Counterparty Credit Risk modelling under
Basel III and FRTB framework
A REGULATORY PERSPECTIVE ON CREDIT VALUE ADJUSTMENT(CVA)
A Master Thesis by
Charalampos Bellos
Charalampos.bellos@post.au.dk
Supervisor
Professor
Dr.Christian Schmaltz
Department of Economics and Business
SPRING 2016
MASTER OF SCIENCE IN FINANCE
AARHUS SCHOOL OF BUSINESS AND SOCIAL SCIENCES
AARHUS UNIVERSITY
Abstract
Counterparty risk and the measurement of this risk through CVA(Credit
Value Adjustment) combines the quantification of market and credit risk
together.The objective of this thesis is to measure the regulatory CVA for
an Equity Call option that trades in the OTC derivative market and to
compute the CVA capital charges under the standardised and the
advanced approach that Basel III proposes.CVA represents a substancial
risk for the financial institutions and the financial system and as such
must be capitalized.The main research question that we will examine in
this paper is whether the CVA capital charges are penalizing the use of
OTC derivatives within a bank and Basel III encourages the use of Central
Counterparties for clearing(CCPs) derivatives instead of bilateral
transactions.As we will aim to investigate further under Basel III
framework,capital requirements for counterparty risk will be large thus
the use of hedging for capital relief will be thoroughly discussed and
analyze the role of a CVA desk within a bank.Last,the Basel Committee for
Banking and Supervision(BCBS) is introducing a new methodology for
measuring credit exposures(SA-CCR) for OTC derivatives replacing both
the old methods such as the Current Exposure Method(CEM) and the
Standardized Approach(SM) where we will highlight some advantages
and disadvantages of the SA-CCR compared to the Internal Model
Method(IMM).
Keywords:Credit value adjustment,Basel III,Capital RequirementsRWA,Central Clearing Counterparties,Over-The Counter derivatives
markets(OTC),collateral-ISDA Master Agreement,credit exposures,Monte
Carlo Simulation,Stochastic processes,Value-At-Risk.
i
Acknowledgements
I am indebted to Professor Dr.ChristIan Schmaltz for his useful advice
during our many discussions that have helped me enormously in shaping
my ideas regarding how to implement the financial models.Last,I would
like to thank my parents for their support and love during all the years of
my studies.
ii
Abbreviations
ATM
BCBS
BIS
CCDS
CCP
CCR
CDF
CDS
CRD
CSA
CVA
DVA
EAD
EE
Eff.EE
Eff.EPE
EQ
G10
G20
IFRS
IMM
IRB
ITM
LGD
MC
MtM
OTC
OTM
PD
PDF
PFE
RC
RW
RWA
SA-CCR
VaR
At-The-Money
Basel Committee for Banking and Supervision
Bank for International Settlements
Contingent Credit Default Swaps
Central Counterparty
Counterparty Credit Risk
Cumulative Distribution Function
Credit Default Swaps
Capital Requirements Directive
Credit Support Annex
Credit Value Adjustment
Debit Value Adjustment
Exposure-at-Default
Expected Exposure
Effective Expected Exposure
Effective Expected Positive Exposure
Equity
The Group of Ten
The Group of Twenty
International Financial Reporting Standards
Internal Model Method
Internal Ratings Based Approach
In-The-Money
Loss Given Default
Monte Carlo Simulation
Mark-to-market
Over-The-Counter
Out-The-Money
Probability of Default
Probability Distribution Function
Potential Future Exposure
Replacement Cost
Risk weight
Risk-Weighted Assets
Standardised
approach
for
measuring
Counterparty credit exposures
Value-at-Risk
iii
WWR
FRTB
KVA
Wrong Way Risk
Fundamendal Review of the Trading Book
Kapital Valuation Adjustment
iv
CONTENTS
Table of Contents
1.Introduction ...........................................................................................4
1.1 Problem Statement and Research Question ...................................5
1.2 Delimitations .......................................................................................7
1.3 Structure ..............................................................................................8
2.Overview of the Regulation ....................................................................9
2.1 The Basel History Evolution...............................................................9
2.2 Capital Basics ..................................................................................11
2.2.1 Definition of Credit Risk and Counterparty Credit Risk .................12
2.2.2.1 Regulatory Credit Risk Capital ...................................................14
3. Credit Exposure Model Definitions ......................................................18
3.1 Netting ............................................................................................19
3.2 Exposure At Default(EAD) ...............................................................23
3.2.1 Collateral......................................................................................23
3.2.2 EAD under the IMM .....................................................................25
3.2.3 EAD under the SA-CCR Method ....................................................27
4 The Need for a New Capital Charge(CVA Capital)...............................31
4.1 The Standardised Formula ..............................................................31
4.2 The Advanced CVA approach ..........................................................33
5. Black-Scholes Model for an Equity Call Option with Counterparty Credit
Risk(CCR) .................................................................................................36
5.1 The Black-Scholes Framework.........................................................36
5.2 Black-Scholes Pricing Formulas For Options ....................................38
5.3 Data and Comparative analysis of EADIMM and EADSA-CCR ................39
5.4 Capital Cost Comparison of Bilateral Transactions and Centrally
Cleared Trades(CCP) .............................................................................42
6. CVA under the Fundamendal Review of the Trading Book(FRTB) ........45
7. Conclusions and Discussion .................................................................48
References...............................................................................................50
1
CONTENTS
2
`
List of Figures
Figure 1: Counterparty Credit Risk(CCR) as shown in the figure lies in the area where
market and credit risk intersect ....................................................................................13
Figure 2 In this figure above is depicted the future Exposure of a Call option under a
scenario across time that has been generated by Monte Carlo ....................................18
Figure 3 In this figure above it is depicted the Expected Exposure of a Call option
across time under the previous simulation path.It is clearly seen as the average of all
exposures across time. ..................................................................................................20
Figure 4 The Expected Positive Exposure of a Call option that is the weighted average
of the simulated Expected Exposures.The weights are the time buckets. ...................21
Figure 5 In this figure it is illustrated the Effective EE and it is observed that the
Effective EE is always above the EE thus a non-decreasing EE as defined earlier. .......22
Figure 6 Illustration of Effective EE and Effective EPE. ..................................................22
Figure 7 Illustration of the red area is the collateral posted by the counterparty.When
the value of the option at day 73 is above the threshold,the counterparty is subject to
a margin call thus the exposure is collateralized. .........................................................25
Figure 8 Collateral Mechanics........................................................................................28
Figure 9 Simulation of 10 paths of the credit spreads of Danske Bank A/S that are
inputs in the calculation of the advanced CVA VaR approach(10-day time horizon at a
99% confidence level) ....................................................................................................33
Figure 10 Illustration of Geometric Brownian Motion Stock Paths of Danske Bank A/S.
.......................................................................................................................................38
Figure 11 Illustration of a bilateral OTC transaction between the two
counterparties.This transaction is subject to a CVA capital charge. .............................42
Figure 12 Illustration of a centrally cleared transaction(CCP trade) between the CCP
and the two clearing members. .....................................................................................43
3
Chapter 1
1.Introduction
During the global financial crisis a significant but so much underestimated
financial risk(CVA risk) was brought to surface.At that time(2007-2008),
highly rated Triple A1 counterparties such as Lehman Brothers(4th biggest
investment bank in the USA),American International Group(AIG) were
perceived by the financial industry as counterparty risk free in the
transactions that they were involved and the so called too big to fail
seemed to be the case.Reality though as most of the times proved to be
different.After the collapse of those big financial institutions huge losses
of billions of dollars were written down by the majority of the solvent
financial institutions.In the fear of having more financial institutions at
default due to the interconnectedness of the financial system,Sovereigns
started to bail out systemic banks from not collapsing.The financial mean
that the latter used was tax-payers money.This action has created a huge
debate on the sociopolitical enviroment on whether Sovereigns should
use tax payers money in order to save financial institutions that are in
stress and not let them to default.On the contrary,Sovereigns argue that
they used tax-payers money in order not to create more chaos in the
banking system.It was obvious that something went completely wrong
and market losses(CVA losses) arising from credit deterioration of the
financial institutions were not measured at all by any regulator.
In the post crisis era the Basel III,A global regulatory framework for more
resilient banks and banking systems document mentions that the ‘’Markto-market2(MtM) losses due to Credit Value Adjustments in OTC
derivative markets were a greater source of losses than those arising from
outright defaults”(Basel III,2009).Therefore as Brigo(2012) mentions’’ The
valuing of risk of default is more dangerous than the risk itself’’.In the
Basel document it is explained also that only one third of losses were due
to actual defaults and the two thirds were due to the uncertainty of
default on Mark-to-market-positions(MtM).Because of this, Basel III
introduces a capital charge on CVA volatility,the so-called CVA VaR.
1
Triple A rating is the highest rating that a financial institution can receive from external rating
agencies.The financial crisis revealed how fragile were those ratings when counterparties defaulted
while been rated as triple A some time ago.Thus the regulators propose that banks must rely on
internal modelsto evaluate counterparties and not in external ratings that proved to be an anecdote
during the financial crisis.
2
The Mark-to-market with respect to a particular counterparty defines what could potentially be lost
today.MtM may be positive or negative depending if the value of the transaction is in an institution’s
favour or not.Jon Gregory(2012)
4
`
Chapter 1
CVA stands for Credit Value Adjustment and the definition of it,in the fair
pricing of a financial derivative value, is:
 Risky value=Risk-free value minus Credit Value Adjustment(CVA).
There are three versions of CVA that banks have to silmutaneously worry
about.The first is the Accouning CVA and it is defined as the official CVA
that is in the books and records.The second version is the Economic CVA
as seen from the trading desk that the bank uses for pricing Counterparty
risk into derivatives and the third version is the Regulatory CVA as we are
more interested in this thesis.The latter is the CVA that measures the
capital requirements due to CVA volatility over the time horizon of the
trade.Thus the Regulatory CVA is not a static banking tool but a dynamic
one especially when the counterparty’s credit spread widen.
We will conclude in this thesis that it is an extremely difficult task to align
the three CVA versions.Factors such as the alpha multiplier,IMM method
and historical calibrations in the models as we will define further in the
thesis forces the Regulatory CVA to be more conservative than the other
two versions.
As we have introduced the definition and significance of the CVA in the
OTC derivatives market,it is clearly seen that from now on all values of
derivatives are risky due to that the counterparties in the transactions
can either default or credit deteriorate to an extent where the derivative
will lose it is market value.In other words,the market price of
counterparty risk is the CVA.
For our regulation purposes the quantification of CVA and VaR(Value-atRisk) poses a significant challenge since both CVA and VaR are complex to
determine.
