provide any insight into how it should construct a portfolio to provide the required payoff
upon a counterparty default. Indeed, constructing this portfolio is often impossible in practice. It is also worth noting that if one regards CVA as an insurance, then the “premium”
should be set aside as a provision against default, yet in reality there is always pressure to
use such assets for other purposes. Moreover, CVAs are not suitable for assets traded on
an exchange in which many different institutions access the same liquidity pool (such as a
limit order book (LOB); see Gould et al. [2013] for a detailed introduction to LOBs), because implementing CVAs would require each institution to set different prices for different
counterparties trading the same asset.
These weaknesses suggest that despite their widespread discussion and implementation,
neither CCP novation nor CVAs constitute a panacea for the issue of counterparty risk. The
failure of these measures to provide a conclusive solution to the problem is strong motivation
for exploring alternative avenues.
2.3
Counterparty Credit Limits
One alternative approach to mitigating counterparty risk is the application of counterparty
credit limits (CCLs). Consider a financial market populated by a set of institutions Θ =
{θ1 , θ2 , . . .}, in which each institution θi assigns a CCL c(i,j) ≥ 0 to each other institution θj .
The CCL c(i,j) specifies the maximum level of counterparty credit exposure that θi is willing
to extend to θj .3 Assigning a CCL to a given counterparty does not require posting collateral;
instead, it simply involves notifying the exchange of the relevant value c(i,j) . Institution θi
cannot engage in any trading activities with θj that would make θi ’s total exposure to θj
exceed c(i,j) or that would make θj ’s total exposure to θi exceed c(j,i) . The maximal amount
that θi and θj can trade is therefore equal to min c(i,j) , c(j,i) . We call this quantity the
bilateral CCL between θi and θj . These bilateral CCLs determine which subset of trading
opportunities are available to each institution. This subset changes over time according to
the relevant institutions’ trading activity.
As argued by Jarrow and Yu [2001], financial institutions face significant counterparty
risks whenever their exposures are concentrated within a small number of counterparties, because the default of any such counterparty would likely cause severe financial distress. CCLs
3
In the FX spot market, trades agreed on day d are settled on day d + 2. Therefore, each trade by an
institution in this market entails exposure to the counterparty during the period between trade agreement
and trade settlement.
5
provide financial institutions with an explicit defense against entering this situation, because
they cap the maximum exposure that an institution can face from any other institution.
If an institution θi perceives another institution θj to be unacceptably likely to default,
then θi can ensure that it never trades with θj by setting c(i,j) = 0, because arranging
any trade with θj would result in a non-zero exposure and would thereby violate this CCL.
Alternatively, if θi perceives θj to be extremely unlikely to default, then θi can also assign
an unlimited amount of credit to θj by setting c(i,j) = ∞. Irrespective of the CCL set by
θi , it still remains open to θj to further restrict the bilateral exposure by choosing c(j,i)
appropriately.
In contrast to CVAs, the application of CCLs does not require institutions to estimate
the market value of their counterparty risk. In contrast to trade novation via a CCP, CCLs
do not require a single, centralized clearing node that constitutes a single point of failure for
an entire market.4 Instead, the application of CCLs enables institutions to specify an upper
bound on each of their counterparty exposures, and thereby to mitigate counterparty risk
by selective diversification of their exposures.
2.4
Counterparty Credit Limits in the FX Spot Market
Several major multi-institution electronic trading platforms in the FX spot market already
offer institutions the ability to implement CCLs. On these platforms, each institution θi
privately declares to the exchange their CCL c(i,j) for each other institution θj . Trade occurs
via a mechanism similar to a standard limit order book (LOB), except that institutions are
only able to conduct transactions that do not violate their bilateral CCLs. More precisely,
when an institution θi submits a buy (respectively, sell) market order, the order matches
to the highest-priority sell (respectively, buy) limit order that is owned by an institution θj
such that neither c(i,j) nor c(j,i) are violated by conducting the given trade. We call this
market organization a quasi-centralized LOB (QCLOB) because different institutions have
access to different subsets of the same centralized liquidity pool. For a detailed introduction
to QCLOBs, see Gould et al. [2016].
Institutions trading on a QCLOB platform cannot in general see the state of the global
LOB. Instead, each institution sees only the active orders that correspond to trading opportunities that it can access (i.e., do not violate any of its bilateral CCLs) at time t.5 More
precisely, for each j 6= i, the volume of each separate limit order placed by θj that is visible
to θi is reduced (if necessary) so that its size does not exceed the bilateral CCL between θi
and θj . Each institution therefore views a filtered set of all limit orders on the platform,
according to its CCLs.
In addition to viewing their filtered LOB, each institution in a QCLOB can access a
trade-data stream that lists the price, time, and direction (buy/sell) of each trade that
occurs. All institutions can see all entries in the trade-data stream in real time, irrespective
of their bilateral CCLs with the institutions involved in a given trade. Therefore, although
institutions in a QCLOB can only see a subset of the trading opportunities available to other
institutions, they do have access to a detailed historical record of all previous trades.
4
We note, however, that the use of CCLs does not exclude the subsequent clearing of trades via a CCP.
We return to this discussion in Section 6.
5
Some QCLOB platforms (such as Reuters and EBS) offer institutions the ability to access an additional
data feed that provides snapshots of the global LOB at regular time intervals in exchange for a fee.
6
3
Data and Analysis
3.1
Sample Selection
Our empirical investigation is based on a data set provided to us by Hotspot FX. The data describes all trading activity on the Hotspot FX platform for the EUR/USD (euro/US dollar),
GBP/USD (pounds sterling/US dollar), and EUR/GBP (euro/pounds sterling) currency
pairs6 for the entire months of May and June 2010. According to the 2010 Triennial Central
Bank Survey [Bank for International Settlements, 2010], global trade for these currency pairs
constituted about 28%, 9%, and 3% of the total turnover of the FX market, respectively.
Therefore, our results enable us to compare and contrast the impact of CCLs across currency
pairs with different traded volumes.
During our sample period, three major multi-institution trading platforms dominated
electronic trading volumes in the FX spot market: Reuters, EBS, and Hotspot FX.7 All
three of these platforms use similar trading mechanics, and, in particular, all three implement
CCLs via QCLOBs. Importantly, however, EBS and Reuters primarily serve the interbank
market, whereas Hotspot FX serves both the interbank market and a broad range of other
financial institutions, such as hedge funds, commodity trading advisers, corporate treasuries,
and institutional asset managers.
Hotspot FX operates continuous trading, 24 hours per day, 7 days per week. However,
the vast majority of activity on the platform occurs on weekdays during the peak trading
hours of 08:00:00–17:00:00 GMT. We exclude all data from outside these time windows to
ensure that our results are not influenced by unusual behaviour during inactive periods. We
exclude 3 May (May Bank Holiday in the UK) and 31 May (Spring Bank Holiday in the UK;
Memorial Day in the US) because market activity on these days was extremely low. We also
exclude any days that included a gap in recording lasting 30 seconds or more.
After making these exclusions, our data set contains the peak trading hours for each of 30
trading days. In Figure 1, we plot the total volumes of market orders and limit orders for each
of the three currency pairs on each of these days. In Table 1, we provide the corresponding
summary statistics. Consistently with the market-wide volume ratios reported by the Bank
for International Settlements [2010], the mean daily volume of market orders for EUR/USD
exceeds that of GBP/USD by a factor of about 3 and that of EUR/GBP by a factor of about
9.
3.2
Data Format
For each currency pair and each day, the Hotspot FX data consists of two files. The first file
is the tick-data file, which lists all limit order arrivals and departures. For each limit order
arrival, this file lists the price, size, direction (buy/sell), arrival time, and a unique order
identifier. For each limit order departure, this file lists the departure time and the departing
order’s unique identifier (which is assigned at its arrival). A limit order departure can occur
for two reasons: because the order is matched by an incoming market order or because the
order is cancelled by its owner. The second file is the trade-data file, which lists all trades.
For each trade, this file lists the price, size, direction (buy/sell), and trade time. In both files,
all times are recorded in milliseconds. For each of the three currency pairs that we study,
the platform’s minimum order size is 0.01 units of the base currency, and the platform’s tick
6
A price for the currency pair XXX/YYY denotes how many units of the counter currency YYY are
exchanged per unit of the base currency XXX.
7
See Bech [2012] for an estimated breakdown of transaction volumes between platforms during this period.
7
●
●
●
●
●
●
●
EUR/USD
GBP/USD
EUR/GBP
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
Panel B: Limit Orders
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
28 June
●
21 June
●
14 June
17 May
3 May
●
●
●
EUR/USD
GBP/USD
EUR/GBP
●
7 June
●●
●●
31 May
●
24 May
●
10 May
Total Daily Volume
0
0.5x1010
1x1010
Total Daily Volume
0
1x1013
2x1013
Panel A: Market Orders
Figure 1: Total daily volumes of (top panel) market orders and (bottom panel) limit orders
for (green circles) EUR/USD, (orange squares) GBP/USD, and (purple triangles) EUR/GBP
activity on Hotspot FX on each day in our sample, measured in units of the counter currency.
See Table 1 for the corresponding summary statistics.
8
Min
Median
Max
Mean
St. Dev.
Min
Median
Max
Mean
St. Dev.
EUR/USD GBP/USD EUR/GBP
Panel A: Volume of Market Orders
2.5 × 109
7.4 × 108
1.0 × 108
8
9
4.4 × 10
1.5 × 10
3.6 × 108
9
9
7.5 × 10
2.5 × 10
1.2 × 109
9
9
4.6 × 10
1.5 × 10
4.0 × 108
9
8
1.2 × 10
4.2 × 10
2.4 × 108
Panel C: Volume of Limit Orders
7.2 × 1012
5.5 × 1012
3.7 × 1012
12
12
9.4 × 10
7.8 × 10
6.2 × 1012
13
12
1.4 × 10
9.7 × 10
7.6 × 1012
13
12
1.0 × 10
7.9 × 10
6.2 × 1012
12
11
1.9 × 10
9.9 × 10
7.9 × 1011
EUR/USD GBP/USD EUR/GBP
Panel A: Number of Market Orders
3.3 × 103
1.6 × 103
1.6 × 102
3
3
5.4 × 10
2.9 × 10
4.9 × 102
3
3
8.7 × 10
4.3 × 10
1.2 × 103
3
3
5.6 × 10
2.9 × 10
5.1 × 102
3
2
1.4 × 10
6.2 × 10
2.1 × 102
Panel D: Number of Limit Orders
3.5 × 106
3.0 × 106
2.0 × 106
6
6
4.4 × 10
4.4 × 10
2.9 × 106
6
6
6.0 × 10
5.3 × 10
3.6 × 106
6
6
4.5 × 10
4.4 × 10
2.9 × 106
5
5
6.5 × 10
5.1 × 10
3.5 × 105
Table 1: Summary statistics for the total daily (Panel A) volume of market orders, (Panel B)
number of market orders, (Panel C) volume of limit orders, and (Panel D) number of limit
orders for EUR/USD, GBP/USD, and EUR/GBP activity on Hotspot FX during May–June
2010. All volumes are in units of the counter currency.
size (i.e., the smallest permissible price interval between different orders) is 0.00001 units of
the counter currency. For further details regarding trade on the Hotspot FX platform, see
Knight Capital Group [2015].
The Hotspot FX data has several features that are particularly important for our study.
First, the tick-data files list all limit order arrivals and departures, irrespective of each order’s
ownership. This enables us to determine the complete set of all limit orders (irrespective
of their owners’ CCLs) for a given currency pair at any time during the sample period. By
determining this set at the time of each trade, we are able to calculate detailed statistics
regarding the impact of CCLs on trade prices. Second, the small tick sizes on Hotspot FX
enable us to observe market participants’ price preferences (i.e., the prices at which they
place orders) with a high level of detail. By contrast, analyzing data from platforms with
larger tick sizes (such as Reuters and EBS) would provide a more coarse-grained view of
such price preferences and and could therefore make the results more difficult to interpret,
particularly among trades for which the influence of CCLs is small. Third, all limit orders
represent actual trading opportunities that were available in the market. This is not the case
on some other FX spot trading platforms, which allow institutions to post indicative quotes
that do not constitute a firm commitment to trade. Fourth, the trade-data files include
explicit buy/sell indicators, which allow us to identify trades without the need for tradeclassification inference algorithms (such as the one introduced by Lee and Ready [1991]),
which can produce inaccurate results.
The Hotspot FX data also has some weaknesses. First, the tick-data files do not contain
information about hidden orders, so there are some trades listed in the trade-data file for
which no corresponding limit order departures are reported in the tick-data file. For each
of the three currency pairs, these trades account for approximately 5% of the total traded
volume. In the absence of further details about these trades, we choose to exclude them from
our study. Second, in some extremely busy periods, several limit order departures can occur
at the same price in very rapid succession. Therefore, for some trades, it is not possible to
determine exactly which limit order departure corresponds to a given trade. For each such
trade, we choose to associate the limit order departure whose time stamp is closest to the
9
reported trade time. We regard any incorrect associations made in this way to be a source
of noise in the data. To ensure that this approach does not influence our conclusions, we
also repeated all of our calculations when excluding all trades for which it is not possible
to associate exactly one limit order departure, and we found that all of our results were
qualitatively the same as those that we report throughout the paper.
If a market order matches to several different limit orders, each partial matching is
reported as a separate line in the trade-data file, with a time stamp that differs from the
previous line by at most 1 millisecond. In the absence of explicit details regarding order
ownership, we regard all entries that correspond to a trade of the same direction and that
arrive within 1 millisecond of each other as originating from the same market order, and we
record the corresponding statistics for this market order only once. For trades that match
at several different prices (i.e., “walk up the book”), we record the volume-weighted average
price (VWAP) as the price for the whole trade, and calculate the corresponding skipping
cost using this VWAP price.8
Although the Hotspot FX data does not include information about market activity on
Reuters or EBS, we do not regard this to be an important limitation for the present study.
Due to the greater heterogeneity among member institutions on Hotspot FX than on Reuters
or EBS (see Section 2.4), it seems reasonable to expect that CCLs have a larger impact on
trade and liquidity on Hotspot FX than they do on these other platforms. For example,
large banks trading on Hotspot FX may be unwilling to trade with small counterparties,
and may therefore assign them a CCL of 0. By contrast, the CCLs between institutions
on Reuters and EBS are likely to be much higher, to reflect the confidence in large trading
counterparties within the interbank market. By studying data from Hotspot FX, we are able
to assess the impact of CCLs among a large and heterogeneous population.
3.3
Bid–Ask Bounce
Bid–ask bounce describes the tendency for consecutive trades of a given asset to alternate
between being buyer-initiated and seller-initiated (see Roll [1984]). Because the bid–ask
spread is by definition strictly positive, the occurrence of bid–ask bounce can cause subsequent trades to occur at different prices, even in the absence of any change to the market
state.
Similarly to the application of CCLs, bid–ask bounce is a microstructural effect that
impacts price series at the trade-by-trade level. Studying all buyer-initiated and sellerinitiated trades together could cause bid–ask bounce to obscure the impact of CCLs in the
trades that we observe. Throughout this paper, we therefore study buyer-initiated and sellerinitiated trades separately, in an attempt to disentangle our results about CCLs from the
possible impact of bid–ask bounce.
4
Empirical Results
4.1
Daily Activity
As a preliminary assessment of market activity, we first consider the time series of price
changes between successive trades. Assume that the k th trade for a given currency pair on
8
Because each partial matching of a single market order is subject to the same CCLs, we regard it as
inappropriate to study each such partial matching as a separate event, as doing so would produce long
sequences of correlated data points from single market orders.