1.1 Problem Statement and Research Question
After the 2008 financial crisis,the Financial Stability Board(FSB) had
several meetings with the G-20 leaders for implementing reforms that
would strengthen the financial stability and reduce the systemic risks of
the financial system.The Board argues that the Over-The-Counter market
for derivatives was responsible for the collapse of the financial system on
2008 and proposed significant OTC reforms that will have a huge impact
5
`
Chapter 1
on the counterparties that transact in the OTC markets.On September
2009 in a meeting in Pittsburg,the heads of the 20 nations decided that
all OTC standardised derivative contracts should be pushed into Central
Clearing and the Financial Stability Board should monitor the
implementation of the market process.
In Europe,the Bank for International Settlements(BIS) is a member of the
Financial Stability Board(FSB) and following the regulatory policies of the
Board for Systemic risks, the Basel Committee of Banking and
Supervision(BCBS) announced on 2012 the new CVA capital charges.
Motivated by the above,the Research Question is as follows:
RQ:Are the new CVA capital charges imposed by the Regulators on banks
going to re-shape the business strategy of the banks in the Over-TheCounter Derivatives(OTC) Markets?
In order to thoroughly examine the RQ the following Sub Research
Questions(SRQ) will be evaluated.
SQR:Does the advanced CVA VaR approach produce lower capital
charges(meaning less capital requirements for the banks) than the
standardised CVA VaR approach?
SQR:Is the new CVA capital charge(CVA VaR) a risk sensitive capital
charge methodology?
SQR:How transactions of derivatives that are cleared in the Clearing
Counterparties(CCPs) benefit with less capital requirements?
SQR:Are the Clearing Counterparties(CCPs) the new too big to fail in the
financial system?
The research question will be investigated by setting up two stochastic
models for measuring the CVA capital charges for a European Εquity Call
option performing Monte Carlo simulation for both the credit
exposures(option values) and for the credit spreads of the counterparty
that we transact with according to the Basel regulation rules.When
implementing the different models,the quantitative part w.r.t
6
`
Chapter 1
present,gathering the data and making the simulations will be conducted
using Microsoft Excel and for the more technical parts on calibration of
the models to the market data MathWorks MATLAB will be used.Also,an
overview of the MATLAB codes will be provided in the Appendix.
1.2 Delimitations
In this thesis we are interested in the CVA risk as it is in the current
framework for banks implementing the Basel III regulatory reforms.Due
to new upcoming regulations,there is a proposed revised framework for
CVA capital charges under the Fundamendal Review of the Trading
Book(FRTB) albeit it is not finalized yet.Thus,we will present the new
market risk methodology under the FRTB that is under debate and the
new approaches in a Chapter, covering only the theoretical
framework.Moreover,we will follow Basel policies that ignore the DebitValue Adjustment(DVA) due to the fact that the regulators argue that it
creates perverse initiatives at reducing the capital requirements for a
bank and increasing gains while the bank’s own credit quality is
deteriorating.The DVA adjustment lies more to the scope of the pricing
CVA and in the accounting fair value adjustments(IFRS).Furthermore,we
are using the classical pricing theory a la Black Scholes for the credit
exposure model and this has some limitations with respect to the
assumptions of the model and most importantly concerning the volatility
of the model that remains constant through time.For a more realistic
model but also more complex one and for a future research the volatility
of the Black-Scholes model could be stochastic but this is out of the scope
of this thesis.Last,we will refer to the backtesting process of the models
but due to time limitations of the thesis we would not address this issue
in an extensive manner but nevertheless it is of a great interest and it
remains again for a future research.
7
`
Chapter 1
1.3 Structure
The thesis is structured as follows.In the first Chapter is the
introduction,the problem statement and the research question with the
delimitations.
The second Chapter of the thesis will contain an overview of the
regulation and the Capital Basics along as defining the Counterparty
Credit Risk(CCR) enviroment.
In the third Chapter we will introduce the definition of Exposure-AtDefault(EAD) under the Internal Model Method(IMM) and the new SACCR method.Exposure-at-Default is the major component in the default
risk and CVA capital charges thus it needs an extensive treatment.
In the fourth Chapter we will model and explain the methodology of the
standardised and the advanced approach of the CVA capital
charges.Moreover,we will refer to the hedging aspects of Counterparty
Credit Risk that the two approaches have embedded for capital relief and
highlight the role of a CVA desk in the bank management.
In the Fifth Chapter,we will present the stochastic models that we
implemented for measuring the CVA capital charges of a European equity
Call option that trades in the OTC market which will be followed by a
comparative analysis of the results.
In the Sixth Chapter,we will introduce the new proposed revised CVA
framework under the Fundamendal Review of the Trading Book(FRTB)
and the future capital impact that it is going to have on banks.
At last,on Chapter Seven, we will conclude on the thesis and provide
answers in the research question and the sub research questions, which
will be followed by a discussion on the future regulations and
implications that they will create in the banking system.
8
`
Chapter 2
2.Overview of the Regulation
They say that when a butterfly move its wings,it has the power to create
a hurricane somewhere else in the world.This example in physics is
known as the butterfly effect3 and we will investigate in this paper how
important this example is when it is applied to Finance and
Regulations.This idea theorises how a small change(in this paper the CVA
capital charge) in a complex system(financial system) can have large
impacts everywhere in the world.As the butterfly in our example is the
Basel Committee for Banking and Supervision(BCBS4),many argue that
when the Committee flap its wings great regulatory evolutions impact the
financial services industry.(BASEL III framework,The Butterfly effect)
2.1 THE BASEL HISTORY EVOLUTION
International banks operate in many countries worldwide.To minimize
the effect that conflicting regulatory policies in different countries may
have on international banks,the Basel Committee was founded by the
Central banks of the G105 countries in 1974.Located in Basel
Switzerland,the role of the committee is to formulate principles and
supervisory standards that reflect its view on the current best
practice.Current members include most of the developed nations of the
world albeit It is up to the Central Banks of the individual nations to
follow the BCBS guidelines and develop their national rules.
The Basel framework is a capital adequacy framework that through
prudential regulation seeks to establish a safer environment for
banks.For the first time in 1988,the BCBS introduced a capital
measurement framework known as the Basel Capital Accord or else Basel
3
The Basel III framework ‘’Butterfly effect’’ from Deloitte.
Basel Committee for Banking and Supervison.The Committee is located at the Bank for International
Settlements(BIS) in Basel,Switzerland.
5
The Group of Ten is made up of eleven industrial countries
(Belgium,Canada,France,Germany,Italy,Japan,the Netherlands,Sweden,Switzerland,the United
Kingdom and the United States) which consult and co-operate on economic,monetary and financial
matters.
4
9
Chapter 2
I.Since then,banks have to take into consideration about five different
Capital adequacy Accords:
 Basel I(1988): RWA6=12,5*M7*VaR8+Specific risk-add9 on.
 Basel ll & 2,5(2004 &2010)=In this framework the regulators added
Stressed VaR to overall VaR requirements.Also,they added for
credit derivatives two new measures –the Incremental Risk
Charge(IRC) and the Comprehensive Risk Measure(CRM)-in order
to measure better the defaults and the credit spread dynamics
 Basel III(2011)=This capital framework and the implementantion of
it by banks addresses to the topic of our thesis.In 2011,the
regulators added a VaR on CVA to measure the potential mark-tomarket(MtM) losses that the Basel II framework failed to
capture.Also,in this document it is introduced new liquidity and
leverage ratios.
 Basel 4=Future regulatory changes concerning the substitution of
VaR with other risk measures.
After Basel I was implemented in the majority of the countries(G10 and
afterwards G2010),Gregory(2012)11 argues that banks find ways to game
the system and since Basel I was lacking risk sensitivities,banks reduced
their minimum capital requirements without reducing their actual
risks.Basel replied to this regulatory arbitrage and issued a new
document that is entitled as “International Convergence of Capital
6
Risk weighted Assets(RWA) is a bank’s assets or off balance sheet exposures weighted according to
risk.
7
M=A supervisory multiplier greater than 3.
8
VaR=Value-at-Risk measure defines risk as mark-to-market loss on a fixed portfolio over a fixed time
horizon.In simple words it means if things go wrong how much we are going to lose.
9
Add-On=It measures the Potential Future Exposure for a financial instrument in a conservative
manner that the regulators have pre determined.
10
The Group of Twenty(G20) Finance Ministers and Central Bank Governors was established in 1999 to
bring together industrialised and developing economies to discuss key issues in the global economy.
11
Jon Gregory “Counterparty Credit Risk and the Credit value adjustment-A Continuing Challenge for
Global Financial Markets”(2012).
10
`
Chapter 2
Measurement and Capital Standards’’(BCBS,2006).This Capital Accord
consists of three pillars:
 Pillar 1,The minimum capital requirements:the first pillar contains
specific rules on how banks should calculate the minimum capital
requirements that have to hold.This Pillar is referred also to the
regulatory credit risk capital that we will address in the following
chapters of this paper and most importantly on how to calculate
Exposure-at-Default according to the regulators.
 Pillar 2,The Supervisory Review:The Committee supervises banks
and monitors their risk activities in order to evaluate whether
banks should hold increased level of capital than Pillar 1.
 Pillar 3,Market Discipline:Banks must make public disclosure about
the methods that they use to calculate their regulatory capital and
provide transparency in their adequacy capitalisation.
In the following paragraphs and chapters we will describe the Capital
Basics of the first pillar(the minimum capital requirement) of Basel II and
converge the regulatory credit risk capital with the Counterparty credit
risk(CCR) capital that Basel III has introduced through the CVA
risk.Therefore, we will link both types of capital that banks must hold and
model the Total Counterparty Credit risk charge under the new revised
Basel III framework.
2.2 CAPITAL BASICS
A key form of regulation is to evaluate and determine the minimum
capital amount that banks must set aside to protect themselves from
going insolvent in stress market times.Capital acts as a buffer to absorb
losses during stress periods in the financial markets.These losses can
come from market risk exposure for example movements in the interest
rates or any other financial variable that affect the bank’s holding of
securities.Negative losses can come also from credit risk or else lending
risk,for example a counterparty defaults on its loan or as we will model
later in this thesis those losses can be CVA losses meaning negative losses
from a financial derivative transaction that the bank is booking NOT
because the counterparty actually defaults but because the pricing of this
11
`
Chapter 2
financial contract has changed for the worst of the bank.In other
words,CVA losses arising from deterioration12 of the credit worthiness of
the counterparty.
Eventually,as it is argued by Gregory(2012) the regulatory capital
requirements determine the leverage under which a bank can
operate.Banks are known as to strive for more and more profits so
accordingly they want to hold the minimum capital requirements in order
to maximize their business and manage their risk appetite13.It is a balance
that the regulators have to determine in order for the bank to hold high
capital reserves and therefore low probability of default of the bank but
not so severe as to penalize the bank and make it less competitive among
the other international banks.Last,the Capital that a bank must hold for
regulatory purposes is tiered into various quality grades:
 Tier 1:Common Equity and Retained Earnings.
 Tier 2:Supplementary capital that includes items such as
revaluation reserves,undisclosed reserves,hybrid instruments and
sub-ordinated debt.Tier 2 capital is considered less reliable than
Tier 1.
 Tier 3:This is mostly sub-ordinated term debt and includes all the
other categories that are not Tier 1 and 2.
2.2.1 DEFINITION OF CREDIT RISK AND COUNTERPARTY
CREDIT RISK
There is a key difference between the credit risk that a bank is facing due
for a example to a mortgage and the Counterparty Credit Risk(CCR) the
latter is facing due that it has enter into a derivative transaction.This
difference is fundamendal for this thesis topic to be well understood in
advance.
 Credit risk is the risk that an obligor does not honor his payments
due to a default event.For example this can apply to
12
This deterioration refers to the widening of the credit spreads of the counterparty thus this creates
the CVA risk over time.
13
Risk appetite can be defined as the amount of risk that a bank is willing to take on in pursuit of
value.For example a bank’s risk appetite in the lending activities can be quite different than their risk
appetite in the OTC markets.
12
`
Chapter 2
loans,bonds,credit cards,mortgages.It is known also as Lending
risk.This type of risk has the following characteristics:
I. The notional amount at risk of the loan,mortgage or bond
value is usually known during the lending period with a
certain accuracy.Therefore,the exposure that a bank has, is
known and fixed.
II. There is only one party that takes the credit risk,thus it is a
unilateral risk.For example a bondholder takes the amount
of credit risk but the issuer of the bond does not face any
losses if the bondholder defaults.
 Counterparty Credit Risk(CCR) is the risk that a debtor/obligor can
default prior to the expiration of a trade similar to credit risk albeit
with two major differences as seen below.A quote back in 2005
argued this:”CCR is probably the most important variable in
determining whether and with what speed financial disturbancies
become financial shocks ,with potential systemic
traits.’(Counterparty Risk Management Policy Group(2005).
Figure 1: Counterparty Credit Risk(CCR) as shown in the figure lies in the area where
market and credit risk intersect
Understanding the previous quote means that ultimately
Counterparty Credit Risk transforms into systemic risk that can
destabilize the financial system as later happen with the collapse of
the Lehman Brothers(2008) and differs in two important
characteristics than Credit risk.
13
`
Chapter 2
I.
The future exposure of the contract is uncertain for both of
the counterparties.For example if a Bank has entered into a
derivative transaction the future exposure can be negative
or positive and it is highly uncertain judging from today’s
market conditions.
II. The risk is bilateral and not unilateral.This means that both
of the counterparties are facing the risk of default for
example in a derivatives transaction.
The main important conclusion regarding the CCR is that the future
exposure is uncertain due to size but also crucial to sign(+ -) as
stated by Gregory(2012).
2.2.2 Regulatory Separation of Risks
 1.The risk associated with the default of the counterparties.
 2.The risk of Mark-to-market losses(CVA losses) due to the
volatility of the CVA of the counterparty across time.
This thesis is more focused on the second type of risk due to that it is the
new capital charge under Basel III nevertheless we will establish the
theoretical background of the counterparty default risk charges that was
introduced in Basel II in order to have a thorough and complete
understanding of the Total Counterparty Credit Risk that the regulators
have proposed.
2.2.2.1 REGULATORY CREDIT RISK CAPITAL
The Regulators compute the Risk-Weighted Asset(RWA)formulas that
values the market risk(RWAMarket),the credit risk(RWACredit)) and the
operational risk(RWAoperational).
Where the Regulatory capital takes the form:
Regulatory Capital
≥ 8% for Basel 2 and 10,5% forBasel 3.
RWAMarket+RWACredit+RWAOperational
14
`
Chapter 2
In the following paragraph we will model the RWA14 of Credit Risk as it is
in Basel II capturing the counterparty defaults.The RWA of Credit can be
decomposed into two sub RWAs.For the Counterparty Credit Risk of
derivatives the Basel II treats the derivatives exposures as loan
equivalents with some modifications.
RWACredit
RWACounterparty Credit
RWACredit-Loans
Risk-Derivatives
RWADefault
RWACVA
There are two approaches for the regulatory credit risk capital:
I. The Standardised approach(Risk weights are defined by
external ratings in order for the bank to assess its risks on
their exposures).This lies more to Basel I.
II. The IRB approach divides into two forms: the Foundation IRB
and the Advanced IRB.In the first approach the bank rely on
their own estimates on some risk components whereas in
the latter all components are internally estimated.The
components are the Default Probability(PD),Loss given
default(LGD),Exposure-at-Default(EAD) and effective
maturity(MA).
In the advanced IRB approach the regulatory credit risk capital for a
counterparty trading position is computed under the simple formula:
RWADefault=RC × 12,515
RC=EAD×RW
RC=EAD×LGD×[PD99,9%-PD]×MA(PD,M) (1)
14
Risk Weighted Assets(RWA) is a broad risk measure that was first introduced under the Base
Accord.RWA is computed by adjusting each asset class with a certain weight according to the risk that
the specific asset class has.
15
RWA=RC*12,5 or RC=RWA*8%.
15
`
Chapter 2
With the following definitions:
LGD=Loss Given Default(1-Recovery rate16 in relation to the EAD)
EAD=Exposure-At Default(For example the notional amount of a bond)
PD=Probability of default of the obligor for one year-PD99,9% at the 99%
confidence level.
MA=A maturity adjustment factor set by the regulators.
Since the Probability of Default(PD) is a major component in the
regulatory credit risk formula for defining regulatory capital under Basel II
but also for defining the economic capital17 that a bank can hold we will
further explain its key role as a parameter and how regulators have
modelled it.
 Probability of Default(PD) defines the credit worthiness of a
counterparty.More formally,it is the likelihood that a counterparty
will default over a particular time horizon(usually within a
year).The Probability of Default is not easy to estimate and it is
expressed by a Probability density function(pdf) which assigns
probability mass to the time points by the associated Cumulative
distribution function(CDF).The significance of defining accurately
the probability of default of an obligor lies to the fact that we gain
a thorough understanding of the credit quality of the counterparty
that we transact with.
The Regulators have proposed a Gaussian copula18 based model and it
defines the capital requirement as the difference between the 99,9%
conditional loss and expected loss over a one year horizon.More
analytically:
16
The fraction amount of the EAD that a counterparty will receive if the other counterparty that it
transacts with,defaults.The regulators propose that a bank must estimate LGD for each facility in
economic downturn conditions.
17
Economic capital is set to protect against unexpected losses and it is internally estimated by the
bank.
18
According to Li(2000) copulas are functions that can model dependence between random variables
by linking marginal distributions into a joint distribution.
16
`
Chapter 2
ȹ(
{(𝛷−1 (𝑝)− √𝑝(𝑝) 𝛷−1 (𝑞) }
)–p
(2)
√(1−𝑝(𝑝))
Where p:is the one year Probability of Default(PD) , 𝛷(. ):is the function
of the standard normal cumulative distribution and 𝛷−1 (.)is its inverse
function.For example at the 99,9 percentile we have 𝛷−1 (0,999) =
3,090232.
and p(p)=0,24-0,12*(1-𝑒 −50𝑝 ).
Moreover, the estimation of the transition adjustment factor or else the
maturity adjustment factor for an asset class is set by the regulators in
the following form:
1+(𝑥−2,5𝑏(𝑦)
MA(x,y)= 1−1,5𝑏(𝑦) (3)
Where b(y)=(0,11852 − 0,05478 ln(𝑦))2 .
As it is obvious the maturity adjustment factor is a complex function set
by the regulators to capture the credit migration risk 19.
Combining (2) and (3) with the Loss Given default, the Risk weight of a
counterparty is the following:
{ (𝛷−1 (𝑝)− √𝑝(𝑝) 𝛷−1 (𝑞 ) }
RW=LGD *(ȹ(
√1−𝑝(𝑝)
) – p)* MA(x,y) (4)
An important finding,as seen equation (1) and (4), is that the Exposure-atDefault is independent of the risk weight of the counterparty.In the
following chapter we will model and explain the EAD which is placed as
seen above in the default risk charges but also in the CVA risk capital.
19
For example when the counterparty’s rating is downgraded.
17
`
Chapter 3
Exposure-At-Default(EAD)
3. Credit Exposure Model Definitions
In the Counterparty Credit Risk(CCR) context in the industry there are
some basic definitions that we should address to better understand how
this risk works.
A. Exposure is the value of the underlying transaction(s).We can
mathematically define exposure as:
Exposure(t)=max{V(t,T),0} (3.1)
where V(t,T) is the value of the transaction and t is the time today with T
being the time to maturity.
30
25
20
15
10
5
0
1
10
19
28
37
46
55
64
73
82
91
100
109
118
127
136
145
154
163
172
Exposure-Option Value
Exposure Profile
Time in Days
Figure 2 In this figure above is depicted the future Exposure of a Call option under a
scenario across time that has been generated by Monte Carlo
The Exposure can be either with a positive Mark-to-market(MtM) value
for a financial institution that has enter into a derivative transaction with
an another counterparty(this means that the institution is gaining from
the transaction) or with a negative MtM value that means that the
institution is losing from the transaction with the counterparty.Here in
our example in the Call option,the exposure is always positive or zero
since we are long in the Call option(we have bought the call option).Thus
the exposure has a floor at zero and this can be seen from the payoff of
the Call=max(S-K,0).To re capitulate,when the exposure has a positive
18
Chapter 3
sign for the institution it is said as being in favour of the institution and
when it has a negative sign it is said that it is against the institution.
The above example is for a single trade with a counterparty and it is
depicted without considering netting.A more suitable treatment of the
exposure should be under netting.
3.1 NETTING
 Netting is the first mitigant for a counterparty/financial institution
to reduce/mitigate its exposure/risk with the other counterparty
that transacts with and in general means that in the same day all
transactions among the counterparties are offsetting partially or
entirely each other.This is known as payment netting.
In case that one of the counterparties defaults, then the solvent
counterparty seizes the payments with the defaulted counterparty and
offsets the remaining trading amount or else close-amount.This second
case is the closeout netting.
The mathematical definition of netting on a portfolio value is:
𝑁
max ∑𝑖=1{𝑉 (𝑡, 𝑇), 0} (3.2)
where N is the number of trades and i is the counterparty.We can prove
that for a netted portfolio it holds that:
𝑁
max ∑𝑖=1{𝑉 (𝑡, 𝑇), 0}
≤ ∑𝑁𝑖=1 𝑚𝑎𝑥{𝑉(𝑡, 𝑇), 0}
(3.3).