10
a given trading day occurs at time t. Let pk denote the price of this trade, and let bk , ak ,
and mk denote, respectively, the bid-, ask-, and mid-prices in the global LOB immediately
before this trade occurs. Let pk0 denote the price of the most recent trade in the same
direction (i.e., buyer- or seller-initiated) as the k th trade. Similarly, let bk0 , ak0 , and mk0
denote, respectively, the bid-, ask-, and mid-prices in the global LOB immediately before
the most recent trade in the same direction as the k th trade. The change in trade price fk
is given by
pk − pk0 , if the k th trade is a buyer-initiated trade,
fk =
(1)
pk0 − pk , if the k th trade is a seller-initiated trade.
Because the prices of trades vary across currency pairs and across time, we normalize
each price change by the mid-price (i.e., the mean of the best bid- and ask-prices in the
global LOB) immediately before the trade occurred. Specifically, we calculate the normalized
change in trade price
fk
f˜k =
,
(2)
mk
which we measure in basis points (where 1 basis point corresponds to 0.01%). Unlike fk ,
the normalized price change f˜k is scaled to be independent of the size of the underlying
exchange rate, and thereby allows like-for-like comparisons across different currency pairs.
Note, however, that this normalization makes the gap between successive values on the
pricing grid (i.e., the scaled tick size) different for each currency pair, and time-dependent.
In Figure 2, we plot the f˜k series on the first day in our sample. The plots for the other
trading days are all qualitatively similar. In these series, it is common to observe normalized
trade-price changes of more than 5 or even 10 basis points. Many of these large price changes
are isolated events that are not surrounded by other price changes with similar magnitudes,
which suggests that they are not a consequence of volatility clustering. A core aim of our
empirical investigation is to assess the extent to which these large changes in the trade-price
series are attributable to CCLs.
4.2
Skipping Costs
We next address the question of how CCLs impact the prices that institutions pay for
individual trades. As we discussed in Section 2.4, when an institution θi on Hotspot FX
submits a buy (respectively, sell) market order, the order matches to the highest-priority sell
(respectively, buy) limit order that is owned by an institution θj such that the bilateral CCL
between θi and θj is not violated by the trade. Therefore, due to the impact of CCLs, the
price at which a given market order matches is not necessarily the best price available to
other institutions at that time.
The Hotspot FX data enables us to calculate the difference between the price at which a
buyer-initiated (respectively, seller-initiated) trade occurred and the lowest price among all
sell (respectively, highest price among all buy) limit orders at the same instant. It thereby
enables us to quantify precisely the additional cost borne by the institution that submitted
the market order, as a result of CCLs preventing this institution from accessing better-priced
liquidity. We call this additional cost the skipping cost,
pk − ak , if the k th trade is a buyer-initiated trade,
rk =
(3)
bk − pk , if the k th trade is a seller-initiated trade.
11
10
0
−10
−20
08:00
09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
14:00
15:00
16:00
17:00
14:00
15:00
16:00
17:00
−20
−10
0
10
20
Panel B: GBP/USD
08:00
09:00
10:00
11:00
12:00
13:00
−10
0
10
20
Panel A: EUR/GBP
−20
EG_dP_4May$dP
GU_dP_4May$dP
Normalized Change in Trade Price (basis points)
EU_dP_4May$dP
20
Panel A: EUR/USD
08:00
09:00
10:00
11:00
12:00
13:00
Time (GMT)
Figure 2: Normalized changes in trade price f˜k for (top row) EUR/USD, (middle row)
GBP/USD, and (bottom row) EUR/GBP trades on Hotspot FX during 08:00:00–17:00:00
GMT on 4 May 2010.
12
As in Equation (2), we also calculate the normalized skipping cost
r̃k =
rk
.
mk
(4)
1.0
1.5
2.0
2.5
0.01
1e−04
1−ECDF
0.5
1e−05
0.5
EUR/USD
GBP/USD
EUR/GBP
0.0
0.001
0.8
0.7
0.6
ECDF
0.9
0.1
1.0
1
In Equation (3), the sign difference between buyer-initiated and seller-initiated trades
reflects that every trade has a non-negative skipping cost. In the extreme case in which the
CCLs are such that all institutions always have access to all trading opportunities, all trades
occur at the best quotes at their time of execution, so pk = qk for all k. In this case, all
trades have a skipping cost of rk = 0, so price formation is equivalent to that in a standard
LOB.
In Figure 3, we show the empirical cumulative density functions (ECDFs) of normalized
skipping costs r̃k . More than half of trades have a normalized skipping cost (and therefore a
skipping cost) of 0, which implies that they occurred at the best price available in the global
LOB at their time of execution. Among the other trades, the distribution of normalized
skipping costs has a similar shape for all three currency pairs. As illustrated by the log–log
survivor functions,9 this similarity extends to about the 99.9th percentile of the distributions.
Beyond this, EUR/USD has a handful of trades with extremely large skipping costs that do
not occur for the other two currency pairs.
3.0
Normalized Skipping Cost (basis points)
EUR/USD
GBP/USD
EUR/GBP
0.1
0.2
0.5
1.0
2.0
5.0
10.0 20.0
Normalized Skipping Cost (basis points)
Figure 3: (Left) Empirical cumulative density function (ECDF) and (right) log–log survivor
function (i.e., one minus the ECDF) for the normalized skipping costs r̃k of (solid green
curves) EUR/USD, (dashed orange curves) GBP/USD, and (dotted–dashed purple curves)
EUR/GBP trades on Hotspot FX during May–June 2010.
In Table 2, we list the corresponding summary statistics about normalized skipping costs
r̃k . For each of the three currency pairs, the mean normalized skipping cost is about 0.2 basis
points and the standard deviation of normalized skipping costs is about 0.5 basis points (i.e.,
0.005%). Consistently with Figure 3, these results suggest that the statistical properties of
normalized skipping costs are similar for each of the three currency pairs.
When considering the raw skipping costs rk (i.e., without normalization to account for the
mid-price), the mean skipping costs range from about 1.8 ticks (for EUR/GBP) to about
3.0 ticks (for GBP/USD). Given that the tick size for each of the three currency pairs is
0.00001 units of the counter currency (see Section 3.2), these skipping costs correspond to a
mean additional cost of about £18.00 and $30.00, respectively, for an institution submitting
9
The survivor function is given by 1 minus the ECDF.
13
Table 2: Summary statistics for the normalized skipping costs r̃k (in basis points) of
EUR/USD, GBP/USD, and EUR/GBP trades on Hotspot FX during May–June 2010.
Minimum
Median
Maximum
Mean
Standard Deviation
EUR/USD
0
0
30.31
0.19
0.46
GBP/USD
0
0
9.65
0.21
0.43
EUR/GBP
0
0
5.62
0.21
0.45
a market order with a size of 1 million units (which is the modal market order size for each
of the three currency pairs). Although these mean skipping costs are relatively small, some
trades in our sample have much larger skipping costs. The largest skipping cost that we
observe exceeds 30 basis points, and would correspond to incurring a total additional cost of
about $3630.00 when submitting a trade of size 1 million euro.
On Hotspot FX, institutions can infer the approximate skipping cost of their trades by
comparing their local bid- or ask-price (which they observe from the filtered set of limit
orders that they observe on the platform) to the prices at which other trades have recently
occurred (which they observe via their trade-data stream; see Section 2.4). Given that this is
the case, why do some institutions perform trades that have extremely large skipping costs?
We believe that the answer to this question lies in the fact that Hotspot FX serves a wide
variety of institutions with varying levels of access to other trading mechanisms, such as
direct telephone trading or voice brokers. At times when submitting a market order would
entail a considerable skipping cost, large institutions would likely instead perform the same
trade via another mechanism. By contrast, small institutions rarely have access to these
other trading mechanisms, so they may have little option other than to accept large skipping
costs as a cost of their trading. In essence, we argue that the large heterogeneity in skipping
costs that we observe is a consequence of the substantial heterogeneity in the types and sizes
of institutions that trade on Hotspot FX.
4.3
Price Changes
Our results in Section 4.2 reveal that the skipping costs borne by institutions vary considerably across the trades in our sample. The existence of some trades with a normalized skipping
cost of several basis points suggests that, due to their CCLs, some institutions have access to
a relatively small fraction of the liquidity available on the platform. This observation raises
the question of how strongly CCLs impact the price changes between successive trades (i.e.,
the fk series). This question is important because if different institutions pay considerably
different prices for the same asset at a similar time (as our results in Section 4.2 suggest
is the case), then the trade-price series could include large fluctuations that do not reflect
similar changes in the asset’s fundamental value. Therefore, the price-formation process as
observed on a platform that implements CCLs could be rather different to that on another
platform in which all institutions can trade with all others.
To assess this question empirically, we introduce the following decomposition of each
term in the fk series into two constituent parts. Using the notation that we introduced in
Section 4.1, the change in quote price gk between the k th trade and the previous trade in
14
the same direction is given by
ak − ak0 ,
gk =
bk0 − bk ,
if the k th trade is a buyer-initiated trade,
if the k th trade is a seller-initiated trade.
(5)
Given a pair of trades k and k 0 , we can similarly calculate the change in skipping cost
hk =
if the k th trade is a buyer-initiated trade,
if the k th trade is a seller-initiated trade.
(pk − ak ) − (pk0 − ak0 ),
(bk0 − pk0 ) − (bk − pk ),
(6)
The following identity provides a useful relationship between the three price-change series.
For buyer-initiated trades, observe that
gk + hk = (ak − ak0 ) + ((pk − ak ) − (pk0 − ak0 ))
= pk − pk0
= fk .
Similarly, for seller-initiated trades,
gk + hk = (bk0 − bk ) + ((bk0 − pk0 ) − (bk − pk ))
= pk 0 − pk
= fk .
Therefore, for both buyer-initiated and seller-initiated trades, it holds that
fk = gk + hk .
(7)
Equation (7) enables us to decompose each change in trade price into the corresponding
constituent change in quote price and change in skipping cost. Specifically, Equation (7)
says that the price change between any pair of trades in the same direction can be expressed
as the sum of the price change of the best quotes and the change in skipping costs of the two
trades. In this section, we perform several statistical comparisons of the fk , gk , and hk series
to quantify the relative impact of CCLs, versus that of quote revisions, on price changes.
In the left panel of Figure 4, we show a quantile–quantile (Q–Q) plot of the fk series
versus the gk series. In this plot, the quantile points cluster tightly along the diagonal. This
implies that the shape of the distribution of the fk series is very similar to that of the gk
series. In the right panel of Figure 4, we show a Q–Q plot of the fk series versus the hk
series. As the plot illustrates, the distribution of changes in skipping costs is more tightly
concentrated around 0 than is the distribution of changes in trade prices. Intuitively, this
suggests that the changes in skipping cost account for only a small fraction of the total price
change between successive trades.
To assess whether the similarities and differences highlighted in Figure 4 also hold at the
trade-by-trade level (and not only at the level of the unconditional distributions), we also
construct scatter plots of the individual terms of the series. In the left column of Figure 5,
we show scatter plots of the fk series versus the corresponding terms of the gk series. For
GBP/USD and EUR/GBP, the points cluster strongly along the diagonal, which indicates
that for each trade, the change in trade price is very similar to the change in quote price.
Some points in the EUR/USD plot occur away from the diagonal, but the vast majority of
15
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Figure 4: Quantile–quantile (Q–Q) plots for (left) changes in trade price fk versus changes in
quote price gk , and (right) changes in trade price fk versus changes in skipping costs hk for
(green circles) EUR/USD, (orange squares) GBP/USD, and (purple triangles) EUR/GBP
trades on Hotspot FX during May–June 2010. In each plot, the points indicate the
0.01, 0.02, . . . , 0.99 quantiles of the empirical distributions. The dashed black lines indicate
the diagonal.
data points still cluster along the diagonal. In the right column of Figure 5, we show scatter
plots of the fk series versus the corresponding terms of the hk series. In contrast to the
plots of fk versus gk , these plots do not reveal any visible relationship between the fk and
hk series for any of the three currency pairs. This finding suggests that application of CCLs
simply manifests as additive noise in the price-formation process.
To examine the relationships between the fk , gk , and hk series across all trades in our
sample, we also calculate the sample correlation ρ between these series (see Table 4.3). For
each of the three currency pairs, the sample correlation between the fk and gk series is
very close to 1, with a very small standard error. This quantifies the strong relationship
between changes in trade price and changes in quote price (see the left panels of Figure 5)
and suggests that changes in trade price are strongly correlated with corresponding changes
in the underlying quotes. By contrast, the sample correlations between the fk and hk series
are very close to 0, and they have similar orders of magnitude to the corresponding standard
errors. This provides further evidence that changes in skipping cost are uncorrelated with
changes in trade price.
Together, our results in this section suggest the following interpretation of Equation
(7). Mechanically, each change in trade price consists of two components: a change in
the underlying quotes and a change in the skipping cost. The change in trade price is
strongly correlated with the change in quotes, but has little or no correlation with the change
in skipping cost. Therefore, although the change in skipping cost sometimes constitutes
a considerable fraction of the total change in trade price, this impact manifests itself as
uncorrelated noise in the trade-price series.
From an economic perspective, the strong positive correlation between the fk and gk
series and the absence of significant correlation between the fk and hk series suggests that
fundamental revaluations in trade prices arise due to corresponding changes in the best
16
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Figure 5: Scatter plots of changes in trade price fk versus (left column) changes in quote
price gk and (right column) changes in skipping costs hk for (top row) EUR/USD, (middle
row) GBP/USD, and (bottom row) EUR/GBP trades on Hotspot FX during May–June
2010. The solid black lines indicate the diagonal.
17
ρ
ρ
EUR/USD GBP/USD EUR/GBP
Panel A: fk versus gk
0.94
0.97
0.99
(< 0.01)
(< 0.01)
(< 0.01)
Panel B: fk versus hk
−0.04
0.00
0.00
(0.03)
(< 0.01)
(0.02)
Table 3: Sample correlation ρ between (Panel A) changes in trade price fk and changes in
quote price gk and (Panel B) changes in trade price fk and changes in skipping cost hk for
EUR/USD, GBP/USD, and EUR/GBP trades on Hotspot FX during May and June 2010.
The numbers in parentheses are the corresponding standard errors, which we estimate by
calculating the sample standard deviation of ρ across 10000 bootstrap samples of the data.
quotes. The fk series can be regarded as a noisy observation of gk series, where the uncorrelated, additive noise is caused by the restriction of institutions’ trading activities to their
bilateral trading partners. The strength of this effect varies across institutions due to the
heterogeneity in their CCLs.
4.4
Volatility
Our results in Section 4.3 suggest that changes in trade price have little or no correlation
with changes in skipping cost. However, given that some trades have large skipping costs (see
Section 4.2), it is still possible that the volatility in the trade-price series differs significantly
from the corresponding volatility of the underlying quotes. In this section, we assess the
extent to which this is the case.
Recall from Section 4.2 that if the CCLs on a given platform were such that all institutions
could access all trading opportunities, then all trades would occur at the best quotes at their
time of execution, so fk would equal gk for all k. In this case, any volatility estimate would
produce the same result when applied to either of these series. However, because CCLs
restrict institutions’ access to liquidity, this is not the case in general. By comparing the
realized volatility of the trade-price series with the realized volatility of the corresponding
quote-price series, it is possible to quantify the difference between the volatility in the prices
that institutions actually pay for their trades to the underlying volatility observable in the
platform-wide best quotes.