As illustrated in (3.3) it is clearly seen the netting benefit that is achieved
under netting all the transactions among the two
counterparties..Furthermore,we can define a netting set that includes a
group of transactions with a single counterparty that are under an ISDA20
Master Agreement.This Agreement forces some standard rules that must
20
ISDA is the International Swaps and Derivatives Association that under its Master
Agreement it enforces netting and collateral provisions.Founded in 1985 this
association has worked towards in making the global derivatives market safer and
more efficient.www.isda.org/about-isda/.
19
`
Chapter 3
be met by both of the counterparties in the contract and enhances the
Counterparty Credit Risk management,in other words mitigates the
Counterparty Credit risk(CCR) that an institution faces to a certain extent.
B.Expected exposure is the average of all exposures.Thus its
mathematical definition is:
Expected Exposure(𝐸𝐸(𝑖,𝑡 ))= E[Ex(t)] (3.4)
30
25
20
15
10
5
0
1
8
15
22
29
36
43
50
57
64
71
78
85
92
99
106
113
120
127
134
141
148
155
162
169
176
Expected Exposure-Average of Option
Values
Expected Exposure-EE(i,t)
Time in Days
Figure 3 In this figure above it is depicted the Expected Exposure of a Call option
across time under the previous simulation path.It is clearly seen as the average of all
exposures across time.
The Expected Exposure(EEi,t ) is against a counterparty i for time t.For
example we are a financial institution and we have a positive exposure21
against the counterparty i.It is crucial to note under which risk measure
the Expected Exposure is considered.In our thesis we will assume that we
are under the risk-neutral measure[Q]22 and all calculations are riskneutral.As we will explain later on Chapter 5 we price an option and
accordingly the option value is the exposure thus when we price products
in arbitrage free markets we need to take expected values of discounted
future cash flows under the risk neutral measure.
21
Positive exposure means that the transaction is in favour of the financial institution
in the example presented above.
22 Risk neutral measure is used for the market price of risk where investors are risk
neutral and the expected return in an asset is the risk-free interest rate,r.
20
`
Chapter 3
C.Expected Positive Exposure(EPE) is the average of all Expected
Exposures(EE(I,t)).Normally the time dimension(t) is discretized into a
fixed number of points tk in order to represent the expected values as a
function of time.Thus the mathematical definition of the Expected
Positive Exposure(EPE) is:
EPE(t1,t2)=
1
𝑡2
∫ 𝐸𝐸𝑥(𝑡)
𝑡1+𝑡2 𝑡1
(3.5)
EE and EPE
Expected Exposure
25
20
15
EPE-Expected Positive
Exposure
10
Expected Exposure
5
1
10
19
28
37
46
55
64
73
82
91
100
109
118
127
136
145
154
163
172
0
Time in Days
Figure 4 The Expected Positive Exposure of a Call option that is the weighted average
of the simulated Expected Exposures.The weights are the time buckets.
Following the Basel rules(Basel 2005) the above measures have been
introduced as Effective Expected Exposure(Eff.EE) that is simply a non
decreasing Expected Exposure and the effective Expected Positive
Exposure(Eff.EPE) that is the average of Effective EE.We will illustrate
below the Basel measures(Eff.EE and Eff.EPE) for a better understanding
and sake of clarity.
21
`
Chapter 3
Exposure Profile
Expected Exposure
30
25
20
15
Expected exposure
10
Effective EE
5
1
9
17
25
33
41
49
57
65
73
81
89
97
105
113
121
129
137
145
153
161
169
177
0
Time in Days
Figure 5 In this figure it is illustrated the Effective EE and it is observed that the
Effective EE is always above the EE thus a non-decreasing EE as defined earlier.
Exposure Profile
35
Exposure
30
25
20
15
10
5
1
7
13
19
25
31
37
43
49
55
61
67
73
79
85
91
97
103
109
115
121
127
133
139
145
151
157
163
169
175
0
Time in Days
Expected exposure
Effective EE
Effective EPE
Figure 6 Illustration of Effective EE and Effective EPE.
The effective EE and the Effective EPE are measures that the regulators
use for capital calculations since they assume that the transactions will be
replaced after maturity.Note that the EEPE> 𝐸𝑃𝐸.The critical input for
22
`
Chapter 3
the estimation of EAD under the Internal Model Method(IMM23) is the
effective EPE(EEPE).
3.2 EXPOSURE AT DEFAULT(EAD)
The crucial input driving CCR capital(both default and CVA capital
charges) is the EAD thus it is of great interest for all financial institutions
to have accurate estimates of EAD.As stated by Gregory24(2012),EAD
represents the regulatory exposure to a given a
counterparty.Gregory(2012) argues also that EAD is difficult to estimate
for two reasons:
 EAD is difficult to estimate for OTC derivatives compared to
standard debt instruments.
 Issues as Collateral make EAD definitions more problematic.
3.2.1 COLLATERAL
The Collateral(margin) is the second mitigant that a financial institution
uses to reduce credit exposure and offers an increased benefit to
mitigate counterparty risk to really low levels.The first mitigant that we
analyzed above is netting and whether the portfolio value after netting all
the transactions between the counterparties has still positive value for
one of the counterparties, then collateralization takes
place.Gregory(2012) has given a precise definition of collateral in the
literature.’’Collateral is an asset supporting a risk in a legally enforceable
way”Gregory(2012).
Types of collateral can be cash(this is an expensive25 form of collateral)
and securities(this is a cheaper form of collateral but is subject to
haircuts26).A counterparty is subject to post collateral through a Credit
23
Internal Model Method is an internal model that the bank uses for computations of credit exposures
and it has received regulatory approval.
24
Jon Gregory ”Counterparty Credit Risk and Credit Value Adjustment-A Continuing Challenge for
Global financial markets,second edition,2012”
25
In finance terms expensive means that the collateral posted in cash is very liquid thus it is expensive
for the counterparty to post cash as collateral because this reduces counterparty’s liquidity therefore
in the end increasing the liquidity risk of the counterparty.
26
A Haircut in the collateral posted by one of the counterparties is a reduction in the value of the
collateral amount.This lies to the fact that the collateral posted if it is not in a cash form its credit
quality can deteriorate over time and it is subject to a haircut.
23
`
Chapter 3
Support Annex(CSA27) master Agreement as we noted earlier in the
netting case above under an ISDA master Agreement.
 A Credit Support Annex defines the following collateral terms(ISDABest practices on Collateral terms,2013):
I. What type of Collateral is eligible to be posted by the
Counterparties.
II. Collateral disputes.
III. The calculation of the collateral posted.
IV. Interest payments on the Collateral(it depends whom has
posted the collateral) and it can be debated now since we
are experiencing negative interest rates.
V. A SCSA is a higher standardized CSA if it is chosen by the
counterparties than the ISDA Master Agreement because it
includes all the portfolio level collateral terms.
VI. Triggers on collateral from credit rating agencies that
downgrade the credit quality of the counterparties thus new
collateral of better quality must be posted.
A key parameter on Collateral28 is the Threshold Amount.This
defines the level of Mark-to-market29(MtM) that collateral is
posted(Gregory et al,2012).In our example with the Call Option
Exposure we will illustrate how the threshold acts as a barrier and
when the option value reaches above the threshold the
counterparty has to post collateral to us(by us meaning the
financial institution).This is referred to as the Variation margin
during the lifetime of the transaction.
27
A CSA can be either a one way CSA Agreement,this means that only one counterparty is subject to
post collateral or two-way CSA Agreement where both counterparties must post collateral whether the
transaction is against them.
28
Besides the threshold amount that defines the collateral posted by a counterparty there are also the
MTA which means the Minimum Transfer amount that is set by both of the counterparties and lies to
the scope of not posting collateral for small amount of exposures and the initial margin that is posted
at initiation of the contract
29
The Mark-to-market with respect to a counterparty defines what is the value that we can lose today
if the counterparty defaults.
24
`
Chapter 3
Figure 7 Illustration of the red area is the collateral posted by the counterparty.When
the value of the option at day 73 is above the threshold,the counterparty is subject to
a margin call thus the exposure is collateralized.
3.2.2 EAD UNDER THE IMM
The Exposure-At-Default is defined as:
EAD=a*EEPE
(3.6)
where EEPE is the Effective Expected Positive Exposure(eff.EPE) as
defined earlier.
The multiplier a it was first suggested by Piccoult(2002) and it adjusts a
variety of effects such as:
Wrong way30 risk in the portfolio,finite granularity of the portfolio and
correlation between the exposures.
Wrong way risk is the most significant hidden risk within a financial
contract.In simple words it means that when the exposure is increasing in
our favour then at the same time the Probability of Default of the
Counterparty is increasing silmutaneously.Thus there is the risk that the
counterparty will default when the Exposure is at its peak value.This kind
of risk was underestimated in the 2008 financial crisis with the results of
30
Wrong way risk can be separated into General Wrong way risk(macroeconomic factors that play a
role in the contract) and specific Wrong way risk as in our example stated above that has to do with
idiosyncratic risk.
25
`
Chapter 3
the collapse of the Lehman Brothers and later with the destabilization of
the financial system due to the melt down of the CDSs OTC market31.
Interpreting the alpha multiplier from a regulatory perspective we can
document that:
 The alpha(a) multiplier under the IMM is set in a fixed value of
1,4.While bigger banks have an option to calculate a this will be
subject to regulatory approval.For example,if a bank has a very well
diversified derivatives portfolio, it is clearly penalized with the
multiplier of alpha in the level 1,4.Thus this can be reduced in a
lower level and provide capital relief for the
bank.However,regulators have set a floor also where the alpha can
not be lower than 1,2.It is argued by the latter that alpha depends
on the robustness of the Internal Model framework and it could
potentially take values lower or even higher32 than 1,4.
Modelling the EAD under the IMM framework it is clearly advantageous
for a big33 bank.The IMM framework takes into account all individual risk
factors thus it is a fully risk sensitive methodology for measuring
exposures that can capture the actual risks that the bank is exposed
to.For example in a derivatives portfolio that is exposed to interest rate
risk,equity volatility,FX risk the IMM framework takes into account full
netting and collateral between the asset classes which provide the
maximum risk mitigation in the contracts that reduce the credit exposure
of the bank.
Moreover, since the EAD is netted and collateralized this will provide
lower capital requirements for the bank thus the institution can capture
the RARoC34 goals that the shareholders have targeted.It is
31
CDSs,Credit Default Swaps that act basically as an insurance when the counterparty defaults, the
buyer of this type of contract will receive the protection leg payment,for example a bondholder that
has a CDS contract on the bond will receive the notional amount of the bond.In order to receive that
amount the buyer pays premium payments periodically to the seller.These kind of products were fully
exposed to wrong way risks,thus they were the more toxic ones in the financial crisis.