In contrast to studying the prices of individual trades, for which the application of CCLs
always creates a non-negative additional cost (due to the addition of the corresponding nonnegative skipping cost), it is not clear a priori whether the application of CCLs will cause
the volatility of the trade-price series to be greater than or less than the volatility of the
corresponding quote-price series. On the one hand, it is possible for quote prices to remain
stable while trade prices fluctuate, because different institutions have access to different
trading opportunities. In this case, the volatility of the trade-price series would be greater
than that of the quote-price series. On the other hand, it is possible for quote prices to
fluctuate while trade prices remain stable, because not all trade owners have access to the
trading opportunities offered at the best quotes. In this case, volatility of the trade-price
series would be less than that of the quote-price series. The aim of this section is to estimate
the realized volatilities of these series and to determine which of these two possibilities occurs
18
on Hotspot FX.
For each currency pair each day, we estimate the sell-side trade-price volatility vA , the sellside quote-price volatility va , the buy-side trade-price volatility vB , and the buy-side quoteprice volatility vb by calculating the quadratic variation of each process, sampled at regularly
spaced intervals in trade time10 and sub-sampled at regularly spaced offsets. We consider
buyer-initiated and seller-initiated trades separately to eliminate bid–ask bounce, which
could obscure our results (see Section 3.3). For a detailed discussion of this methodology,
see the Appendix.
Following Liu et al. [2015], we present our results for K = 108 regularly spaced sampling
intervals each day (which corresponds to a mean interval length of 5 minutes, when measured
in calendar time) and sub-sampled at L = 10 regularly spaced offsets. We also repeated all of
our calculations for a variety of different interval numbers, ranging from K = 50 to K = 500,
and a variety of different numbers of sub-sampling offsets, ranging from L = 5 to L = 20.
We found our results to be qualitatively similar in all cases.
In Figure 6, we show scatter plots of the quote-price volatility versus the trade-price
volatility for each day in our sample. For all three currency pairs, and for both buyer-initiated
and seller-initiated trades, the points on the scatter plots cluster tightly on the diagonal. To
help quantify the strength of this relationship, we also calculate the corresponding sample
correlation coefficients, measured across all 30 days in our sample (see Table 4.4). In all
cases, the sample correlation is very close to 1 and has very small standard error. Together,
these results imply that each day’s quote-price volatility is very similar to the corresponding
trade-price volatility.
ρ
ρ
EUR/USD GBP/USD EUR/GBP
Panel A: vB versus vb
0.997
0.985
0.986
(< 0.01)
(< 0.01)
(< 0.01)
Panel B: vA versus va
0.997
0.993
0.985
(< 0.01)
(< 0.01)
(0.01)
Table 4: Sample correlation ρ between realized trade-price volatility versus realized quoteprice volatility for (Panel A) seller-initiated and (Panel B) buyer-initiated EUR/USD,
GBP/USD, and EUR/GBP trades on Hotspot FX during May and June 2010. The numbers
in parentheses are the corresponding standard errors, which we estimate by calculating the
sample standard deviation of ρ across 10000 bootstrap samples of the data.
In Figure 6, some points lie slightly above the diagonal, while others lie slightly below
the diagonal. To assess the deviation from the diagonal, we calculate the log-ratio
log (vB /vb ) for seller-initiated trades,
z=
(8)
log (vA /va ) for buyer-initiated trades,
for each currency pair each day. A positive value of z denotes that the trade-price volatility
exceeds the quote-price volatility, while a negative value of z denotes that the quote-price
10
In this way, the number of seconds between successive samplings of the price series varies according to the
inter-arrival times of trades. We also repeated all of our calculations by sampling the same series at regularly
spaced intervals in calendar time, and we found our results to be qualitatively similar to those that we obtain
with regularly spaced intervals in trade time.
19
0.00012
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0.00000
vA
0.00006
0.00000
vB
0.00012
GBP/USD
0.00000 0.00004 0.00008 0.00012
0.00000 0.00004 0.00008 0.00012
vb
va
0.00012
0.00006
0.00000
vA
0.00006
0.00000
vB
0.00012
EUR/GBP
0.00000 0.00004 0.00008 0.00012
0.00000 0.00004 0.00008 0.00012
vb
va
Figure 6: Scatter plots of realized trade-price volatility versus realized quote-price volatility
for (left column) seller-initiated and (right column) buyer-initiated (top row) EUR/USD,
(middle row) GBP/USD, and (bottom row) EUR/GBP trades on Hotspot FX during May–
June 2010. The solid black lines indicate the diagonal.
20
volatility exceeds the trade-price volatility. In Table 4.4, we list the mean and standard
deviation of z for buyer-initiated and seller-initiated trades for each of the three currency
pairs. In all cases, the mean value of z is slightly positive, which suggests that, on average,
the trade-price volatility on a given day typically exceeds the corresponding quote-price
volatility. However, the magnitude of this effect is less than one standard deviation, which
suggests that its strength is very weak.
z
z
EUR/USD GBP/USD EUR/GBP
Panel A: Seller-Initiated Trades
0.022
0.020
0.010
(0.049)
(0.064)
(0.116)
Panel B: Buyer-Initiated Trades
0.015
0.012
0.022
(0.045)
(0.050)
(0.114)
Table 5: Mean values of z for (Panel A) seller-initiated trades and (Panel B) buyer-initiated
trades for EUR/USD, GBP/USD, and EUR/GBP trades on Hotspot FX across all trading
days in our sample. The numbers in parentheses are the corresponding standard deviations.
Together, our results in this section reveal that on average, the realized volatility of the
trade-price series slightly exceeds that of the quote-price series, but only by a small margin.
Therefore, the vast majority of volatility in the trade-price series is also directly observable
in the quote-price series. This implies that the volatility observable in both the quote-price
and trade-price series is dominated by a common, underlying volatility that supersedes the
idiosyncratic impact of CCLs on the trade-price series.
5
A Model of Trade with CCLs
In Section 4, we used data from Hotspot FX to analyze how CCLs affect trade in a real
market. Studying historical data is, however, only one aspect of understanding how this
mechanism might affect financial markets more generally, because such analysis does not
provide insight into how these results might change were institutions to make substantial
modifications to their CCLs. Because the underlying network of CCLs in a real market
is fixed and unobservable to us, empirical analysis does not provide a way to address this
important question. In this section, we therefore complement our empirical work by introducing and studying a model of trade in which institutions assign CCLs to their trading
counterparties.
In our model, each institution updates its buy and sell prices for a single asset and
performs a trade whenever it identifies a trading counterparty offering to buy or sell at a
mutually agreeable price. A crucial feature of our model is that not all institutions can
trade with all others; instead, each institution can only trade subject to its CCLs, at prices
that depend not only on other institutions’ buy and sell prices, but also on the underlying
network of bilateral CCLs between them.
Our motivation is to provide a direct link between the institutions’ interaction topology
(via the network of CCLs) and the corresponding trade prices. By studying quantitative
relationships between the CCL network and the trade-price series, while holding all other
model parameters constant, we are able to assess how restricting the trading opportunities
available to specific institutions affects both the prices of individual trades and the volatility
21
of the trade-price series. Modelling approaches that ignore the heterogeneous impact of
CCLs would not facilitate such investigation, so our approach is a natural framework for
studying this problem.
The setting for our model is an infinite-horizon, continuous-time market populated by a
set of N institutions Θ = {θ1 , θ2 , . . . , θN } that trade a single risky asset. Each institution
θi ∈ Θ maintains a private buy-valuation Bti and a private sell-valuation Ait . The values of Bti
and Ait vary across the different institutions to reflect differences in the institutions’ opinions
regarding the likely future value of the asset, as well as differences in their inventory, cashflow, financing constraints, and so on. To focus on the impact of CCLs without considering
the impact of strategic activity (which could make our results more difficult to interpret),
we model these prices with stylized stochastic processes.
For each institution θi , we rewrite the buy and sell prices in terms of a mid-price Mti =
(Bti + Ait )/2 and spread sit = Ait − Bti , so that
Bti = Mti −
sit
,
2
Ait = Mti +
sit
.
2
We describe the dynamics of the spread in detail below; for now, we only remark that the
values of sit are constrained such that they are never smaller than some minimum value
s0 > 0.
5.1
Temporal Evolution
Before simulating the temporal evolution of our model, we choose an initial state in which
no trading is possible. We provide details of this initialization in Section 5.5. Leaving aside
the behaviour of sit and Mti at trade times, which we describe in Section 5.3, we assume that
between trades the sit are governed by
dsit = −κ sit − s0 dt,
(9)
for some constant κ > 0, and that the Mti are governed by
i
dMti = γMti dWtM ,
(10)
1
where γ > 0 is the mid-price volatility (with units (time)− 2 ) and WtMi are mutually independent Brownian motions.11
Equation (9) causes each institution’s spread to approach its minimum value s0 as time
increases after a trade. Were there no trading, the processes Mti would be geometric Brownian
motions with no drift. This model minimizes the complications associated with the mixing
of price and time scales in the model parameters; indeed, the temporal evolution is directly
influenced only by the parameter γ (whose inverse defines a timescale) and by trading via the
network of CCLs. Although a geometric Brownian motion with no drift has constant mean,
its variance increases with time. In the absence of trading, our mid-prices would therefore
disperse and spread out progressively and indefinitely over time. As we see in Section 5.3,
however, the occurrence of trades ensures that prices remain grouped together. By using
the same values of γ for each institution, we ensure that the behavior of each institution
is ex-ante identical apart from their different access to trading opportunities because of the
heterogeneous CCL network. We now discuss this feature in more detail.
11
m
A possible refinement of the model would be to include a common market
factor wT in addition to
p
i
i
m
Mi
2
the idiosyncratic noise terms, writing dMt = γMt ρi dWt + 1 − ρi dWt
, where ρi is a (common)
correlation coefficient. This adds little to our analysis, however.
22
5.2
The CCL Network
We assume that each institution θi assigns a CCL to each other institution θj . In order to
perform a time-stationary analysis of our model, we assume that each institution’s access
to trading opportunities does not vary over time, and, specifically, that it does not vary
according to the trading history. For each pair of institutions θi and θj , we model the
bilateral CCL with a binary indicator: either θi and θj are trading partners or they are not.
For simplicity, we allow trading partners to trade arbitrarily large amounts.
The CCLs can thus be represented via an undirected network in which the nodes represent
the institutions and the edges represent the extant bilateral credit relationships: θi and θj
can trade with each other if and only if the edge θi ↔ θj exists in the network. We call such
a network a CCL network. We show some example CCL networks in Figure 8.
Although using a binary CCL network represents a simplification of the impact of CCLs
in real markets, it enables us to focus on the impact of CCLs in a simple yet adequately
realistic equilibrium-pricing framework. However, we note one constraint imposed by our
model: the CCL network must be connected. If this is not the case, then disconnected
components can drift apart as there is no means to link them together.
5.3
Trading
We assume that a trade occurs at each time t∗ such that a pair of institutions θi and θj with
a bilateral CCL have prices that satisfy Bti∗ = Ajt∗ . We call this price the trade price.
Recall that in our empirical analysis in Section 4, we classify trades according to whether
they are buyer-initiated or seller-initiated. To aid comparisons between the output of our
model and our empirical results, we implement the following simple rule to classify trades.
Let
N
1 X i
M̄t =
Mt
(11)
N
i=1
denote the empirical mean of the N institutions’ mid-prices at time t. Consider a trade that
occurs between θi and θj at time t∗ and with trade price p = Bti∗ = Ajt∗ . If p > M̄t , we label
this trade as buyer-initiated, and we call θi the initiator and θj the acceptor. Otherwise, we
label this trade as seller-initiated, and we call θj the initiator and θi the acceptor.
For each trade, we think of the initiator as having submitted a market order at the trade
price, and we think of the acceptor as having owned a limit order at the trade price, which
is then matched by this market order. The initiator trades at a relatively unfavorable price,
and the fewer bilateral CCLs this institution has, the further this price is expected to be from
M̄t . We thus mimic the relative competitive disadvantage of poorly connected institutions.
Whenever a buyer-initiated (respectively, seller-initiated) trade occurs, we record the
lowest price among all institutions’ sell prices (respectively, the highest price among all
institutions’ buy prices), in order to calculate the skipping cost of the trade. We then adjust
the mid-prices of θi and θj by subtracting s0 /2 from Mti∗ and adding s0 /2 to Mtj∗ (respectively,
subtracting s0 /2 from Mtj∗ and adding s0 /2 to Mti∗ ) and widening each of sit and sjt by s0 /2.
Finally, we re-set the values of Bti∗ , Ait∗ , Btj∗ , and Ajt∗ according to these new mid-prices and
spreads. This has the effect of separating Bti∗ = Ajt∗ by 3s0 /2. All other prices (including
Btj∗ and Ait∗ ) remain unchanged. This feature models a decrease in trading desire from the
initiator and acceptor, due to the execution of the trade. At a technical level, widening the
spread removes the undesirable possibility of the initiator’s price and acceptor’s price being
equal infinitely often in an arbitrarily small interval after they first meet.
23
We now see how trading stops the mid-prices from spreading out. If the mid-prices of θi
and θj diverge by the average of their spreads, then the buy price of one trader meets the
sell price of another from below and a trade is triggered. The mid-prices are then moved
back together by s0 , reversing the previous divergence. The spreads then revert towards s0 ,
which has the effect of stopping them from growing indefinitely as trades occur.
5.4
Adjustments for Discrete Time-Stepping
We simulate the evolution of our model in discrete time, with a time step ∆t > 0, using
a simple explicit (Euler–Maruyama) differencing. In general, this implementation produces
an overshoot before we detect that a trade should take place. Therefore, whenever a buyerinitiated trade occurs between a buyer θi and a seller θj , we actually observe Bti > Ajt , rather
than Bti = Ajt . In the simplest (and, for small spreads, generic) case, no other relevant prices
are sandwiched between the buy and sell prices in question. Whenever this happens, we
deem a trade to have taken place at the end of the time step and at a price equal to the
mean of Bti and Ajt .
In a small number of cases, the overshoot caused by explicit differencing may be so large
as to create more than one trading opportunity. For example, the price moves that occur
in a discrete time step might cause θi ’s buy price to exceed the sell prices of both θj and a
third institution θk . In such a case, we first deal with the trade that occurs furthest from
M̄t . After recording this trade and changing the buyer’s and seller’s mid-price, spread, buy
price and sell price (see Section 5.3), if other trading opportunities exists, we then process
the one whose trade price is furthest from the updated M̄t , and so on until there are no
further trading opportunities to consider.
5.5
Parameter Choices and Implementation
The primary aim of our model is to understand how CCLs impact liquidity, trade prices,
and volatility. We therefore hold the values of γ, κ and s0 fixed, and study how our model’s
output varies when we vary the edges in the CCL network.
We first set M̄0 = 1 and s0 = M0 , where we take the dimensionless parameter to be
0.001, implying spreads of about 0.1%. We choose κ = 1, which sets the (otherwise arbitrary)
√
time unit as 1/κ = 1, and we choose the volatility γ = κ = 0.001 to balance the changes
in the spread and the changes in the mid-price.
We initialize the mid-prices M i by drawing them randomly from a normal distribution
with mean M̄0 and standard deviation , and we set all the spreads equal to s0 . We then run
the trade-processing algorithm described in Section 5.3 to adjust the mid-prices and spreads
of all institutions for whom this initial state would cause trading to occur. We repeat this
trade-processing step until no trading opportunities remain (i.e., until Bti0 < Ajt0 for each
pair of institutions such that θi ↔ θj ).
The final parameter in our model is the discretization time step. The dominant term in
the discrete evolution of the system is the noise term, which in relative terms√(i.e., relative to
the value of the relevant quantity at the beginning of the time step) is O(γ ∆t). Accurate
discretization of the stochastic processes requires that this term be small. Moreover, we wish
to avoid the situation where the discrete time steps regularly create multiple simultaneous
trading opportunities.