32
For example in concentrated portfolios.
33
A big bank is obvious that trades a larger amount of OTC derivatives(more end users-clients)
compared to smaller banks in size therefore the cost of implementing an Internal Model framework is
far less than the actual gains that the bank will have from gains in the transactions and the overall
reduction in the capital requirements.
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑃𝑟𝑜𝑓𝑖𝑡
34
Risk Adjusted Return On Capital: RARoC=
𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑
26
`
Chapter 3
fundamendally important for the financial institution that the derivative
transactions that enters to be profitable or else there is no economic
meaning to enter a transaction that has a capital cost greater than the
profit it generates.To conclude,a successful bank will strive to have a
competitive profit-to-capital ratio in their derivatives transactions.
3.2.3 EAD UNDER THE SA-CCR METHOD
The new methodology for measuring credit exposures in the OTC market
that the regulators have proposed is the SA-CCR.This is a standardized
methodology on the contrary to the IMM that we defined above and
comes to replace both the old approaches meaning the CEM35 method
and the SM approach.Those latter methods are also called non-internal
model methods(NIMM) and have been heavily criticized as being risk
insensitive36 methodologies. The calculation of EAD under the SA-CCR
approach is similar to the CEM albeit the new method as we will aim to
investigate is far more complex and risk sensitive:
EADSA-CCR=a ×(RC+PFE) (3.7)
Where definitions are:
 a is the alpha multiplier as we have defined earlier in the IMM
approach and it is at the same level again thus 1,4.
 RC is defined as the Replacement Cost and it represents the value
that if the counterparty defaults today how much it will cost to the
solvent counterparty to replace the transaction.All calculations of
the replacement cost are under the close-out netting that we
highlighted before in equation 3.2.
 PFE is the Potential Future Exposure and it is calculated for each
asset class within a netted set as the replacement cost earlier.PFE
practically is an Add-On as we defined previously in the CEM
35
The Current Exposure Method was first introduced in 1988 under Basel 1 accord and it measures the
credit exposures with a formula of current exposure plus an add-on which reflects the potential future
change of the current exposure according to the asset class.
36
The Industry argues that they were to simplistic to actually capture real risks that they banks were
exposed to and furthermore they were static methods i.e not capturing the future benefits of netting
and collateral in the transactions.
27
`
Chapter 3
method.Gregory(2012) states that the PFE ‘’is the worse exposure
that we could have at a certain time in the future’’.To calculate the
PFE,we need to set up a confidence level,for example at 99% level
and this risk measure looks very similar to the VaR measurement of
losses.
As mentioned before the Replacement Cost(RC) is calculated under a
netting set level.Assuming that there is no collateralization in the
transaction then the RC is the Mark-to-market value of the
derivative.Thus RC=max(Vt,0).Assuming now that there is posted
collateral in the derivative transaction as in most of the derivatives
trading today then the RC=max(Vt-C,0).We will further illustrate how
collateral exchanges enter into the SA-CCR in the figure below and
explain how the collateral mechanics work and make the SA-CCR a risk
sensitive methodology with respect to collateral.
Replacement
Cost(RC)
Collateral
No collateral
Figure 8 Collateral Mechanics
Unmargined
Margined
--kfk
RC=max(Vt-C,0)
RC=max(Vt-C;TH+MTA-NICA,0) RC=max(Vt ,0)
 For margined trades as it is depicted above V is the value of the
derivative transactions,C is any collateral held for example by
the bank,TH is the Threshold Amount as we have defined in
figure 7 previously,MTA is the minimum transfer amount and
28
`
Chapter 3
NICA is a new parameter that defines the initial margin that has
been posted by both counterparties at initiation of the
transaction.For the sake of clarity NICA is defined as
Independent Collateral amount and according to BIS:
 NICA=ICAPosted to the Bank -ICAposted by the bank(unsegregated37).
As it is stated in the BIS technical document NICA represents the
largest exposure that would not trigger a Variation38 Margin Call.By
introducing the term NICA the BIS has made the methodology risk
sensitive by capturing the collateral as the counterparty may have
posted to the bank as initial margin.This amount is then reduced
from TH+MTA thus makes the calculation precise by reflecting both
the actual exposure that will not trigger a Variation margin call and
the collateral held by the bank/counterparty.The regulators have
floored the above formula at zero so it can not exist a negative
replacement cost (RC) due for example to over collateralization.
 The second component of the new SA-CCR is the Potential
Future Exposure(PFE).The old method CEM was based at an
Add-On for the potential future exposure and technically it is
the same concept in the SA-CCR also.Thus depending on the
asset class a future exposure can be mathematically written:
PFE=multiplier*AddOnAggregate
(3.8)
where the multiplier is a so called Supervisory Factor(SFi)
depending on each asset class.For example,in this thesis the SFiEQ
for a stock option is 32% and the Add-On is the Effective Notional
Amount of the trade or the Effective notional amount aggregated
37
Segregation of collateral is a protection measure for the counterparty that posts collateral and has
the purpose that the collateral is transferred in an independent third party custodian and not to the
receiver of the collateral.This protects the counterparty that has posted collateral for not losing the
collateral in case the other counterparty in the transaction default.
38
Variation Margin is the collateral posted throughout the maturity of the transaction when the initial
margin is not enough to cover the exposure.Thus for example if a counetraprty has posted initial
margin to the bank but the market exposure has moved against the counterparty in an amount more
than the initial margin, then the counterparty has to post variation margin in order to collateralize
further the exposure.
29
`
Chapter 3
whether we have a portfolio of trades.For an Equity Option the
Effective Notional is equal to:
Effective Notional=dj × δι × ΜF (3.9)
 The dj parameter is calculated simple regarding to the other
asset classes and straightforward as it is the amount of
options(bought or sold) multiplied by the current price of the
option.
 δi is the supervisory delta for the stock option and it is stated
𝑆
𝐾
𝛷(ln( )+0,5∗𝑇∗𝜎%))
by the regulators as the
𝜎 2 √T
.it is (+)
when we are taking a long position(buy the option) and (–)
when we are short in the option(sell the option).
 Last the Maturity Factor whether the transaction is margined
or unmargined takes the regulatory form:
a) Unmargined MFi=√𝑀𝑖𝑛(𝑇; 1𝑦𝑒𝑎𝑟)/1 where T is the
transaction remaining maturity floored by 10 business days.
3
b) The Margined MFi= √𝑀𝑃𝑂𝑅/1𝑌𝑒𝑎𝑟,where MPOR is the
2
parameter of Margin Period of Risk.In Basel III the MPOR is
set at 20 business days and it is a new change from Basel
II.By MPOR the regulators define the true time required for
the bank to liquidate the collateral that a given counterparty
posted to finance its exposure.
To summarize,in this chapter we have analyzed the regulatory
treatment of the Exposure-at-Default with the IMM method
and the Non-IMM method which is the new SA-CCR.As we will
document in the next chapter the EAD is a crucial input for
measuring CVA capital under the standardised formula and
banks have to choose under which methodology they will
calculate EAD for counterparties in order to have the minimum
regulatory capital requirements set aside.
30
`
Chapter 4
CVA Capital Charges under BASEL III
4 THE NEED FOR A NEW CAPITAL CHARGE(CVA CAPITAL)
After the melt down of the CDS OTC derivatives market and following the
collapse of the Lehman Brothers,investors and regulators realized that no
financial institution was too big to fail.If the fourth biggest investment
bank of the United States defaulted then all other counterparties/banks
could potentially default.In order to respond to this new financial risk 39
that arised in 2008 and became real by forcing investors and institutions
to lose billions of dollars/euros, the regulators announced a new capital
charge on capturing the credit deterioration of the counterparties before
they actually default.Thus,the CVA capital charge is added on the existing
default risk capital charge that we pointed out on Chapter 2 and it is
argued by the BCBS that it provides a better capitalized framework for
banks.The latter are able to implement the new CVA capital charge on
two flavours:
4.1 THE STANDARDISED FORMULA :This formula is used for Banks
without IMM approval and it is a simple formula whereas the credit
spread of the counterparty is set as the risk weight of the credit
quality40 of the counterparty(credit ratings).In order to illustrate and
make this formula friendly to the reader we will assume that no
hedging is taking place for capital relief.Thus:
𝐾 = 2,33 × √ℎ × √[∑𝐼 0,5 × 𝑋𝑖]2 + ∑𝑖 0,75 × 𝑋𝑖 2
( 4.1)
Where the definitions are h:is the time horizon and it is set by the
regulators to one year, 2,33 is the normal inverse cumulative distribution
at the 99% confidence level and XI is the volatility in the CVA.Thus in VaR
terms the above formula can be interpreted as the worst case that the
CVA can move over a time horizon of one year and at a confidence level
of 99% as noted earlier which is 2,33.The movement in the CVA is
represented by the Xi which is a product of three terms:
39
CVA risk meaning the risk to book negative losses due to credit deterioration of the counterparty
with whom the institution have entered into a derivative contract.
40
The Credit Quality of the counterparty is its credit standing today.For example a high rated
counterparty such as AA(double A) will enjoy a reduction in its risk weighted calculation of exposure.In
simple words it means that the counterparty is less risky to default with respect to other
counterparties in the market.Although aspects such as jump-to-default may change completely the
credit rating of a counterparty in stressed times and thus the ongoing criticism to the external rating
agencies.
31
Chapter 4
Xi =wi × Mi × EADi
(4.2)
 Wi: a weight according to the rating of the counterparty
i.From the BIS table the risk- weights
are:0,7%(AAA),0,8%(AA), 1,0%(A), 2,0%(BBB) etc.The worse
is the rating, the higher the volatility as it is clearly seen.
 Mi :The effective maturity which represent the maturity of
the exposure to the counterparty.
 EADi:As we explained in Chapter 3 this is the exposure at
default that is an input into the standardised formula and
thus the banks can choose one of the two methodologies to
model it depending on whether they have regulatory
approval(EADSA-CCR or EADIMM).