If we expect the separation of the mid-prices to be O(M0 /N ), we
√
require that γ ∆t is smaller than this. We therefore take ∆t = 1/3N 2 . This choice of ∆t is
also sufficiently small that errors associated with the numerical integration of the stochastic
differential equations are negligible.
24
1.00
0.95
Price
1.05
For the results that we present in Section 5.7, we use N = 128 institutions. We also
repeated our simulations with several different choices of N in the range 100 to 1000 (and
with appropriately modified values of ∆t), and we found that our results were qualitatively
similar in each case. For each CCL network that we study, we simulate the temporal evolution
of our model from t = 0 to t = 10. We then discard all activity before t = 2 as a burnin period, to remove the transient behaviour that occurs before the model settles into its
equilibrium state. We verified that these choices were sufficiently large by examining the
numerical stability of our results using a range of different burn-in periods and total time
lengths. We found that our results were numerically stable for all burn-in periods longer
than about t = 1 (which, for the parameter choices that we use in our simulations, is the
time scale for reversion of the Bti and Ait ), and for all total lengths greater than about t = 2.
In Figure 7, we show a single simulation run of the model, using a simple CCL network and
the parameter choices listed in Section 5.5. As the figure illustrates, the prices of subsequent
trades can deviate from each other considerably. Therefore, the model does a good job at
capturing how heterogeneity in institutions’ access to trading opportunities (which arises as
a direct consequence of their CCLs) can manifest in the trade-price series. We now turn to
a more quantitative analysis of how this effect is related to the CCL network.
0
2
4
6
8
10
t
Figure 7: An example simulation of the model, using a CCL network with N = 3 institutions
in which θ1 ↔ θ2 and θ1 ↔ θ3 , but in which θ2 and θ3 cannot trade with each other. The
blue curves indicate the institutions’ private buy valuations Bti and the red curves indicate
the institutions’ private sell valuations Ait . The black crosses indicate trades.
25
5.6
CCL Networks
For any CCL network with N nodes, the maximum possible number of edges is N (N − 1)/2.
Therefore, a CCL network with N nodes and n edges has edge density
d=
2n
.
N (N − 1)
(12)
Our model can be used to investigate any CCL network with any number of nodes and any
configuration of edges. However, to highlight the most salient features of our results, we
restrict our discussion to two classes of networks with specific topological structures.
The first class of CCL networks that we discuss are Erdős–Rényi random networks [Erdős
and Rényi, 1960], in which a specified number of edges are placed uniformly at random
between pairs of nodes. We use this class of networks to model a market in which institutions
choose their trading partners uniformly at random. Although this assumption is likely to
be a poor reflection of how institutions set CCLs in a real market, studying this class of
networks enables us to investigate the temporal evolution of our model in a simple, stylized
framework with no deterministic structure.
To construct our Erdős–Rényi random networks, we fix a choice of d, then use Equation
(12) to calculate the required number of edges n to produce this edge density. We place
these n edges uniformly at random among the N nodes of the network, then check whether
each node is connected to at least one other node. If so, we accept the CCL network; if
not, we reject the CCL network and re-draw an alternative network using the same rules.12
For a given choice of d, we create a sample of 1000 such CCL networks, then simulate 1000
independent runs of the model for each of these 1000 CCL networks, where each run uses
a different initial seed for the pseudo-random number generator. The left panel of Figure
8 shows a schematic to illustrate a single random draw of an Erdős–Rényi random network
with N = 12 institutions and n = 14 edges.
The second class of CCL networks that we consider are core–periphery networks (see
Csermely et al. [2013]). Core–periphery networks consist of two groups of nodes: core nodes
and periphery nodes. All core nodes are connected to all other core nodes. All periphery
nodes are connected to exactly one core node, such that the degree of no two core nodes
differs by more than 1. The right panel of Figure 8 shows a schematic to illustrate our
construction of a core–periphery CCL network with N = 12 institutions.
We use core–periphery networks to model a market in which a core group of institutions
assign each another very high CCLs, but in which all other institutions only have a credit line
with one large institution within the core. Several recent studies of market organization have
suggested that many large financial markets have an approximate core–periphery structure,
in which the core consists of large, international banks and the periphery consists of smaller
financial institutions such as small banks, hedge funds, or mutual funds (see, e.g., Craig
and von Peter [2014] and Fricke and Lux [2012]). Therefore, our core–periphery structure
represents an approximation of the complex structure of real markets, albeit simplified to a
convenient deterministic form.
To construct our core–periphery networks, we first fix the fraction ψ of periphery nodes.
When ψ = 0, all institutions are core institutions, so the CCL network is complete and all
institutions are able to trade with all others. For a given choice of ψ (and therefore of d),
we create a single CCL network, then simulate 1000 independent runs of the model for this
12
Recall from Section 5.2 that we restrict our attention to cases in which the CCL network is connected,
to prevent disconnected components from drifting apart.
26
Figure 8: Schematics of CCL networks. (Left panel) An Erdős–Rényi random network with
N = 12 institutions and n = 14 edges, and (right panel) a core–periphery network with
N = 12 institutions, of which 3 nodes are core nodes (shown in dark grey) and 9 nodes are
periphery nodes (shown in light grey).
CCL network, where each run uses a different initial seed for the pseudo-random number
generator.
5.7
Results
We now present our simulation results for the two classes of CCL network topologies described in Section 5.6. We studied buyer-initiated and seller-initiated trades separately by
implementing the trade-classification algorithm described in Section 5.3. In line with our
expectations (due to the symmetry of buyers and sellers in our model), our results are qualitatively the same for buyer-initiated and seller-initiated trades. To increase the size of our
sample, we present our results for all trades together (i.e., we aggregate buyer-initiated and
seller-initiated trades).
In Figure 9, we plot the number of trades that occur for each edge density d. For both
Erdős–Rényi random networks and core–periphery networks, CCL networks with lower edge
densities produce fewer trades. The intuition is simple: the lower the edge density, the
lower the number of bilateral trading partners in the population, and therefore the lower
the number of trades that occur within a given time horizon. Figure 9 also illustrates that
the mean number of trades that occur for a given CCL network depends on the network
topology, not just its edge density. Specifically, the mean number of trades that occur in a
core–periphery network is much smaller than the mean number of trades that occur in an
Erdős–Rényi random network with the same edge density. This result is interesting from
a practical perspective because it suggests that the influence of CCLs depends not only on
how many trading partners each institution has, but also on who those trading partners are.
In Figure 10, we plot the mean skipping costs among the trades that occur for each
edge density d. For both Erdős–Rényi random networks and core–periphery networks, CCL
networks with lower edge densities produce higher skipping costs. Intuitively, this result
illustrates that the more restrictive CCLs are to institutions’ access to trading opportunities,
the greater the skipping costs institutions pay for their trades.
Figure 10 again illustrates that the CCL network’s topology, and not just its edge density,
plays an important role in market dynamics. For any edge density d, the mean skipping cost
among trades for an Erdős–Rényi random network is lower than the mean skipping cost
amoung trades for a core–periphery network.
For both classes of networks, the mean skipping cost decreases rapidly as the edge density
27
80000
60000
40000
20000
Number of trades
0
Random network
Core−periphery network
0.0
0.2
0.4
0.6
0.8
1.0
Edge density
0.12
Figure 9: Mean number of trades that occur for the (green) Erdős–Rényi random networks
and (purple) core–periphery networks. The solid curves indicate the mean across all independent runs of the model and the dashed curves indicate one standard deviation.
0.06
0.00
0.02
0.04
Skipping cost
0.08
0.10
Random network
Core−periphery network
0.0
0.2
0.4
0.6
0.8
1.0
Edge density
Figure 10: Mean skipping costs of trades for the (green) Erdős–Rényi random networks and
(orange) core–periphery networks. The solid curves indicate the mean across all independent
runs of the model and the dashed curves indicate one standard deviation.
28
increases from 0 to about 0.1. For Erdős–Rényi random networks, the mean skipping cost is
very close to 0 for all edge densities above about 0.3. In this case, the impact of CCLs on
individual trade prices is very small. For core–periphery networks, the mean skipping cost
remains much higher before eventually decreasing to 0 as the edge density reaches 1 (in which
case the CCL network is complete, so all trades have 0 skipping cost by definition). Moreover,
the standard deviation of skipping costs is much larger for core–periphery networks than for
the Erdős–Rényi random networks.
In Figure 11, we plot the trade-price and quote-price volatility that occur for each edge
density d. We calculate both types of volatility using the same methodology13 as described
in Section 4.4.
1e−02
1e−03
1e−05
1e−04
Realized volatility
1e−01
Trade−price volatility, random network
Quote−price volatility, random network
Trade−price volatility, core−periphery network
Quote−price volatility, core−periphery network
0.0
0.2
0.4
0.6
0.8
1.0
Edge density
Figure 11: Realized trade-price volatility for the (green) Erdős–Rényi random networks and
(orange) core–periphery networks, and realized quote-price volatility for the given (blue)
Erdős–Rényi random networks and (pink) core–periphery networks. The solid curves indicate
the mean across all independent runs of the model and the dashed curves indicate one
standard deviation.
For the Erdős–Rényi random networks, the trade-price volatility exceeds the quote-price
volatility when the CCL network’s edge density is very low. As the edge density increases, the
trade-price volatility decreases more quickly than the quote-price density. For edge densities
larger than about 0.1, the trade-price volatility is approximately equal to the quote-price
volatility.
Intuitively, this result makes sense because the quote-price volatility is determined by
the maximum among all buy prices (respectively, the minimum among all sell prices) in
the market, and therefore is influenced only by the extreme prices among the population.
By contrast, the trade-price volatility depends on the prices of all trades conducted by
13
When studying our model, we only considered event-time estimators of volatility. We did not repeat our
calculations using calendar-time volatility estimators, because our choice of timescale is arbitrary.
29
all institutions. As the edge density across the population increases, the influence on the
number of bilateral CCLs for the extremum institution is relatively small, because only a
small fraction of all possible edges in the CCL network involve this institution. Therefore,
its influence on the quote-price series is much smaller than its influence on the trade-price
series, which is affected by all bilateral CCLs among all institutions.
For the core–periphery networks, the quote-price volatility is approximately stable across
all edge densities, except for values of d close to 0 and 1. By contrast, the trade-price volatility
first increases sharply as d increases slightly above 0, then decreases gradually, then decreases
sharply as d increases beyond about 0.95. This result illustrates that for the core–periphery
networks, the edge density has a much stronger influence on trade-price volatility than it
does on quote-price volatility.
Recall from Equation (7) and Section 4.4 that trade-price volatility can be regarded
as the underlying volatility observable in the best quotes, plus an additional contribution
caused by CCLs. Therefore, consistently with our results for skipping costs (see Figure 10),
Figure 11 suggests that as the edge density of the CCL network decreases, the strength of
this additional impact on trade-price volatility from CCLs increases, for both Erdős–Rényi
random networks and core–periphery networks.
In Figure 12, we plot the corresponding z ratios of the realized quote-price volatility and
the realized trade-price volatility (see Equation (8)). For the Erdős–Rényi random networks,
the z ratios are close to 0 (and sometimes even slightly negative) for edge densities greater
than about 0.1, but positive for edge densities smaller than about 0.1. For the core–periphery
networks, the z ratios are positive for almost all edge densities, and often have considerable
a magnitude. In these cases, the application of CCLs causes the volatility in the trade-price
series to exceed the volatility observable in the underlying quotes by a considerable margin.
When this happens, only a very small fraction of the volatility in the trade-price series is
explained by a corresponding volatility in the underlying best quotes.
5.8
Discussion of Simulation Results
Consistently with our expectations, we find that institutions trade less and pay greater
skipping costs when their CCLs cause them to experience more severe restrictions in their
access to trading opportunities. We also find that CCLs have a considerable impact on tradeprice volatility, but much smaller impact on quote-price volatility. Therefore, as the CCLs
become progressively more restrictive, the ratio z (which measures the relative magnitudes
of the volatility in the trade-price and quote-price series) increases considerably. Moreover,
by comparing different network structures, it is apparent that a CCL network’s topology,
and not just its edge density, plays an important role in the determining the extent to which
CCLs impact trade and volatility.
Aside from the decreased frequency of trading, there is no difference in the dynamic
evolution of our model for different choices of CCL networks. Therefore, the strong variability
in z ratios that we observe in Figure 12 is directly attributable to the impact of CCLs in our
model. This result is very interesting from a practical perspective, because it suggests that
even if CCLs do not impact institutions’ trading strategies, they can still strongly influence
the price-formation process, simply because they influence institutions’ access to the total
available liquidity pool.
Together, our model simulations suggest that when CCLs cause severe restrictions to
institutions’ access to liquidity, they can significantly impact both trade prices and volatility.
Two features are particularly interesting. First, as the edge density of a CCL network falls,
30
4
2
0
−2
z ratio
−4
Random network
Core−periphery network
0.0
0.2
0.4
0.6
0.8
1.0
Edge density
Figure 12: Mean ratio z of the realized quote-price volatility and the realized trade-price
volatility for the (green) Erdős–Rényi random networks and (orange) core–periphery networks. The solid curves indicate the mean across all independent runs of the model and the
dashed curves indicate one standard deviation.
both the skipping costs of individual trades and the trade-price volatility increase. This
increase is not accompanied by a similar increase in quote-price volatility, so the z ratio falls.
Second, the impact of CCLs depends not only on the edge density, but also on the specific
topology of the CCL network. Therefore, forecasting how a change in the edge density d will
impact skipping costs and trade-price volatility also requires detailed knowledge of the CCL
network’s topology. Intuitively, this result implies that understanding the possible impact of
CCLs in financial markets requires not only knowledge of how many institutions are trading
partners, but also of which institutions are trading partners with which others.
In situations where financial institutions’ CCLs severely restrict their access to liquidity,
our results suggest that it is indeed plausible that CCLs could serve to exacerbate systemic
risk, by forcing them to either trade at extremely unfavourable prices, or not trade at all.
Moreover, our results highlight that the strength of this effect is not solely determined by
the edge density of the CCL network, but also by its topology. This presents a difficult
question for regulators: how can the state of the CCL network between institutions in real
markets be monitored in real time? In a market that utilizes CCLs, any sensible forecast
of volatility must incorporate this information, so understanding both the edge density and
topology of this network will become an important step in many risk-management processes
and option-pricing methodologies.
31
6
Conclusion
We have investigated how the application of CCLs impacts liquidity and trade in financial
markets. We first addressed this issue empirically, by studying a novel data set from a
large electronic trading platform in the FX spot market that utilizes CCLs to facilitate
trade. Although we found that CCLs have little or no impact on most of the trades in our
sample, we also found that CCLs contribute a considerable skipping cost for some trades.
We argued that the substantial heterogeneity in skipping costs that we observe is a natural
consequence of the heterogeneity among the type and size of institutions trading on the
platform. By implementing CCLs, Hotspot FX can facilitate trade for a wide variety of
different financial institutions while providing these institutions with the ability to decide
for themselves whether or not to trade with specific counterparties. Because of this direct
control of counterparty exposures, there is no need for the platform to set high barriers to
entry for new participants. Indeed, the two most recent BIS Triennial Central Bank Surveys
have both noted that a new trend for direct participation from small, non-bank institutions
has been a key driver for sustained growth in FX volumes since the start of the decade [Bank
for International Settlements, 2010, 2013]. Our findings are consistent with the hypothesis
that a wide variety of different financial institutions, with varying access to liquidity, interact
simultaneously on Hotspot FX.
We also considered how CCLs impact volatility. By decomposing price changes into two
components – one attributable to changes in the best quotes, and the other attributable to
contemporaneous changes in the impact of CCLs – we observed that the volatility observable
in the trade-price serices can be regarded as the underlying volatility observable in the best
quotes, plus an additional contribution caused by CCLs. We found that CCLs contribute a
small additional volatility to the trade-price series on Hotspot FX, when compared with the
corresponding volatility observable in the best quotes.
To complement our empirical analysis, we also introduced a model of a single-asset market
in which institutions assign CCLs to their trading counterparties. In our model, the network
of CCLs provides explicit control over the interaction topology between different institutions.
By holding the model parameters fixed and varying only this network of CCLs, we were able
to study how CCLs impact trade in our artificial market. Our main observation is that both
the edge density and topology of the CCL network play an important role in determining
the skipping costs of trades and the corresponding volatility in the trade-price series. When
the restrictions imposed by CCLs are particularly severe, they can cause large skipping costs
and a high level of volatility in the trade-price series. This high trade-price volatility is not
accompanied by a similarly high quote-price volatility.
Several possible extensions to our model could help to provide further insight into the
impact of CCLs. For example, the temporal evolution of institutions’ buy and sell prices
could incorporate jumps or stochastic volatility, to more closely reflect the behaviour observed
in real markets. There are also several possible ways to incorporate strategic considerations
into the model. As one example, different institutions could implement different time-update
rules for their buy and sell prices, to reflect heterogeneity in their trading styles. As another
example, each institution could also choose how to update its buy and sell prices according to
its CCLs. For example, institutions could be less willing to revise their buy price downward
or their sell price upward if they can see from the price of recent trades that they are already
likely to be paying a large skipping cost. We anticipate that these extensions will provide
useful avenues for future research.
We believe that our results help to illuminate several important questions in regulatory
32
debate surrounding CCLs. To our knowledge, ours is the only empirical or theoretical study
to address the use of this mechanism in a quantitative framework. Our empirical results
indicate that the liquidity restrictions imposed by CCLs do not strongly impact the prices of
the vast majority of trades on Hotspot FX. We therefore argue that the application of CCLs
(and the consequent creation of skipping costs) may be regarded as a necessary consequence of
providing direct market access to a widening selection of different financial institutions, rather
than a weakness of this market design. However, our model simulations also suggest that as
CCLs become progressively more restrictive, trade-price volatility can escalate rapidly. In
such situations, it seems plausible that the application of CCLs could serve to exacerbate
systemic risk by severely restricting institutions’ access to trading opportunities. Therefore,
much like CVAs and trade novation via a CCP (see Section 2.2), CCLs do not provide a simple
solution to the problem of counterparty risk. However, our empirical results suggest that
CCLs can constitute a sensible approach to this problem under normal market conditions,
when liquidity is plentiful and CCLs are not too restrictive.
An important open question is whether (and how) CCLs might be implemented alongside
other measures to mitigate counterparty risk. For example, it is possible that a platform
could offer institutions the ability to apply CCLs, even if trades were still novated by a CCP.
This configuration could, in principle, provide institutions with a double-layered protection:
trades would still be novated by a CCP, but in the event of a CCP failure, institutions could
ensure that they were only exposed to specified counterparties, and only up to a pre-specified
limit. Before this configuration could be adopted, however, many important questions about
the possible interactions between these two mechanisms would need to be addressed. How
should trades novated by the CCP count towards a given institution’s CCLs? Should they
count at all? Or should the institutions also have a separate CCL directly with the CCP, to
limit their exposure in the case of a CCP failure? Given the relatively low impact of CCLs
that we observe on Hotspot FX, we strongly encourage further research in this area, to help
address the many open questions on this topic and to improve understanding of this deeply
interesting but hitherto unexplored market mechanism.
Acknowledgments
We thank Franklin Allen, Bruno Biais, Julius Bonart, Jean-Philippe Bouchaud, Yann Braouezec,
Damiano Brigo, Rama Cont, Jonathan Donier, J. Doyne Farmer, Ben Hambly, CharlesAlbert Lehalle, Albert Menkveld, Stephen Roberts, Cosma Shalizi, Thaleia Zariphopoulou,
Ilija Zovko, and seminar participants at the 2012 Institut Louis Bachelier Market Microstructure Conference, the 2015 Financial Risk and Network Theory Conference, the University of
Oxford, Imperial College London, the IESEG School of Management, Humboldt-Universität
zu Berlin, the Brevan Howard Centre for Financial Analysis, and the Imperial–ETH Workshop for helpful comments and discussions. MDG gratefully acknowledges support from the
James S. McDonnell Foundation, the Oxford–Man Institute of Quantitative Finance, and
EPSRC (Industrial CASE Award 08001834).
References
T. G. Andersen, T. Bollerslev, F. Diebold, and P. Labys. Great realisations. Risk Magazine,
13(3):105–109, 2000.
33
The Basel Committee on Banking Supervision. Supervisory guidance for managing risks
associated with the settlement of foreign exchange transactions. Technical report, Bank for
International Settlements, available at http://www.bis.org/publ/bcbs241.pdf, 2013.
The Counterparty Risk Management Policy Group. Toward greater financial stability: A
private sector perspective. Technical report, The Counterparty Risk Management Policy Group, available at http://www.crmpolicygroup.org/crmpg2/docs/CRMPG-II.pdf,
2005.
Appendix: Estimating Realized Volatility
In this appendix, we describe our methodology for estimating the realized variance of the
quote-price and trade-price series. For a detailed discussion of this methodology and its
empirical performance, see Liu et al. [2015].
For concreteness, we describe our methodology for buyer-initiated trades; the corresponding definitions for seller-initiated trades are similar. For a given currency pair on a
given trading day, let D denote the total number of buyer-initiated trades that occur, let
A1 , A2 , . . . , AD denote the prices of these trades, and let a1 , a2 , . . . , aD denote the ask-prices
immediately before the arrival of these trades. For a given number K of intervals, and a
given number L of sub-samples, let
T := D/K
denote the sample width and let
τ := T /L
denote the sub-sample width. For a given value of j, we calculate the sell-side trade returns
riA (j) = log Ab(i+1)T +jτ c − log AbiT +jτ c , i ∈ {1, . . . , K − 1} ,
(13)
where bxc denotes the largest integer less than or equal to x. We then calculate
vA (j) :=
K−1
X
2
riA (j) .
i=1
We repeat this process for each j = 0, 1, . . . , L − 1, and finally calculate the sell-side tradeprice quadratic variation
L−1
1 X
vA =
vA (j).
(14)
L
j=0
We calculate the sell-side quote-price quadratic variation vb similarly, using the a1 , a2 , . . . , aD
series.
To identify a suitable range of intervals K to consider, we created volatility signature
plots (see Andersen et al. [2000]).We found that these plots were stable for values of K less
than about 540 (which corresponds to T = 1 minute) for EUR/USD and GBP/USD and for
values of K less than about 200 (which corresponds to T ≈ 3 minutes) for EUR/GBP. For
our results in the main text, we use the value K = 108, which is within the stable range for
all three currency pairs.
36
A Study of Counterparty Credit Risk and Credit
Value Adjustment
by
Dong Shen
An essay submitted to the Department of Economics
in partial fulfillment of the requirements for
the degree of Master of Arts
Queen’s University
Kingston, Ontario, Canada
August 2013
copyright c Dong Shen 2013
Abstract
In this study, I examine the importance of Counterparty Credit Risk (CCR)
in financial risk management, and the role played by Credit Value Adjustment
(CVA) when pricing and hedging CCR. Regulatory frameworks and ways of
mitigating for CCR are introduced. I derive and explain different types of CVA
formula including generalized unilateral CVA formula, with/without wrongway risk, with collateral and netting, and Bilateral CVA formula. I discuss the
key components of CVA for the purpose of hedging CCR. Static hedging and
dynamic hedging are explained using examples. The credit default swap (CDS)
is introduced as the key product in the hedging of CCR. I then discuss the CDS
risks which are specific to CCR.
i
Contents
Abstract
i
Acknowledgements
ii
1 Introduction
1
2 Literature Review
3
3 Counterparty Credit Risk
5
3.1
Defining CCR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
3.2
CCR and Credit Derivatives . . . . . . . . . . . . . . . . . . . . . . .
6
3.3
CCR and Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
3.4
Mitigating CCR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
4 Pricing CCR
14
4.1
A general unilateral CVA formula . . . . . . . . . . . . . . . . . . . .
15
4.2
Without/with wrong-way risk . . . . . . . . . . . . . . . . . . . . . .
17
4.3
With collateral and netting
. . . . . . . . . . . . . . . . . . . . . . .
19
4.4
Bilateral CVA formula . . . . . . . . . . . . . . . . . . . . . . . . . .
22
5 Hedging CCR
25
5.1
Components of CVA . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
5.2
Static hedging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
5.3
Dynamic hedging . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
5.4
CDS risks in hedging CCR . . . . . . . . . . . . . . . . . . . . . . . .
29
6 Conclusion and future works
30
References
34
iii
1
Introduction
Over the last two decades, financial risk management has experienced revolutionary
changes. The changes were mostly triggered by the collapse of some large financial
institutions that had inadequate risk management, for example, a few well-known
ones, Lehman Brothers (2008), WorldCom (2002), Enron (2001), Long Term Capital
Management (1998), and Barings (1995). The losses from underestimating financial
risks are huge, and are very likely not only to destroy the financial institution itself,
but to create a chain effect to harm the whole well-being of the host country’s financial
system. Without the government rescue, there would be more disasters of huge losses
raised from insufficient risk management. American International Group Inc. is an
example, who required over US$100 billion from the US government to cover its losses.
Financial risks are normally recognized as market risk, liquidity risk, operational
risk, and credit risk etc. More recently, Counterparty Credit Risk (CCR) is considered
as one of the key financial risk factors. CCR is defined as the risk that the counterparty
to a financial contract will default prior to the expiration of a trade and will not
therefore make the current and future payments required by the contract. It is one of
the most complex risks to deal with in risk management. To fully understand CCR,
it requires a good knowledge of financial risks since it is driven by the combination of
all possible risks. The large and growing over-the-counter (OTC) derivatives market
is subject to CCR. As a common knowledge in financial field, OTC derivatives is a
powerful instrument. However, dealing with derivatives potentially can cause huge
losses without caution. This also makes CCR the key component of risk management.
Now CCR is one of the hottest topics within the financial markets with much
interest around Credit Value Adjustment (CVA)as the market value of CCR. Credit
Value Adjustment (CVA) is defined as the difference between the risk-free portfolio
value and the true portfolio value that takes into account the possibility of a counterparty’s default. CVA is one of the most important parts in the Basel Accords. The
Basel Accords refer to the banking supervision recommendations on banking regu1
lations (Basel I, Basel II and Basel III) issued by the Basel Committee on Banking
Supervision (BCBS). Under the current Basel II standards, banks are subject to a
capital charge primarily to cover the losses arising from the actual default of a counterparty of an over-the-counter (OTC) derivative contract. Under the proposed Basel
III framework, the capital charge will be enhanced by a new charge, called the Credit
Valuation Adjustment Risk Capital Charge.
Many years before 2007, most market participants had underestimated the magnitude of CCR because of the implicit of “too big to fail” assumption. The consequence
of the disastrous derivatives and financial risk management is the credit crisis in 2007
and its onwards negative waves throughout the global financial markets. A typical
example is the collapse of Lehman Brothers (2008). Many banks and other financial
institutions use CVA as the measurement of the market value of CCR. This leads to
another important aspect of current risk management - how to correctly implement
CVA system. Based on Basel Committee on Banking Supervision (2009), roughly
two-thirds of CCR losses were due to CVA losses and only one-third were due to
actual defaults. Now many banks start to price and actively hedge CVA.
The plan for the remainder of this paper is as follows. In Section 2, I provide
some reviews of recent literature concerning CCR and CVA. In Section 3, I introduce
in detail of the background knowledge needed to understand, quantify, and mange
CCR. Section 4 analyzes different types of CVA formula including no wrong-way risk,
with wrong-way risk, with collateral, with netting, and Bilateral CVA formula. Section 5 discusses the main components to be hedged in the CVA including default
probability, recovery rate, exposure, cross-dependencies, and term structure. In Section 6, I conclude and summarize some of the key areas for future development and
improvement.
2
2
Literature Review
There has been no shortage of relevant previous literature on CCR and CVA. Pykhtin
and Zhu (2006) presented the treatment of CCR of OTC derivatives under Basel
II. They showed a framework for calculating the minimum capital requirements for
CCR. They also provided a modelling framework for calculating expected exposure
(EE) profiles. Their paper discussed a general approach to capturing collateralized
exposure. This approach can be used to compute the collateral at a future time as a
function of uncollateralized exposure at another date1 . Pykhtin and Zhu introduced
two methods to compute collateral. One is a straightforward approach using Monte
Carlo simulation to determine the amount of transferred collateral. However, this
approach requires more computation time. Thus, they suggested another method
which is simple and fast by avoiding the simulation of exposure at the secondary dates.
In 2007 Pykhtin and Zhu provided a guide to modelling credit exposure and CCR.
They defined CVA as the price of CCR and discussed approaches to its calculation.
Pykhtin (2011) developed a general framework for CCR capital requirement according
to both Basel II and Basel III. The paper showed the importance for banks to calculate
a CVA capital charge. Two applications of this framework were introduced under the
market risk approach and the credit risk approach. All the works done by Pykhtin
and Zhu motivate my study on the concept of CVA risk capital charge for CCR under
Basel II and Basel III.
Arora, Gandhi, and Longstaff (2012) argued that CCR had become one of the
highest-profile risks facing by participants in the financial market. Instead of developing a framework like in the case of Pykhtin and Zhu, their paper examined CCR
pricing using an extensive proprietary data set of contemporaneous credit default
swap (CDS) transaction prices and quotes on the same underlying firm. The result
identified directly how CCR affected the prices of the credit derivatives. Under the
assumption of CDS liabilities are unsecured, they found that the price of CCR seems
1
Collateral agreement is discussed in section 3.
3
to be too small to be explained by models, but, seems consistent with the standard
market practice of requiring full collateralization. Strong evidence were found that
more and more firms began to price CCR after 2007 crisis. They also analyzed different behaviours of CDS dealers in the US, Europe, and Asia. The result showed
that CDS dealers adjusted pricing of CCR based on the industry to which the underlying firm belongs. In sum, they showed the importance of correctly pricing CCR
and discussed the changes in CCR pricing before and after 2007 financial crisis. This
also motivates me to examine about how CCR is actually priced. In section 4, I will
discuss CCR pricing in details.
Saunders (2010) focused in detail on CVA calculation by demonstrating some examples. The unilateral and bilateral CVA calculation were introduced as the market
value of CCR. He also explained the role played by CVA in risk management. Numerical examples and analytic approximations were provided in computing CVA. Saunders
used example from Pykhtin and Rosen (2010) to demonstrate a general result that
exposure correlations only matter if netting and collateral are considered when calculating the contribution of each instrument in a counterparty portfolio to the CVA.
CVA contributions (can be positive or negative) are increasing in mean exposure, exposure volatility and correlation. Saunders also discussed the hedging of CVA from
the credit risk perspective and market risk perspective. He used example from Gregory (2009) to present CVA as spread and hedging. Issues of hedging CVA were listed
in his study. Some key points are multiple sources of risk, bilateral CVA property,
and uncertainty in recoveries, etc. This leads to my study of main components of
CVA to be hedged such as recovery rate, exposure, and term structure.
Kjaer (2011) extended some results from past papers and books such as Pykhtin
and Zhu (2007), Brigo (2008), and Gregory (2009) to propose a generalized CVA
formula and extended it to derive some commonly used cases such as the regular
unilateral CVA and the regular bilateral CVA. The result could be used for unified
calculation of different types of CVAs. Kjaer used an example to show that the CVA
4
could vary widely depending on different types of agreement between counterparties.