The standardised formula has been formulated by the regulators to
capture the increase in CVA capital from a credit spread widening of the
counterparties with a correlation parameter among the credit spreads of
the counterparties at ρ=50%.This regulatory formula allows for hedges
that take the form of a Single name CDS and Index CDS.If we include the
hedges in the upper formula then we can re-write that:
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑠𝑒𝑑
𝛫𝐶𝑉𝐴
=2,33× √ℎ × √[∑𝐼 0,5 × 𝑤𝑖 × 𝑌𝑖 − ∑𝑖𝑛𝑑 𝑊𝑖𝑛𝑑 × 𝑀𝑖𝑛𝑑 × 𝐵𝑖𝑛𝑑 ]2 + ∑𝑖 0,75 × 𝑊𝑖2 × 𝑌𝑖 2
(4.3)
ℎ𝑒𝑑𝑔𝑒
Where now 𝑌𝑖 =𝑀𝑖 × 𝐸𝐴𝐷𝐼 − 𝑀𝑖
× 𝐵𝑖 .With the new definitions
𝐵𝑖 being the notional amount of Single name CDS, 𝐵𝑖𝑛𝑑 the notional
ℎ𝑒𝑑𝑔𝑒
amount of the index hedge, 𝑀𝑖
is the weighted maturity of the singe
name CDS hedge, 𝑀𝑖𝑛𝑑 is the weighted maturity of index CDS hedge.
The first component in equation 4.3 can be explained as being the
systematic risk and the second as the counterparty specific
risk(idiosyncratic).The factors 0,5 and 0,75 shows that part of the credit
spread component is systemic and it can be hedged efficiently with Index
CDS hedges.As we have analyzed the formula both with hedges and
32
`
Chapter 4
without, we can distinguish that the single name hedges can reduce both
terms.Although single name hedges(buying CDSs) for illiquid
counterpartιes will be expensive and difficult to find in the market they
can potentially reduce the capital requirement to zero.
4.2 THE ADVANCED CVA APPROACH
In order for banks to implement the advanced approach they are
required to have an IMM regulatory approval.The advanced CVA
approach uses the banks VaR model for bonds to model spreads of the
counterparties.Thus the key difference from the standardised
approach that we explained previously is that the credit spreads of the
counterparties are not risk weights from the BIS table but they are
modelled with simulation methods and internal bank models41.An
illustration is given below:
300
250
200
150
100
50
0
1
8
15
22
29
36
43
50
57
64
71
78
85
92
99
106
113
120
127
134
141
148
155
162
169
176
Spreads in Basis points
Initial spread 124 bp
Monte Carlo Simulation of credit spreads using a CIR
process
Time in days-Counterparty's Credit Spread Danske Bank A/S
Figure 9 Simulation of 10 paths of the credit spreads of Danske Bank A/S that are
inputs in the calculation of the advanced CVA VaR approach(10-day time horizon at a
99% confidence level)
41
Internal Models for credit spread modelling are similar to interest rate modelling.Such models that
the industry uses are the Vasicek model.the one factor Hull and White model,the Cox Ingersoll Ross
model.
33
`
Chapter 4
The advanced CVA approach is set by the regulators as:
𝑇
𝐶𝑉𝐴 = 𝐿𝐺𝐷𝑚𝑘𝑡 × ∑ 𝑚𝑎𝑥 {0;
𝑖=1
𝑒𝑥𝑝−𝑠𝑖−1∗𝑡𝑖−1 𝑒𝑥𝑝−𝑠𝑖 ∗𝑡𝑖 𝐸𝐸𝑖−1∗𝐷𝑖−1
−
}(
𝐿𝐺𝐷𝑚𝑘𝑡
𝐿𝐺𝐷𝑚𝑘𝑡
+ 𝐸𝐸𝑖∗𝐷
2
𝑖
)
𝑒𝑞(4.4)
Equation 4.4 is the so called Regulatory CVA.There are three
components in the above formula and this is very similar to the
Economic CVA formula that a bank uses for pricing CVA risk in
trades.Thus with this approach there is a better alignment between
the regulatory CVA approach for capital requirements and the
Economic CVA market risk approach for pricing trades that the banks
use.Although,there are still some significant differences that causes
discrepancies between of them as we will highlight below.The
definitions in the above formula are:
a. LGDmkt is the Loss Given Default of the Counterparty and it is
market implied as seen.
b. The 𝑚𝑎𝑥 {0;
𝑒𝑥𝑝
−𝑠𝑖−1∗𝑡
𝑖−1
𝐿𝐺𝐷𝑚𝑘𝑡
−
𝑒𝑥𝑝−𝑠𝑖 ∗𝑡𝑖
𝐿𝐺𝐷𝑚𝑘𝑡
} is the Probability of Default
in the interval {ti-1,ti}.
c. 𝑠𝑖 is the credit spread of the counterparty(it is the CDS that we
find in the market-thus this formula uses market implied CDS
spreads and becoming risk-neutral as the pricing CVA that banks
use for pricing,hedging and trading).
d. The Expected Exposure EEi at time ti.
e. Di is the discount factor.
The volatility in the regulatory CVA formula arises from the volatility in
the credit spreads.Therefore,the regulators with this formula consider
only the credit spread volatility for the 10-day time horizon and holds
the exposure component fixed.This means that the Monte Carlo re
calculation of the regulatory CVA is performed with the changes in the
credit spreads of the counterparty and not in the
exposure.Therefore,no Monte Carlo simulation is required to re
calculate any potential changes in the exposure during these 10 days
time period.This is a major critique upon the regulatory CVA that the
industry has expressed its views and cautions.Furthermore,this lack of
market risk sensitivity has made the regulators to take initiatives and
34
`
Chapter 4
propose future regulatory changes that are still under discussion with
the industry participants and as we will clarify more on Chapter 6,
these are the changes in the CVA framework under the Fundamendal
Review of the Trading Book.The FRTB42 is a market risk framework
that tries to balance market risk sensitivity and regulatory capital
requirements.
To conclude,the market risk hedges in the current framework were
not addressed by the regulators as eligible therefore did not generate
any capital relief43 for banks and this is a point that the industry
argues intense and has to be changed according to the latter.A last
remark on this chapter is,that the CVA landscape and the associated
CVA capital charges as explained above will have a huge capital impact
upon banks in their OTC trading business and we will aim to measure
this capital impact in the next chapter.
42
The Fundamendal Review of the Trading Book(BCBS,2013b)
A hedge is performed from an institution in order to offset the actual risk that the latter is exposed
to.The regulators have made market risk hedges not eligible thus there is no recognition of them for
capital relief and this may create moral hazard for some banks by not performing hedges whereas this
will increase the overall risk of the bank in the end.The regulatory purpose is to strengthen the banking
system and to set capital requirements aligned with actual risks that banks face thus this exemption is
highly contradicted.
43
35
`
Chapter 5
Stochastic Model Implementation for CVA capital
5. Black-Scholes Model for an Equity Call Option with
Counterparty Credit Risk(CCR)
As we have noted earlier on chapter 3 and 4, in the calculation of CVA we
need to have an Expected Exposure model.The most difficult task in the
computation of CVA is to built an exposure engine model that generates
Expected Exposures(EE) according to the primary risk factors44 of the
derivative45.After we are able to find the EE profile of the asset class,we
can then move towards to accurately calculate the Effective Expected
Positive Exposure (Eff.EPE) that Basel proposes for capital
measurements.By acquiring the latter risk measure, then we can
straightforward calculate the Exposure-at-Default in the IMM framework
as it is shown earlier in eq. (3.6).The idea in this thesis is for the exposure
engine to use the classical Black-Scholes formulae to price the European
Option and then generate risk exposures for the lifetime of the option
with Monte Carlo Simulation.In simple words,the simulation will generate
future scenario paths that the option values can take according to the
movements of the underlying stock price.In the Counterparty Credit Risk
world the option values minus the CVAoption are risky values(when the
counterparty defaults the values are extinguished).
5.1 THE BLACK-SCHOLES FRAMEWORK
The definition of a call option according to Wilmott(2007) is the right to
buy a particular asset for an agreed amount at a specified time in the
future.The agreed amount is often referred as the strike price(K) and the
specified time is referred as time to maturity.There are two kind of
options trading in the derivatives market.The European Option that the
holder of the option has the right to exercise it only at the time to
maturity and the American Option that the holder has the right to
exercise anytime during the lifetime of the option.This is a distinct
difference between the two options.Moreover,there are many other
option forms in the OTC market that are very different from a Call
option.For example Asian Options,Bermudan Options,Barrier Options and
these are options with different characteristics(the so called Exotic
44
This can be for example an interest rate.FX rate or as in our example in this thesis it is the
movements in the underlying stock price(asset).
45
A derivative is a financial instrument whose price derives from an another asset-the so called
underlying asset.In the call option example the value of the option is derived from the volatility of the
stock price(asset).
36
Chapter 5
Options) than the plain vanilla option that we described above.In this
thesis we are focusing on the pricing of the plain Vanilla European Call
Option.A last important term of the options is the so called moneyness of
the option.An ATM option(At-The-Money) defines as the strike price(K)
being equal to the stock price.If the price of the stock is above the strike
then we define it as ITM(In-The-Money) option whereas if the stock price
of the option is less than the strike then it is OTM(Out-of-The Money).
In 1973 Fishcer Black and Myron Scholes46 derived a closed form solution
for a Call Option.In their paper the stock price is following a Geometric
Brownian Motion(GBM).The GBM process describes the random
behaviour of the stock price St over time.The GBM is defined as follows:
𝑑𝑆𝑡 = 𝜇𝑆𝑡 𝑑𝑡 + 𝜎𝑆𝑡 𝑑𝑊𝑡 eq.(5.1)
Where 𝑆𝑡 denotes the stock price, μ is the drift of the process,σ is the
volatility and 𝑑𝑊𝑡 is a Brownian motion.
The GBM is the most fundamendal process in financial modelling.This is
the underlying process in the Black-Scholes formula for pricing European
Call Options.As seen in eq.(5.1) the W is a standard Brownian motion that
is characterized by independent identically increments(iid) that are
normally distributed with zero mean and a standard deviation equal to
the square root of the time step.The solution of the GBM using stochastic
calculus can be obtained as:
1 2
𝑆𝑇 = 𝑆0 × 𝑒𝑥𝑝({𝜇−2𝜎 }𝑇+𝜎𝑊𝑇 ) eq (5.2)
where 𝑆𝑇 is the stock price at the future time T, and 𝑆0 is the stock price
at time t=0.
 For our simulation purposes we have used the discretized form of
the GBM:
46
See F.Black and M.Scholes, ‘’The pricing of Options and Corporate
Liabilities,’’Journal of Political Economy 81(May/June 1973).
37
`
Chapter 5
1
𝑆𝑡𝑖+1 = 𝑆𝑡𝑖 𝑒𝑥𝑝 [{𝜇 − 2𝜎 2 } (𝑡𝑖+1 − 𝑡𝑖 ) + 𝜎√𝑡𝑖+1 − 𝑡𝑖 𝑍𝑖+1 ]
𝑒𝑞(5.2.1)
To note,there is no discretization error due to the fact that the GBM has
an explicit(closed form) solution where 𝑍1 , 𝑍2 ,…𝑍𝑛 are independent
random draws from the standard normal distibrution.