The result showed that the generalized CVA could be hedged in the fully independent
credit model. It depended on the fact that the hedging of the counterparty risk-free
value can be funded at the risk-free interest rate. In addition, under certain situations,
CCR could be accounted by discounting with the risky curve of the counterparty. This
result made it relatively easier to calculate the CVA of portfolios with positive cash
flows.
Not like all works mentioned above, Alavian, Ding, Laudicina, and Whitehead
(2010) used another approach to demonstrate a basic and introductory review of the
components to the CVA which were derived by decomposing a single portfolio’s value
into a set of binary states. These states were a set of market values of the portfolio
(can be positive or negative), default states (default or no default) and recoveries
(recover the recovery amount or not). As they mentioned in the article there were
some issues for the application of the CVA formula such as strong assumptions on
the goodness of the input values, the interdependence of the processes, and the fact
that in reality there are many portfolios instead of a single portfolio. However, the
purpose of their paper is to encourage and motivate the readers for future work and
to represent opportunities for further developments.
3
Counterparty Credit Risk
3.1
Defining CCR
CCR is defined as the risk that the counterparty to a financial contract will default
prior to the expiration of a trade and will not therefore make the current and future
payments required by the contract. Compare to other types of financial risks, such
as market risk, credit risk, operational risk, and liquidity risk, CCR is commonly
considered as the most complicated one.
Sometimes, people treat CCR as a special form of credit risk, since for both risks
the cause of loss is due to the obligor’s default. However, there are two main features
5
that make CCR different from common forms of credit risk. First, the counterparty
credit exposure is uncertain. Counterparty credit exposure is the cost of replacing
the contract if the counterparty defaults, which is the maximum of the contract’s
market value and zero (assuming zero recovery value). The unpredictable changes
in the contract market value over time as the market moves make the current credit
exposure known with certainty, but future credit exposure is uncertain. Second,
CCR has bilateral nature, which is due to the fact that the contract market value
can change sign and either counterparty can default. To better understand CCR, it
requires knowledge of all financial risks, since it is important and necessary to identify
the nature of CCR by examining the interaction of different types of financial risks.
Therefore, it is crucial to understand and manage CCR for the future health and
growth of derivatives products and worldwide financial markets.
3.2
CCR and Credit Derivatives
Not all the derivatives products are subject to CCR. Typically, exchange-traded
derivatives are not affected by CCR, because one function of the exchange is to guarantee the contract payment by the derivative to the counterparties2 . CCR affects
financial products whose contacts are privately negotiated between counterparties.
There are two main categories of such products over-the-counter (OTC) derivatives
and security financing transactions (SFT).
The market for OTC derivatives has grown dramatically in the last decade. Table
1 shows the notional amounts outstanding in global OTC derivatives market during
the period of 2002 to 2012. According to the semi-annual OTC derivatives statistics release from the Bank for International Settlements (BIS)3 , OTC derivatives
notional amounts outstanding totalled US$633 trillion at end-December 2012 compare to US$128 trillion at end-June 2002, and it reached the peak at US$707 trillion
2
After 2007 financial crisis, there are more topics about what if the exchange itself fails to cover
its obligations. There are more regulations on exchange now, for example, it is required to hold
sufficient collateral in hand to cover all its obligations.
3
The publication is available on the BIS website (www.bis.org).
6
in 2011. By examining three-year period of growth in OTC derivatives, the rate of
growth of notional amounts outstanding was 32% annually in the period 2004-2007.
During post-crisis period 2007-2010, the rate of growth was 5% annually. The notional
amounts outstanding of OTC derivatives market at end-December 2010 was US$583
trillion, 15% higher than the level recorded in the 2007 survey.
2012/H2
2012/H1
2011/H2
2011/H1
2010/H2
2010/H1
2009/H2
2009/H1
2008/H2
2008/H1
2007/H2
2007/H1
2006/H2
2006/H1
2005/H2
2005/H1
2004/H2
2004/H1
2003/H2
2003/H1
2002/H2
2002/H1
Global OTC derivatives market1
Notional amounts outstanding, in billions of US dollars
Credit
Interest Equity
Foreign
Commodity
default Others3
Exchange
rate
linked
contracts
swaps2
Contracts contracts contracts
67,358
489,703
6,251
2,587
25,069
41,611
66,645
494,427
6,313
2,994
26,931
42,057
63,349
504,117
5,982
3,091
28,626
42,610
64,698
553,240
6,841
3,197
32,409
46,498
57,796
465,260
5,635
2,922
29,898
39,536
53,153
451,831
6,260
2,852
30,261
38,329
49,181
449,875
5,937
2,944
32,693
63,270
48,732
437,228
6,584
3,619
36,098
62,291
50,042
432,657
6,471
4,427
41,883
62,667
62,983
458,304
10,177
13,229
57,403
81,719
56,238
393,138
8,469
8,455
58,244
71,194
48,645
347,312
8,590
7,567
42,581
61,713
40,271
291,582
7,488
7,115
28,650
39,740
38,127
262,526
6,782
6,394
20,352
35,997
31,364
211,970
5,793
5,434
13,908
29,199
31,081
204,795
4,551
2,940
10,211
27,915
29,289
190,502
4,385
1,443
6,396
25,879
26,997
164,626
4,521
1,270
22,644
24,475
141,991
3,787
1,406
25,508
22,071
121,799
2,799
1,040
21,949
18,448
101,658
2,309
923
18,328
18,068
89,955
2,214
777
16,496
Grand
Total
632,579
639,366
647,777
706,884
601,046
582,685
603,900
594,553
598,147
683,814
595,738
516,407
414,845
370,178
297,670
281,493
257,894
220,058
197,167
169,658
141,665
127,509
1 Source: Bank for International Settlements OTC derivatives statistics.
2 By the request from the Committee on the Global Financial System (CGFS), the BIS was
initiating the publication of statistics on the market for credit default swaps (CDS) in 2004.
3 Estimated positions of non-regular reporting institutions.
Table 1: Global OTC derivatives market: Notional amounts outstanding
7
The notional amounts outstanding provides a measure of market size and a useful information on the structure of the OTC derivatives market but should not be
interpreted as a measure of CCR, rather it is a useful measure of the aggregate level
of activity. On the other hand, gross market values are defined as the sums of the
absolute values of all open contracts with either positive or negative replacement values evaluated at market prices prevailing on the reporting date. Thus, if a dealer’s
outstanding contracts were settled immediately, the gross market values would represent claims on counterparties. Therefore, gross market values provide a more accurate
measure of the scale of financial risk transfer taking place in OTC derivatives market.
Table 2 shows the BIS OTC derivatives statistics for gross market values during the
period of 2002-2012.
8
2012/H2
2012/H1
2011/H2
2011/H1
2010/H2
2010/H1
2009/H2
2009/H1
2008/H2
2008/H1
2007/H2
2007/H1
2006/H2
2006/H1
2005/H2
2005/H1
2004/H2
2004/H1
2003/H2
2003/H1
2002/H2
2002/H1
Global OTC derivatives market1
Gross market value, in billions of US dollars
Credit
Foreign
Interest Equity
Commodity
default
Others3
Exchange
rate
linked
contracts
swaps2
Contracts contracts contracts
2,304
18,833
605
358
848
1,792
2,217
19,113
645
390
1,187
1,840
2,555
20,001
679
481
1,586
1,976
2,336
13,244
708
471
1,345
1,414
2,482
14,746
648
526
1,351
1,543
2,544
17,533
706
458
1,666
1,789
2,070
14,020
708
545
1,801
2,398
2,470
15,478
879
682
2,973
2,816
4,084
20,087
1,112
955
5,116
3,927
2,262
9,263
1,146
2,209
3,192
2,303
1,807
7,177
1,142
1,898
2,020
1,790
1,345
6,063
1,116
636
721
1,259
1,266
4,826
853
667
470
1,609
1,136
5,445
671
718
294
1,685
997
5,397
582
871
243
1,659
1,141
6,699
382
376
188
1,818
1,546
5,417
498
169
133
1,613
867
3,951
294
166
1,116
1,301
4,328
274
128
957
996
5,459
260
100
1,081
881
4,266
255
86
871
1,052
2,467
243
79
609
Grand
Total
24,740
25,392
27,278
19,518
21,296
24,697
21,542
25,298
35,281
20,375
15,834
11,140
9,691
9,949
9,749
10,605
9,377
6,395
6,987
7,896
6,360
4,450
1 Source: Bank for International Settlements OTC derivatives statistics.
2 By the request from the Committee on the Global Financial System (CGFS), the BIS was
initiating the publication of statistics on the market for credit default swaps (CDS) in 2004.
3 Estimated positions of non-regular reporting institutions.
Table 2: Global OTC derivatives market: Gross market value
Despite the crisis related declines, the recent survey from BIS and the International
Swap and Derivative Association (ISDA) shows that the size of OTC derivatives
market is unlikely to fall dramatically and would still have a trend to grow. The
financial entities do need a solid understanding and proper measuring and managing
of CCR.
9
3.3
CCR and Regulation
The Basel Accords (Basel I 1988, II 2004, and III 2010) refer to the banking supervision Accords (recommendations on banking regulations) issued by the Basel Committee on Banking Supervision (BCBS). BCBS was established as the Committee on
Banking Regulations and Supervisory Practices by the central-bank Governors of the
group of ten countries at end of 1974, now it has 27 member countries. The Committee
does not possess any formal supranational supervisory authority. Rather, it formulates broad supervisory standards and guidelines and recommends statements of best
practice in the expectation that individual authorities will take steps to implement
them through detailed arrangements.
The most recent Basel III proposals were developed in response to the deficiencies
in financial regulation revealed by the 2007 financial crisis4 . Compare to Basel I and
II (Basel II is the one that implemented by most central banks at current time), there
are some changes focused on CCR such as promoting more integrated management
of CCR, adding the CVA-risk due to deterioration in counterparty’s credit rating,
strengthening the capital requirements and risk management of counterparty credit
exposures, providing additional incentives to move OTC derivative contracts to central
counterparties, and raising CCR management standards by including wrong-way risk.
The Basel III proposals for counterparty credit risk contain significant enhancements
related to CVA and in particular the needs to account for variation in CVA with a
regulatory CVA Value at Risk (VaR) computation.
As I mentioned early, the Basel Committee does not possess any formal supervisory
authority, and its conclusions do not, and were never intended to, have legal force.
There are difficulties to implement Basel III as an international agreement such as
facing different cultures, different structural models, complexities of public policy, and
existing regulations. In fact BCBS has received a lot of interpretation questions since
the publication of Basel III regulatory frameworks especially for the CCR section.
4
The Basel III document is available at www.bis.org/publ/bcbs189.pdf.
10
Following this, the Committee has released four sets of document of frequently asked
questions that related to the CCR sections of Basel III rules text. There are also
some critics, for example, the American Banker’s Association argues that the Basel
III proposals, if implemented, would hurt small banks by increasing their capital
holdings dramatically and then would hurt economic growth. As a result of those
implementing difficulties and critics, the BCBS extended Basel III full implementation
schedule to 2019. But those facts just reflect the caution of financial entities when
they are dealing with CCR. All the discussion above shows that banks and financial
institutions demand a solid understanding, proper measuring and managing CCR. In
the following, I will discuss some key points regarding to mitigating CCR.
3.4
Mitigating CCR
Due to the complexities of CCR, mitigating of counterparty risk is not an easy task.
The following discussions are in general sense, and we make no particular assumptions
on the type of financial institution and the type of financial instrument facing CCR.
Mitigating CCR is a task based on dealing with the key components of CCR
including credit exposure, default probability, and expected loss given default (or
equivalently to deal with recovery rate). These three key components can be treated
separately. However, two or more components are needed to be combined under
certain consideration. For example, a CCR with the combination of a small exposure
and a large default probability might be considered preferable to the one with a larger
exposure and a smaller underlying default probability. The main issue is focused on
reducing current and potential future credit exposures. For a long time before 2007
crisis, the most obvious way to mitigate CCR was to trade only with higher credit
quality counterparties. With the failure of institutions used to be considered as “too
big to fail”, this area has proved to be a deadly weakness in spite of overall strength,
that can actually or potentially lead to downfall. Here I will introduce two commonly
used methods to reduce credit exposure: netting agreements and margin agreements
11
(collateralization).
A netting agreement is a legally binding contract between two counterparties that
allows aggregation of transactions between these counterparties in the event of default.
The purpose of a netting agreement is to control the exposure to a counterparty across
two or more transactions. It is specific to transactions that may take both positive
and negative mark-to-market (MtM) values (such as in the case of derivatives). The
maximum loss for the surviving counterparty is equal to the sum of the contractlevel credit exposures. With netting the credit exposure from all transactions is the
maximum of the net portfolio or zero. The following example illustrates the impact of
simple bilateral netting on CCR. Suppose there are two trades between counterparties
A and B. Institution A has MtM values (+5) and (-4), so B has MtM values (-5) and
(+4). If there is default (assume zero recovery rate), the loss will be (+5) without
netting and (+1) with netting for A. For B, the loss will be (+4) with no netting and
zero with netting. It is clear that netting can reduce CCR for both parties. Note that
the example here is the simplest bilateral form of netting for illustration purpose. In
practice, there are technical issues such as multilateral netting, negative or positive
initial MtM, and correlation between the MtM values. Also, it is necessary to consider
other legal and operational risks created by netting.
I just showed that netting can significantly reduce CCR exposure but still limit
trading activities with certain counterparties, for example, maybe no institutions want
to trade with less credit worthy counterparties. The use of margining (sometimes
called collateral) provides the further mitigation of CCR and allowing the market to
include less credit sounds counterparties. A margin agreement is a legal collateral
support document signed between counterparties which contains the terms and conditions under which they will operate. For instance, there are two counterparties A
and B. Under a bilateral collateral agreement, base on margin call frequency (daily
margining is becoming a market standard) both counterparties mark all positions to
market and check their overall netting value. If counterparty A’s netting portfolio
12
value is positive and exceeds B’s threshold5 , A will check the terms and conditions of
the agreement to calculate the incremental exposure will be collateralized, and B is
required to post the collateral (either cash or other securities). Thus, the collateral
can be used to reduce the CCR exposure in the event of B’s default, since it is not
needed to return the collateral in this case. As the market changes, if the excess part
of uncollateralized exposure over the threshold decreases, some amount of posted collateral will be returned by the agreement. According to each counterparty’s credit
rating, there is a specified minimum transfer amount defined as the smallest amount
of collateral to be transferred with margin call. This is used to reduce the frequency
of insignificant collateral transfers.
The example described above shows that how collateralization can mitigate further CCR exposure beyond netting. Meanwhile, it can potentially create other risks
such as operational risk, market risk, and legal issues. It requires implementing with
cautions. But there is a market trend that many counterparties will not trade on an
uncollateralized basis. Margining agreement still is the most widely used method on
CCR mitigation. The use of collateral has increased dramatically since 2003, and it
reached a peak in 2008 at almost US$4.0 trillion with a growth rate of 86 percent.
According to ISDA Margin Survey 2013, the amount of collateral in circulation in
the non-cleared OTC derivatives market was US$3.70 trillion by the end of 2012, and
73.7 percent of all OTC derivatives trades were subject to collateral agreements.
Besides the two CCR mitigating methods just mentioned, there are other ways can
be used to mitigate CCR such as dealing with central counterparties and hedging. All
methods can reduce CCR, but with additional operational cost and following by other
financial risks such as liquidity risk and operational risk. Thus, mitigating CCR can
potentially be counterproductive without caution. This point was explained in detail
in Gregory (2010).
This section introduced some key aspects of CCR including definition, CCR with
5
A threshold is a level of exposure below which collateral will not be called, therefore represents
an amount of uncollateralized exposure.
13
OTC derivative market, and ways to mitigate CCR. Those points can be helpful to
better understand CCR. The next plausible question will be how to accurately price
CCR. In the following section, I will analyze some generalized formulas for pricing
CCR. This involves another important concept in risk management - Credit Value
Adjustment (CVA) which is the market value of CCR.
4
Pricing CCR
The main idea of correctly pricing CCR with a given counterparty is to calculate
the market value of the risk of all outstanding positions. It requires combining credit
exposure and default probability with a given counterparty. Credit Value Adjustment
(CVA) is defined as the difference between the risk-free portfolio value and the true
portfolio value that takes into account the possibility of a counterparty’s default.
Thus, CVA is the market value of CCR, and calculating CVA is the key for pricing
CCR.
Prior to 2007 crisis, some banks had started to price and hedge CVA. However,
the standard practice for many financial institutions was to mark the portfolios to
market without considering CVA. The cash flows were simply discounted by LIBOR
curve as risk-free values. Since the crisis, treatment of CVA has changed dramatically
in financial market. Banks currently calculate and actively hedge CVA using different
models for pricing CCR. Recently, more and more banks either set up central CVA
desk or implement CVA desk in their main business units. Managing CVA is already
a part of their trading books including daily MtM, active hedging and enforce market
risk limits.
In section 3, I mentioned the bilateral nature of CCR. This makes the calculation
of CVA more difficult. There are many models dealing with pricing CCR involved
CVA calculation. For example, Pykhtin and Zhu (2007) define CVA as the price
of CCR and discuss approaches to its calculation. Alavian, Ding, Whitehead and
Laudicina (2010) provide an overview of CVA within the context of collateralized
14
and uncollateralized trading relationships. Saunders (2010) introduces calculating
CVA, CVA and wrong-way risk, and hedging CVA. Kjaer (2011) derives a generalized
standard bilateral CVA as well as non-standard CVAs. In section 4.1, I will derive a
standard unilateral CVA formula where CVA is calculated as an adjustment to the
risk-free value of derivatives positions within the netting set to account for CCR.
4.1
A general unilateral CVA formula
In this section, I will derive an equation for a netted set of derivatives positions as an
example of general formula for CVA by using the following notations from Gregory
(2010). Let V (t, T ) be the risk-free MtM value of the netted portfolio at time t with
maturity date T . For notational simplicity, we assume that the MtM value is already
including discounting. Thus, for any s such that t < s ⩽ T , the future uncertain
MtM value of the portfolio is V (s, T ). Denote Vr (t, T ) as the associated risky value
with counterparty’s default time as τ . Based on these notations, the associated CVA
term we are looking for can be expressed as:
CVA(t, T ) = V (t, T ) − Vr (t, T )
(1)
The idea is to find the risky value Vr (t, T ) as an expression of risk-free value V (t, T )
using risk-neutral measure which is the commonly used pricing method for derivatives.
Using the indicator function:
(
I(θ) ≡
1, if θ = true
0, if θ = f alse
(2)
the risky value is:
Vr (t, T ) = EQ [I(τ > T )V (t, T )
+ I(τ ≤ T )V (t, τ ) + I(τ ≤ T ) RV (τ, T )+ + V (τ, T )−
(3)
where V (τ, T )+ = max{V (τ, T ), 0} , V (τ, T )− = min{V (τ, T ), 0}, and EQ [·] denotes
the risk-neutral expectation.
The first term of equation (3) captures the risky value without counterparty’s default. It is just the risk-free value, V (t, T ), since I(τ > T ) = 1 when the counterparty
15
does not default before T . The last two terms count the portfolio value when the
counterparty does default at time τ (t < τ ≤ T ). The second term is the value of the
portfolio that would be paid by the counterparty before the default time τ . The last
term is the payoff at default. It involves two possibilities. If the MtM portfolio value
at time τ, V (τ, T ), is positive then RV (τ, T )+ is the recovery fraction of the risk-free
value will be received by the surviving counterparty, where R is the recovery rate
defined as the proportion of a bad debt that can be recovered. If the MtM value is
negative then V (τ, T )− is the amount need to be paid from the default counterparty.
By using the relationship V (τ, T ) = V (τ, T )+ + V (τ, T )− we have:
Vr (t, T ) = EQ [I(τ > T )V (t, T )
(4)
+ I(τ ≤ T )V (t, τ ) + I(τ ≤ T ) (R − 1)V (τ, T )+ + V (τ, T )
Now, using the fact that V (t, T ) ≡ V (t, τ ) + V (τ, T ) and re-arranging equation (4)
we obtain:
Vr (t, T ) = EQ [I(τ > T )V (t, T )
(5)
+ I(τ ≤ T )V (t, T ) + I(τ ≤ T ) (R − 1)V (τ, T )
+
Notice that the first two terms of equation (5) can be combined together, since
V (t, T ) ≡ I(τ > T )V (t, T ) + I(τ ≤ T )V (t, T ), finally we have the general formula
for CVA:
CVA(t, T ) = V (t, T ) − Vr (t, T )
= EQ (1 − R)I(τ ≤ T )V (τ, T )+
(6)
As I mentioned at the beginning of this section, here we assume that the future
uncertain MtM value includes discounting. Without this assumption, equation (6)
becomes:
CVA(t, T ) = E
Q
+ B(t)
(1 − R)I(τ ≤ T )V (τ, T )
B(τ )
(7)
where B(t) is the value of money-market account at time t.
Equation (6) is a simple unilateral CVA formula given by the risk-neutral expectation of the discounted loss. It is a general framework for calculating CVA for pricing
16
CCR. However, the complex features of many financial instruments make it difficult
to calculate CVA for pricing CCR in practice. In the following parts of this section,
I will introduce some practical CVA formulas that can be used for pricing CCR.
4.2
Without/with wrong-way risk
The equations (6) and (7) in section 4.1 can be used for valuing derivatives transactions
when we make a simplifying assumption of no dependence between exposures and
default events, this also refers to no wrong-way risk assumption. I will show that under
this assumption how the CVA calculation could be expressed as the expected exposure
(EE) multiplied by default probability, where the EE is defined as the average of only
the positive MtM values in the future. But with the presence of wrong-way risk, it
is not possible to use the multiplication to calculate CVA since the co-dependence
between exposures and default probability. Wrong-way risk refers to the tendency
for exposures to be high when default probability is high and vice versa. As an
unfavourable dependence, wrong-way risk can cause a substantial increase in CCR. It
is also possible to have “right-way risk” where exposures tend to be low when default
probability is high. Compare to wrong-way risk, right-way risk is considered as a
favourable one since it will reduce CCR. In the following, I will extend equation (6)
to derive a new one that can be used in the case of no wrong-way risk.
In order to derive CVA formula without wrong-way risk, I use the approach of
survival probability and default probability which were developed by Jarrow and
Turnbull (1992, 1995). Let SP(t, T ) be the risk-neutral survival probability in the
time interval between t and T , where SP(t, T ) = E [I(τ > T )] with a negative slope.
The negative slope means that the survival probability will decrease as time increases.
Then, 1 − SP(t, T ) is the risk-neutral default probability. With a constant recovery
rate R, the equation (6) can be rewritten as expression (8) as below:
CVA(t, T ) = (1 − R)EQ I(τ ≤ T )V (τ, T )+
(8)
Since the default time τ can be any point in the interval (t, T ), we can calculate the
17
term inside the expectation by using integration over (t, T ). We have:
Z T
Q
+
CVA(t, T ) = −(1 − R)E
B(t, s)Ṽ (s, T ) d(SP(t, s))
(9)
t
where B(t, s) is the risk-free discount factor and Ṽ (s, T ) = V (s, T )|τ = s denotes the
future exposure, V (s, T ), knowing that default of the counterparty has happened at
τ = s. The negative sign in the front is because of the negative slope of SP(t, s). Under
assumption of independence between exposure and default, knowing counterparty’s
default has no effect on the expected value of the underlying positions. Therefore,
without wrong-way risk we have Ṽ (s, T ) = V (s, T ). In the case of Ṽ (s, T ) 6= V (s, T ),
usually referred as with wrong-way risk, will be discussed later. Now, equations (9)
can be rewritten as:
Q
Z T
B(t, s)V (s, T ) d(SP(t, s))
+
CVA(t, T ) = −(1 − R)E
t
Z T
= −(1 − R)
B(t, s)EQ V (s, T )+ d(SP(t, s))
(10)
t
The second line of the above equation is due to the assumption of no wrong-way
risk (no co-dependence between exposures and default probability), also the discount
factor and survival probabilities are deterministic, so we can take them out of the
expectation operator. Thus, we only have one term inside the expectation which is
EQ [V (s, T )+ ]. This is just the EE under risk-neutral measure, which can be denoted
as EE(s, T ) = EQ [V (s, T )+ ]. Finally, we have the formula for CVA without wrongway risk:
Z T
CVA(t, T ) = −(1 − R)
B(t, s)EE(s, T )d(SP(t, s))
(11)
t
Note here that, if we want to show in more general form and assuming without wrongway risk, equation (11) should be like:
Z T
Q
CVA(t, T ) = −(1 − R)E
B(t, s)EE(s, T )d(SP(t, s))
(12)
t
However, the exact discounted EE is very difficult to calculate in practice. In stead,
there is a commonly used practical framework to simulate the exposure at a fixed set
18
of simulation dates such as:
CVA(t, T ) ≈ (1 − R)
N
X
B(t, tj )EE(t, tj )DP(tj−1 , tj )
(13)
j=1
where DP(tj−1 , tj ) = SP(t, tj−1 ) − SP(t, tj ) is the marginal default probability in the
interval between date tj+1 and tj . The idea is to divide the time interval (t, T ) into
N periods denoted by (t0 , t1 , ..., tN ) such that t0 = t, ..., tN = T . Note that there is no
negative sign in the front of equation (13) since it has default probability instead of
survival probability. This gives a good approximation for CVA calculation. It requires
reasonably large N , typically N = 12 per year.
With the presence of wrong-way risk, the unfavourable dependence between exposure and counterparty’s default event will increase CVA. However, how to adjust the
equation (13) to calculate CVA under wrong-way risk is not a easy job. One approach
is to adjust the EE or default probability upwards to reflect the wrong-way risk. It
is hard to quantify the magnitude of the adjustment in CVA formula (13). Gregory
(2010) gives some examples of measuring wrong-way risk including forward trade,
foreign exchange (FX), and CDS examples. There is another theoretical approach
for calculating CVA with wrong-way risk. It requires to examine the economic relationship between exposure and counterparty’s default event. However, it is extremely
hard to define and quantify CVA in this method.
4.3
With collateral and netting
Equation (13) can be considered as stand-alone CVA formula without wrong-way risk
for a given transaction. As discussed in section 3.4, mitigating CCR is an important
part of risk management. Therefore, for any practical CVA calculation, we need to
take risk mitigation into account such as collateral and netting. In the following, I
will discuss how to modify equation (13) when considering the impact of collateral
and netting6 .
6
The rest of this section is still following the assumption of no wrong-way risk.
19
First, consider equation (13) for the case of CVA formula with collateral. There
is no influence of collateral on the default probability of the counterparty. The only
part needed to be adjusted is the expected exposure. Gregory (2010) gives a good and
detailed example to compute the CVA where various different collateral assumptions
are considered. Four cases of CVA are calculated by using same formula with different
EE profiles. The cases are no collateral, collateralization with a 10-day remargin
period, the addition of a minimum transfer amount, and the addition of a threshold.
Four different CVA calculations are compared. The results show that the impact of
collateral reduces the CVA by over five times in the case of collateralization with 10day remargin period compared to the case without collateral. The cases of minimum
transfer amount and threshold also can reduce the CVA by over half. The result also
shows that increasing in minimum transfer amount and threshold will increase the
CVA towards the case of no collateral.
In the case of CVA formula with netting, incremental CVA is needed to be calculated. Incremental CVA is defined as the difference between the CVA of a portfolio or
netting set with and without a given trade. This implies that pricing the new trade is
the key to consider the influence of netting on the CVA before and after a new trade,
that is:
∆CVA = CVA(N S, trade) − CVA(N S) = V (trade)
(14)
where N S (netting set) denotes the set of netted trades with a counterparty and
V (trade) is the risk-free value of the new trade, then CVA(N S) is the CVA for current
trades within the netting set and CVA(N S, trade) is the CVA including the new trade
in the netting set. The first equality in the above equation is just the change in CVA.
The second equality shows that the change can be represented by the pricing of the
new trade with considering the netting impact. This is because any increase in CCR
should be charged for by netting, i.e. there should be no change in the risky value of
20
all trades when adding a new trade. Therefore, we need to have:
Vr (N S, trade) = Vr (N S)
(15)
By equation (1), we can rewrite this as:
V (N S, trade) − CVA(N S, trade) = V (N S) − CVA(N S)
(16)
Using linearity of the risk-free values of the netted values, the above equation becomes:
V (N S) + V (trade) − CVA(N S, trade) = V (N S) − CVA(N S)
(17)
cancelling the terms, we have the second equality in equation (14):
V (trade) = CVA(N S, trade) − CVA(N S)
(18)
The result shows that the price (the risk-free value) of a new trade should at least
offside the change in CVA due to the CCR of the trade. Now, we can modify the
general formula (13) to get the formula for incremental CVA:
∆CVA ≈ (1 − R)
N
X
B(t, tj )∆EE(t, tj )DP(tj−1 , tj )
(19)
j=1
where ∆EE(t, tj ) is the only difference between equations (13) and (19) which is the
term for incremental change in EE within each time interval caused by the new trade.
For any financial instrument, there are some facts when comparing stand-alone and
incremental CVA. First, with netting the incremental CVA cannot be higher than
the stand-alone CVA. The reason is that netting could not increase exposure as we
discussed in section 3.4. Secondly, the incremental CVA can be negative because of
hedging effect. For example, if there is a strong negative correlation between the
existing trade and the new trade, then the new trade may lead to a loss from the
reduction in CVA. Finally, if a new trade has stronger correlation with the existing
portfolio (netting set), then it will have a higher incremental CVA. In other words, if
a new trade is strongly correlated with existing exposures, then there will be a small
change in incremental CVA.
21
4.4
Bilateral CVA formula
So far we talked about unilateral CVA formula in general. We discussed what is the
difference between without and with wrong-way risk. We also showed how to modify
the generalized formula with consideration of collateral and netting. Those formulas
are most commonly used before 2007 crisis. CVA as pricing for CCR is the charge for
a transaction received by the better credit quality counterparty. In most cases, CVA
is charged by the bank that trading with corporate counterparties according to the
credit quality of the corporate and the expected exposures in the transaction. Post
2007 crisis, “too big to fail” does not hold any more. When pricing CCR, one need
to consider the bilateral feature of CCR. CVA calculation needs to be adjusted to
consider the possibility that the bank itself may default. For the rest of this section,
I will discuss how to derive an expression for Bilateral CVA (BCVA).
Consider the case of trading between a bank and a corporate counterparty, I
will use subscript “B” and “C” to stand for the bank and the corporate counterparty.
Same as previous section, let V (t, T ) be the risk-free MtM value of the netted portfolio
at time t with maturity date T . Denote Vr (t, T ) as the associated risky value with
counterparty’s default time as τC and the default time of the bank as τB . Following
these notations, the actual default time τd is equal to min{τC , τB }, i.e. the default
time of either the bank or the counterparty that defaults first. RB and RC will be the
recovery rates for the bank and counterparty respectively. Using the same risk-neutral
measure and notations as in section 4.1, the risky value is:
Vr (t, T ) =EQ [I(τd > T )V (t, T )
+ I(τd ≤ T )V (t, τd )
+ I(τd ≤ T )I(τd = τC ) RC V (τd , T )+ + V (τd , T )−
(20)
+ I(τd ≤ T )I(τd = τB ) RB V (τd , T )− + V (τd , T )+
The above expression follows the same logic as in section 4.1. The first line gives
the risky value such that neither the bank nor the counterparty will default. The
second term is the portfolio value would be paid before any default event. The third
22
line captures the payoff if the counterparty defaults first before the maturity time T .