500 Simulation Paths of Stock Prices following a
GBM process
350
Stock Price
300
250
200
150
100
50
1
8
15
22
29
36
43
50
57
64
71
78
85
92
99
106
113
120
127
134
141
148
155
162
169
176
0
Time in Days
Figure 10 Illustration of Geometric Brownian Motion Stock Paths of Danske Bank A/S.
5.2 BLACK-SCHOLES PRICING FORMULAS FOR OPTIONS
After deriving the Black-Scholes equation(shown in the Appendix of the
thesis)we have that any derivative must satify this differential equation:
𝜕𝑓
𝜕𝑡
𝜕𝑓
𝜕2 𝑓
+ 𝑟𝑆 𝜕𝑆 + 12𝜎 2 𝑆 2 𝜕𝑆 2 = 𝑟𝑓
(5.3)
Eq 5.3 is the Black-Scholes partial differential equation and the solution
of this equation for our European Call Option depending on 𝑓 =
max(𝑆𝑇 − 𝐾, 0) is:
𝑐 = 𝑆0 𝑁(𝑑1 ) − 𝐾𝑒 −𝑟𝑇 𝑁(𝑑2 ) (5.3.1)
38
`
Chapter 5
𝜎2
Where: 𝑑1 =
𝑙𝑛(𝑆0⁄𝐾)+(𝑟+ 2 )𝛵
𝜎 √𝑇
, 𝑑2 = 𝑑1 − 𝜎√𝛵
N(x) Is the function of the cumulative normal distribution function for a
variable with a standard normal distribution.
The variable c is the European Call option price and this value is the
positive exposure of our trade.We are assuming that we are long in the
option.thus it means that we buy the Call Option of Danske Bank in the
OTC markets and then we generate from the BSM model 500 simulating
paths(future scenarios of the option value) with MC47 across the lifetime
of the option in order to acquire the total exposure profile of the option
until it matures.
Therefore,we are now in a position to calculate the Exposure at Default
of the option(Counterparty Danske Bank) under the IMM and the SA-CCR
methodology as we documented previously at Chapter 3.We will
compare and examine which of the two methods is more conservative
and which offers the minimum capital requirements before netting and
collateral is applied to mitigate the EAD for both methods.
5.3 DATA AND COMPARATIVE ANALYSIS OF EADIMM AND EADSACCR
Option Details
Nr of options(1.000.000)
Counterparty
OTC market
Danske Bank A/S
Call Price 19,53 DKK
Spot
177 DKK
Strike
170 DKK
Implied Volatility
0,2943
Maturity
0,5
Interest rate
0,03
Expiration month June 2016
Source Bloomberg
47
Monte Carlo simulation methods.To produce a random sample from a standard normal distribution
in EXCEL we write the command NORMSINV(RAND()).
39
`
Chapter 5
EAD under SA-CCR for an Equity European Call Option
Nr of instruments
1000000
Replacement Cost
19.530.000 DKK
Effective Notional Amount
8.712.696 DKK
Supervisory Delta
0,6309
Maturity Adjustment Factor
0,7071
Potential Future Exposure(Add-On)
2.788.062 DKK
Supervisory Factor SF(i) and Supervisory volatility
SF=32% ,
σ
σ=120%
EAD for counterparty Danske Bank
31.245.288 DKK
EAD under the IMM for an Equity European Call Option
Effective Expected Positive Exposure
18.220.000 DKK
Simulation Paths
Black-Scholes Model
500
IMM a
1,4
EAD for counterparty Danske Bank
25.508.000 DKK
For the single trade transaction the results from the EAD SA-CCR
methodology indicate that it is a more conservative methodology than
the EAD-IMM.Therefore,the IMM methodology if chosen by the bank
offers less capital requirements.As stated in the previous chapters in
order for a bank to implement the IMM,the latter need to have
regulatory approval and that is also an extra cost implementation
40
`
Chapter 5
compared to the objective SA-CCR.Moreover,It is interesting to note that
one reason that the SA-CCR methodology is more conservative is due to
the fact that it is calibrated to stress market periods by the
regulators.This has been applied for regulatory prudence in order for the
method to perform better in turbulent financial market
conditions.Thus,in the BIS technical document the Add-On and the
multiplier for the asset class of an Equity Option(EQ) is calculated with a
supervisory volatility of 120% and a multiplier of 32% for a single name
company.The multiplier is else called a supervisory factor and it describes
the volatility of the trade.In the IMM approach the calibration48 is
performed internally by the bank which means that the bank model for
generating exposures has been backtested for at least a one year period
and has received regulatory approval to perform future simulations.In the
option trade above we performed the calibration of the stochastic
process(GBM) that the underlying stock follows with the Maximum
Likelihood estimation and used three year(2013-2016) historical market
data as the regulators propose.We generated an estimated parameter of
σ=0,24 and used that parameter to perform the future simulations of the
underlying stock(entity Danske Bank).One of the recent changes in the
Basel III framework is that the regulators propose also the use of stressed
data for the calculation of the Expected Positive Exposure(Stressed
EPE).This is performed not at the counterparty level as we have
illustrated here but in the whole portfolio of trades with many
counterparties.A rational assumption is that when we will calibrate the
EPE model with a period of one year stressed data in the three year
period data as the regulators propose,then the volatility will increase
respectively thus producing a higher EAD.Comparing the two capital
methodologies is certainly a difficult task because with different asset
class than the option class, the methodologies will produce different
results.At last,the most important reason of all that a bank should strive
48
We performed the calibration of the stochastic process(GBM) that the underlying stock follows
based on historical returns of the stock.The calibration method is the Maximum Likelihood
estimation.As it is stated by the name,the Maximum likelihood estimation suggests the parameter
Θ(μ,σ) for the probability mass function that will maximize the likelihood or the probability of having
observed the given data sample for the random modelling distribution.Thus the Θ will yield to the best
fit of the historical dataset.This technique is from a paper named ‘’Stochastic Processes Toolkit for Risk
Management’’Damiano Brigo,Matthias Neugebaurer et al.
41
`
Chapter 5
to have an IMM approval for measuring the Exposure-at-Default lies in
the two mitigants, netting and collateral.In a portfolio sample,the IMM
approach recognizes full netting among the asset classes where in the SACCR the netting efficiency is limited due to the fact that netting is only
allowed into the same asset classes(the regulatory name is hedging sets)
and not across the hedging sets.While the SA-CCR methodology has been
formulated to be more risk sensitive by capturing the initial margin that a
counterparty might have posted as collateral to the bank,the IMM
approach models besides the current collateral,the future collateral
also.Therefore,the IMM approach will produce significantly lower EAD for
the whole portfolio of transactions that will lead to less capital
requirements for the bank overall.
5.4 CAPITAL COST COMPARISON OF BILATERAL TRANSACTIONS
AND CENTRALLY CLEARED TRADES(CCP)
Basel III increases capital requirements for derivative transactions that
are bilaterally cleared between the counterparties and is introducing the
new CVA capital charge as we mentioned previously in Chapter 4.An
illustration of the bilateral transaction that is subject to the CVA charges
is the following:
Investment Bank
OTC trade
Option writer(Danske
Bank)
Figure 11 Illustration of a bilateral OTC transaction between the two counterparties.This transaction is
subject to a CVA capital charge.
On the other hand,chanelling transactions to a Central Counterparty for
clearing49(CCPs) required until recently no capital held for the traded50
exposures that a financial institution had to the CCP(Basel II).To note,a
CCP is a clearing house for derivative transactions that stands between
the counterparties and receives the counterparty risk of both of the
counterparties.In other words,the financial institution(here in our
49
Clearing is a process that occurs after the execution of a trade.The CCP stands between the
counterparties and acts as a guarantor of performance of the trade.
50
Trade Exposures are considered the current Mark-to-market(MtM) value of the transaction,the
Potential Future exposure and the initial margin if any posted by the institution.
42
`
Chapter 5
example the Investment Bank) now has as a counterparty the CCP and
the transaction is centrally cleared.The same counterparty terms hold for
the other counterparty(Danske Bank) also.To better illustrate our analysis
on CCPs we have depicted below a figure on how a CCP intermediates
between the two counterparties.We are assuming that the CCP is a
qualifying51 one whereas both the financial institution(Investment Bank)
and the counterparty(Danske Bank) are clearing members52 of the CCP.
CCP
Investment
Bank
Danske
Bank
Figure 12 Illustration of a centrally cleared transaction(CCP trade) between the CCP and the two
clearing members.
Basel III now requires banks to hold capital for cleared trades also
meaning that the risk weight to CCPs is not zero as in Basel II. A risk
weight of 2% of the traded exposures has been imposed by the regulators
to the CCP trades thus now there are capital requirements for bank
exposures to CCPs.
We will aim to measure the CVA capital charges(bilateral trade) for the
European Call option and compare them with the capital requirements
that we would have to set aside if the option trade is centrally cleared in
a CCP.We assume that we are the Investment Bank and we have bought
the call option of Danske Bank in the OTC market.In the CCP clearing case
we assume that we are as an Investment Bank a Clearing member of the
CCP and shift the transaction towards to central clearing without taking
into consideration any default fund contributions to the CCP capital
charges.
51
A qualifying central counterparty is an entity that is licensed to operate as a CCP and it is permitted
by the appropriate regulator with respect to the products offered.Annex 4,Section I.General terms.BIS
Capital requirements for bank exposures to CCPs.
52
There are certain rules and conditions to be met before a financial institution/bank can be a clearing
member in a CCP.
43
`
Chapter 5
Asset
Class:Equity
European Call
Option
Counterparty
Danske BankRating A-Risk
weight
0,8%(from BIS
table)
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑠𝑒𝑑
𝐾𝑎𝑝𝑖𝑡𝑎𝑙𝐶𝑉𝐴
582.412 DKK
Estimated with the
EAD SA-CCR
𝐴𝑑𝑣𝑎𝑛𝑐𝑒𝑑 𝐴𝑝𝑝𝑟𝑜𝑎𝑐ℎ
𝐾𝑎𝑝𝑖𝑡𝑎𝑙𝐶𝑉𝐴
𝐶𝐶𝑃𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐶ℎ𝑎𝑟𝑔𝑒
190.368 DKK
CVA=118.767 DKK
446.361 DKK
2% of Current
MtM+2%*PFE
It is worth noticing that the advance approach for calculating CVA capital
that a financial institution has to set aside produces the least capital
charges for the Investment bank.Furthermore, this will reduce also the
cost of holding regulatory capital for the institution known as
KVA53.Albeit,as we have already mentioned the IMM approval has
additional implementation costs.Nevertheless,large banks that trade
large amount of derivatives will optimize their capital requirements by
choosing the advanced approach for CVA capital.