All those terms are similar to the unilateral CVA formula structure. The last line
of equation (20) is the extra term compared with unilateral CVA case. It gives the
payoff when the bank defaults first before the maturity time T . Notice that the bank
and the counterparty have exactly opposite payoff structure with their own default
time and recovery rate. Our goal is to find the BCVA formula as:
BCVA(t, T ) = V (t, T ) − Vr (t, T )
(21)
Same as unilateral CVA case, using relationship V (τd , T ) = V (τd , T )+ + V (τd , T )−
to replace V (τd , T )− and V (τd , T )+ in the third and fourth line of equation (20), we
have:
Vr (t, T ) =EQ [I(τd > T )V (t, T )
+ I(τd ≤ T )V (t, τd )
+ I(τd ≤ T ) [I(τd = τC )V (τd , T ) + I(τd = τB )V (τd , T )]
+ I(τd ≤ T )I(τd = τC ) RC V (τd , T )+ − V (τd , T )+
+ I(τd ≤ T )I(τd = τB ) RB V (τd , T )− − V (τd , T )−
(22)
Again, as before using the fact that V (t, T ) = V (t, τd ) + V (τd , T ). Then the second
and third terms can be combined to get I(τd ≤ T )V (t, T ). Thus the above equation
can be expressed as:
Vr (t, T ) =EQ [I(τd > T )V (t, T ) + I(τd ≤ T )V (t, T )
+ I(τd ≤ T )I(τd = τC ) RC V (τd , T )+ − V (τd , T )+
+ I(τd ≤ T )I(τd = τB ) RB V (τd , T )− − V (τd , T )−
(23)
Notice that I(τd > T )V (t, T ) + I(τd ≤ T )V (t, T ) = V (t, T ) and rearrange terms, we
finally have BCVA formula as:
BCVA(t, T ) = V (t, T ) − Vr (t, T )
= EQ I(τd ≤ T )I(τd = τC )(1 − RC )V (τd , T )+
+ I(τd ≤ T )I(τd = τB )(1 − RB )V (τd , T )−
23
(24)
If we follow the same methodology with no wrong-way risk assumption as in section
4.2, furthermore, under assumption of no default at the same time between the bank
and the counterparty, we will have similar practical BCVA formula as unilateral case.
It can be approximated as:
BCVA(t, T ) ≈ (1 − RC )
N
X
B(t, tj )EE(t, tj )SB (DPC (tj−1 , tj ))
j=1
− (1 − RB )
N
X
(25)
B(t, tj )NEE(t, tj )SC (DPB (tj−1 , tj ))
j=1
where SB and SC denote the survival probabilities of the bank and counterparty respectively; DPB and DPC are the default probabilities of the bank and counterparty.
Other terms follow the same meaning of equation (13) (unilateral case), the term
NEE(·) denotes the negative EE from the point of view of the counterparty. The first
term in equation (25) is quiet similar with unilateral case. The difference comes from
the multiplicative factor which is the bank’s survival probability times the counterparty’s default probability. It means that if the bank defaults before the counterparty,
there is no need for the bank to concern about any loss from counterparty’s default.
The second term in above equation works like a mirror image of the first one which
is from the point of view of the counterparty.
From the above argument, we can say that the BCVA equation (25) is a more
generalized case from unilateral case with the possibility that the bank itself may
default. We can find some facts and implications of the BCVA formula. First, equation
(25) is symmetric. It implies that if two counterparties agree on the BCVA formula,
the total amount of CCR in the market would be zero, i.e. the prices of CCR from
two counterparties should have same absolute value with opposite sign. Second, the
BCVA can be negative which implies that it is possible to have a higher risky value
of a portfolio than the risk-free value.
24
5
Hedging CCR
CVA as the pricing of CCR is introduced in section 4. There is an obvious question
followed previous discussion: what is the hedging of CCR associated with CVA. In
this section, I will discuss some topics dealing with the hedging of CVA.
5.1
Components of CVA
Recently, more banks start to actively hedge CVA. There are some motivations for
financial institutions to hedge CVA. When trading with counterparties, banks want
to be as flexible as possible in the types and sizes of transactions. In order to increase
earnings, financial institutions need a highly competitive pricing. An institution always tries to avoid potential huge losses from highly volatile CVA. Those goals can
be achieved by actively and efficiently hedge CVA.
Same as the case of CVA calculation, hedging CVA involves multiple market variables such as recovery rate, expected exposure, default probability, and term structure. Sometimes the correlation between some variables is needed to be considered for
hedging CVA. For example, the correlation between expected exposure and default
probability is a key component of hedging CVA with wrong-way risk. For a netted
portfolio, there may be a large number of CVA terms to be hedged. Thus, the primary
task of hedging CVA is to locate which components of CVA are the ones should be
hedged and which ones can be ignored. In practice, this is not a easy task to do. In
fact hedging of CVA probably can never be perfect. This is not only because many
different market variables get involved, but also some variables simply just cannot
be hedged. There are two main reasons make the inability to hedge some variables.
First, there may be no such financial instrument available in the market can be used
to hedge. Second, the hedging costs are too high to implement. So far we learned
the importance of identifying key components of CVA that should be hedged and
some issues facing by hedging CVA. Next, I will give a brief introduction of the key
components of CVA to be hedged.
25
For the purpose of hedging, the main components of CVA to be hedged are recovery
rate, expected exposure, default probability, cross-dependencies, and term structure.
Default event such as default probability and recovery rate usually can be hedged
by using credit default swaps (CDSs). A credit default swap is a financial swap
agreement that the seller of the CDS will compensate the buyer in the event of a
loan default or other credit event. CDS is the mostly taken form of credit derivatives
which transfers the default risk from one party to another. For example, in a singlename CDS, the protection buyer pays a premium to the protection seller for a certain
notional amount of debt of a reference entity7 . For the exposure term, one should
realize that all the variables involved exposure are needed to be hedged. For example,
both foreign exchange risk and foreign exchange volatility should be considered for
a foreign exchange forward contract. Cross-dependencies and term structure are the
components normally being ignored in practice. However, if they have a significant
influence on the sensitivity of CVA, then it is necessary to consider these terms in the
hedging of CVA.
All discussions above are in general sense. There are more hedging strategies need
to be taken into account. Gregory (2010) examines all of the possible components in
detail from the hedging perspective. Next sections will discuss two hedging strategies:
static hedging and dynamic hedging.
5.2
Static hedging
Static hedging by buying CDS protection is considered as a reasonable hedging strategy for traditional debt securities such as bonds and loans. Generally speaking, it is
an efficient hedging for the credit risk of fixed rate bonds. The idea of this kind of
strategy is quiet straightforward. For example in the hedging of a bond, the protection buyer holds the bond with certain face value and buys the same notional of CDS
protection referencing the bond issuer. If there is any credit event from the bond
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The reference entity may be a corporate, a sovereign or any other form of legal entity which has
incurred debt.
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issuer, the default loss is hedged by the CDS protection payoff . The CDS payoff will
be the bond face value less recovery.
As we mentioned before, there is almost no perfect hedge in the real world. There
are issues of the above example of hedging the default risk in a bond with a CDS.
An obvious one is the effect from the movement of interest rate in the market. With
a CDS protection settlement on a fixed notional value, the CDS hedge notional is
the par value of the bond. Thus, the hedge will lead to a loss if the bond is trading
above par prior to bond issuer’s default. A bond trading below par will have the
opposite effect. However, the static hedging of a fixed rate bond still be considered
as a reasonable one, since fixed rate bond is most unlikely to trade more than 5-10%
away from its par value.
The static hedging also can be used to hedge CCR on a derivative. This is more
complicated than the simple standard CDS case due to the uncertainty of the expected
exposure at default time. In addition, the hedge is based on the worst case exposure.
These points make the static hedging sometimes inefficient and costly. To hedge
the uncertain credit exposure at default time from the perspective of hedging CCR,
a contingent credit default swap (CCDS) is developed. A CCDS works exactly as
standard CDS with one difference that the notional amount of protection is referenced
to the MtM value of a specific transaction. Theoretically, a CCDS can be used to
perfectly hedge the CCR on a derivative since the notional amount of protection can
be linked to the exposure. However, there are practical issues make it not a popular
use in hedging CCR. First, it involves a complex documentation. All the details
of the transaction must be specified including maturity date, underlying, payment
frequency, etc. Second, a CCDS deals with a single transaction. Netting is not
available to reduce exposure. Thus, a CCDS is most likely to overhedge the trade.
Finally, to hedge CCDS itself involves same amount of work as hedging CCR, since a
CCDS simply just transfer the CCR from one party to another.
Let us reconsider the simple standard CDS protection on a bond as a static hedge.
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If we want to take interest rate effect into account, the hedge position should be
adjusted as the bond price moves with interest rate change, i.e. moves away from
the par value. It involves another hedging strategy known as dynamic hedging. It is
explained in succeeding section.
5.3
Dynamic hedging
We learned that static hedging can be used under certain conditions. Now, let us
discuss some aspects of dynamic hedging. One must realize that there will be other
risks followed by dynamic hedging. Think about a dynamic hedging with CDS protection example, there will be another risk need to be considered which is annuity risk.
In the past, CDS contracts normally traded with a running spread and no upfront
payments. This will lead to a mismatch between the duration of the bond and CDS
contract. In other words, there is a mismatch between the delta hedge and default
hedge8 . Therefore, the notional amount of CDS protection used to hedge the bond
issuer’s CDS premium will not hedge the default risk of the bond. Nowadays, trade
with fixed premium and upfront payments in CDS contracts are used to solve the
above problem. But this kind of dynamic hedging still does not work perfectly unless
the bond spread and the fixed CDS premium are the same.
The above example is relatively simple comparing to other exotics risks associated
with more complex derivatives which should be hedged dynamically. For the hedging of exotics risks in CVA, it must be achieved by implementing dynamic hedging
carefully. For example, to hedge the credit spread of a 5-year interest rate swap, it
cannot be achieved simply by a 5-year CDS protection. Even with fixed CDS premium, a movement in interest rate requires to adjust the credit hedge significantly.
The constant readjustment makes the hedging difficult and costly in practice.
Another consideration for the hedging of the CVA is the jump-to-default risk.
The jump-to-default risk refers to the risk associated with potential severe credit
8
A delta hedge is a simple type of hedge to reduce (hedge) the risk associated with the price
movements in the underlying asset.
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deterioration and /or a sudden credit event. The hedging requires at least two different
CDS protection contracts to hedge both the credit spread and jump-to-default risk.
Jump-to-default risk can potentially cause a large loss if it is not properly hedged.
All the cases discussed so far are using CDS as the hedging instrument. This is
because CDS was designed and used as a key product in the hedging of CCR and
credit risk in general. However, CDSs themselves can also have significant CCR due
to wrong-way risk and along with other risks. They should be implemented with
caution for the hedging of CCR. Next section will briefly discuss some CDS risks that
are worth mentioning.
5.4
CDS risks in hedging CCR
The credit derivatives market has grown dramatically due to the highly demand by
financial institutions for a means of hedging and diversifying credit risks. Most credit
derivatives take the form of the credit default swap (CDS). CDS is considered as the
key product in the hedging of CCR and credit risk in general. Since it is widely
used in financial market, it is important to be aware of the risks associated with CDS
contracts.
As an instrument for the hedging of CCR, CDS itself is subject to CCR as well.
Consider the case in which a CDS protection buyer buys credit protection on a reference firm from a protection seller. If the reference firm underlying the CDS contract
has an unanticipated default, then the protection seller could suddenly face a huge
loss. This could potentially drive the protection seller into distress. The protection
buyer may not receive the promised payment specified in the CDS contract. The
problem caused by the default of protection seller is one of the sources of CCR in the
CDS market.
Another CDS associated risk is recovery risk which is specific to CCR. Consider
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a case of hedge of a risky bond with a CDS contract. With physical settlement9 , the
protection buyer has the option to find the cheapest bond to deliver to the protection
seller. The cheaper bond has a lower recovery on the hedge than on the contract.
This will lead to a gain for the institution hedging CCR. This “cheapest-to-deliver
option” problem is a concern that the protection buyer may push the reference firm
into bankruptcy in order to make a gain. Another problem caused by recovery risk
is called “delivery squeeze”. Again with physical settlement, CDS protection buyers
need to buy bonds and deliver them to protection sellers for the purpose of hedging
CCR. Without well defined deliverable obligations, the strong demand of the bond will
push up the price. The higher bond price will most likely cause a loss for the institution
hedging CCR. Finally, there is a potential mismatch between settled recovery and
actual recovery10 . Almost any hedging of CCR is facing this kind of problem. The
mismatch comes from the immediate settlement of the CDS contract and much slower
recovery claim process. The more complex of a recovery process, the more uncertain
of the actual recovery. For example, if the reference firm goes into bankruptcy, the
process may take a significant time.
There are more CDS related risks than the issues we discussed. The point here is
that using CDS as an instrument for the hedging of CCR must be implemented with
careful considerations. Any mistake may lead to a large economic loss and result in a
systemic problem in financial market.
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Conclusion and future works
During the last twenty years, the collapse of some large financial institutions brought
market participants’ attention on financial risk management. Especially after the 2007
9
In physical settlement, the protection buyer will deliver to the protection seller defaulted securities of the reference entity with a par value equal to the notional amount of the CDS contract. In
return, the protection seller must make a payment of par in cash.
10
Settle recovery is achieved from a CDS auction cash settlement or from trading the debt security
in the market. Actual recovery is the final recovery paid on the debt following a bankruptcy or
similar process.
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crisis, counterparty credit risk (CCR) is commonly thought as the key financial risk.
To fully understand and manage CCR, it requires the knowledge of all other financial
risks such as market risk, liquidity risk, operational risk, and credit risk. In this
paper, I introduced some regulatory frameworks and different aspects of mitigating
CCR. The aim is to help market participants to better understand the importance of
CCR and methods can be used to deal with CCR in practice.
Correctly pricing and hedging CCR become the key component of the risk management. There have been many models proposed for pricing CCR. I first introduced
the credit value adjustment (CVA) as the measure (pricing) of CCR. Then, briefly
discussed some past works such as Pykhtin and Zhu (2007) and Kjaer (2011). I used
risk-neutral pricing CCR. A generalized unilateral CVA formula is derived and then
be modified to derive other types of CVA formula such as with/without wrong-way
risk, with collateral and netting, and Bilateral CVA formula. The formula is generalized meaning that it is not specified to certain financial instrument. It helps to give
a general idea about how to price CCR in risk-neutral measurement.
For the hedging of CCR, I discussed some key components of CVA should be
hedged and the importance of identifying those components. The credit default swap
(CDS) was introduced as the key product in the hedging of CCR. I used a CDS
protection contract on a risky bond example to demonstrate two hedging strategies:
static hedging and dynamic hedging. Some practical hedging issues were explained
along with the example. I discussed some of the CDS risks which are specific to the
hedging of CCR. The purpose is to help market participants to better understand the
hedging of CCR.
Finally, future research is required to better understand and manage CCR. Financial risk management has experienced revolutionary changes over the last two decades.
It is most likely that the CCR also will experience a similar revolution. In financial
market, the CCR is still facing lots of challenges such as implementing CVA system,
controlling credit exposure, and the need of well designed regulatory frameworks.
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There is much work to do to build and maintain a healthy financial market.
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