53
Kapital Valuation adjustment is measuring the cost of capital in a specific trade during the lifetime of
that transaction.
44
`
Chapter 6
FRTB CVA and Basic CVA framework
6. CVA under the Fundamendal Review of the Trading
Book(FRTB)
There have been recent changes and proposals to the current CVA
framework.One reason for that,as we have analyzed on Chapter 4 it was
that the regulatory CVA formula held the exposures fixed during the 10
day time horizon of computing the advanced CVA VaR capital
charges.Thus only the credit spreads contribute to the variability of the
CVA and only the single CDS or Index CDS hedges were eligible,excluding
the market risk hedges.The latter means that the market hedges did not
provide any capital relief to the banks.Now,the Fundamendal Review of
the Trading Book can be seen as providing market risk sensitivity and
complexity in the regulatory capital rules while promoting consistency
that many argue that it is lacking in the current framework.As it is stated
in the recent revised document from BIS,the proposed framework will
capture the exposure component of CVA risk along with its associated
hedges in the capital charge(BIS February 2015).From a recent
study(Deloitte and Solum Financial Partners,2013) it is shown that large
banks were in fact actively manage their CVA risk by mitigating their
market risk exposures by entering into transactions to hedge those risk
factors that arose from the exposure component.This approach as stated
by BIS it will align more the economic risks(Economic-Accounting CVA)
and the capital charge(regulatory CVA) while reducing the incentive that
some banks were leaving their exposures unhedged due to the fact that
those hedges did not offer any capital relief for the bank.
The Fundamendal Review of the Trading Book for CVA capital charges
comes in two flavours for banks to implement:
a. The FRTB-CVA framework:This framework is for banks that
calculate their CVA market risk sensitivities and fulfil several
fundamendal conditions for their risk management of CVA.Under
the FRTB framework,there are two approaches.The SA-CVA and the
IMA-CVA.The first approach is the standardised CVA approach and
whether a bank has regulatory approval to use the FRTB-CVA
framework then automatically can use the SA-CVA.In order for the
bank to use the IMA-CVA approach meaning the Internal model
that a bank has for their CVA, then the latter need to meet
45
Chapter 6
additional regulatory provisions derived from the trading book
application of the approach IMA-TB.These provisions include P&L
attribution and backtesting performance of the banks internal
models.Furthermore,it may exist a period of time that the
regulators need to monitor the internal CVA model before they can
approve to the bank to use the IMA-CVA.As stated earlier one of
the conditions for a bank to have the FRTB-CVA framework is to be
able to calculate the CVA risk sensitivities for many risk
factors.Besides that this is very computationally intensive,the
regulators require also for the bank to have a mapping procedure
for calculating the credit spreads of illiquid54 counterparties.The BIS
propose that in certain cases the bank can map an illiquid
counterparty to a single name liquid spread that is related with the
illiquid counterparty.An example that they present is the mapping
of a municipality’s credit spread with its home country.The
rationale behind the mapping procedure is that in every mapping
of an illiquid credit spread, the bank must reason and justify its
choice to single name references.
As it is obvious all these methodologies and procedures need to be
implemented internally in the bank by a dedicated risk
management team that deals only with CVA risk
management.Many banks recently have created the so called CVA
desk and in order to have regulatory approval to use the FRTB-CVA
framework nowadays the CVA desk is a requirement(BIS
paper,October 2015).
b. The Basic-CVA framework:The regulators have proposed this
framework when banks can not or unwilling to calculate CVA
market risk sensitivities for their CVA risk.This framework is very
similar with the standardised formula for measuring CVA capital
that we calculated and illustrated on Chapter 5.The new difference
is that now it allows for credit hedges such single name CDS not
54
An illiquid credit spread of a counterparty is a spread that it is not quoted in the CDS market due to
the fact that the counterparty could be a small entity.Also,not all counterparties have traded spreads.
46
`
Chapter 6
only to be referenced directly but to reference an entity legally
connected to the counterparty and furthermore to reference an
entity that belongs to the same sector and region as the
counterparty.However,it does not capture any market risk hedges
as the FRTB-CVA framework thus there is no capital relief for
hedging the market risk exposure for banks under the Basic-CVA
framework.A simple formula for calculating the CVA capital is
proposed by the regualtors which is:
𝐾 = 𝐾𝑠𝑝𝑟𝑒𝑎𝑑 + 𝐾𝐸𝐸 eq.(6.1)
Where Kspread is the contribution of credit spread volatility and KEE is
the contribution of EE volatility to CVA capital.
A last important remark is that under the Fundamendal Review of
the Trading Book the VaR risk measure is being replaced with the
risk measure of the Expected Shortfall(ES).The ES measure is a
more coherent risk measure than the VaR due to the fact that it
captures better the tail risk.This means that the ES measures the
losses beyond the single quantile that VaR captures and averages
all losses above the confidence level.Therefore the ES is considered
to be a more conservative measure than the VaR .For a normal
distribution at 97,5% level and the VaR at 99% confidence level
they produce almost the same results meaning 2,34 and 2,33
respectively.
An another difference is that the 10 day time horizon that we
implemented on Chapter 5 in the advanced CVA capital charges
might change based on the liquidity of the underlying.Those last
changes are still debatable and future regulations will clear further
the challenging CVA landscape.
47
`
Chapter 7
CONCLUSION
7. Conclusions and Discussion
The purpose of the Basel III CVA capital charges is to capitalize the risk of
future changes in CVA.As we mentioned in the Introduction this is the so
called CVA volatility that arises from credit spread volatility but also from
market risk exposures.The advanced CVA capital charge produces less
capital requirements for the financial institution that we implemented on
Chapter 5 than the standardised formula for measuring CVA capital.This
can be explained due to the fact that the advanced CVA capital charges
uses as an input the lower Expected Exposure metric while the
standardised formula is being penalized by inserting the Exposure-atDefault(EAD) which is a larger risk metric.
It is obvious that smaller banks that can not have an IMM approval will
have to set aside huge capital requirements for offering derivatives to
their clients.This may lead some banks to withdraw from the derivatives
market or only offer derivatives and specific asset classes that maximize
their profits.On top of that,the CVA capital charge is added on the default
risk capital charge for the calculation of the Total Counterparty Credit
risk(CCR) that a bank faces.This will dry even more the liquidity that a
bank has thus the regulators incentive is to shift the OTC derivatives
business in the Central Clearing Counterparties.This was clearly seen in
the Basel II regulations that the bank exposures to CCPs received a 0%
risk weight where afterwards the regulators change it, to a 2% risk weight
in Basel III.To note,this is the smallest risk weight applied in all
frameworks.
An another interesting discussion is whether the CVA risk methodology
and capital charges that have been imposed on banks are a risk sensitive
methodology that actually captures the real risks that a financial
institution is facing in the OTC derivatives market.As we have
documented on Chapter 5 and 6 the industry argues that there is no
capital relief for market hedges thus the current CVA methodology was
not risk sensitive to capture future changes in the market exposures and
the associated market hedges that banks performed.Under the FRTB
framework the regulators are trying to align the Economic CVA for trades
with the Regulatory CVA for capital requirements albeit the hedging can
48
CONCLUSION
never be perfect since the regulators do not take into consideration the
DVA of the bank(they consider the bank as default free) where the DVA
of the bank would reduce the CVA losses.Therefore,there is a shadow
quantity between those two versions of CVA that makes the regulatory
CVA more conservative.As we noted in the advanced CVA VaR
approach,in the current framework the regulators tried to align the
regulatory formula with the Economic CVA by inserting risk
neutral(market-implied) CDS spreads of the counterparty where under
the FRTB all the parameters that are inserted into the internal models will
be risk neutral for hedging efficiency and alignment with the internal
Economic CVA model that a bank uses.
In the pre-crisis era many financial institutions were receiving Triple A
ratings and they were considered too big to fail as we see now with the
Central Counterparties as being almost risk-free.The hidden risks of a CCP
must be exploited and not hidden in any circumstances.The funding of
the CCPs is injected if it is going to default from lack of liquidity by the
Central Banks and this means that we may have again the financial
history to repeat itself by the Central Banks using tax-payers money to
bail out systemic institutions as CCPs.Although,the use of a CCP will make
the transactions transparent to all the market participants,it gives
incentive to the dealers not to measure the counterparty risk since the
CCP is receiving it now.Moreover,there is the risk of moral hazard since as
we mentioned earlier the institutions do not concern for the CCR of the
transaction thus they might enter into toxic transactions with
counterparties and shift the trades to the CCP.I would like to end this
thesis by saying that the Counterparty Credit Risk(CCR) is a systemic risk
that has the potential to destabilize the entire financial system and the
monitor of it should never as history taught us be neglected.
49
`
References
References
[1] BCBS 189,BASEL III:A global regulatory framework for more resilient
banks and banking systems.http://www.bis.org/publ/bcbs189.pdf
[2] Basel Committee on Banking and Supervision.Consultative
document,A Review on the Credit Valuation Adjustment Risk
Framework.Bank of International Settlements October 2015.
[3] Basel Committee on Banking and Supervision.Capital requirements for
bank exposures to central counterparties.Bank of International
Settlements April 2014.
[4] Basel Committee on Banking and Supervision.The standardised
approach for measuring credit exposures.Bank of International
Settlements,March 2014.
[5] Basel Committee on Banking and Supervision.Basel Capital
Accord:International convergence of capital measurement and capital
standards.Bank of International Settlements,July 1988.
[6] Basel Committee on Banking Supervision.Basel II:International
Convergence of capital measurement and capital standards.Bank of
International Settlements,June 2006.
[7] Counterparty Risk Management Policy Group(2005).Towards Greater
Financial Stability:A private sector perspective.
[8] Jon Gregory:Counterparty Credit Risk and the Credit Value
Adjustment:A continuing challenge for global financial markets 2nd
Edition.
[9] International Swaps and Derivatives Association(ISDA)-Best practices
on collateral terms(2013).
[10] Basel III framework:The butterfly effect.Deloitte 2013.
50
References
[11] Financial Stability Board.Implementing OTC Derivatives Market
Reforms.October 2010.
[12] G20 Leaders Statement:The Pittsburg Summit.September 2009.
[13] Basel Committee on Banking and Supervision.Regulatory Consistency
Assessment Programme(RCAP)-Report on risk-weighted assets for
counterparty credit risk(CCR).October 2015.
[14] EBA-Emplehlungen zur Behandlung von CVA Risiko.February 2015.
[15] Lectures on Capital requirements,credit risk,collateral and
centralized clearing.Aarhus Quant Factory,January 2014.
51
`
References
52
`