Head of RCCAD Quantitative Research

02
Introduction to LVA
13
Introduction to CVA
19
Impact of CSA on CVA
26
A New Pricing Framework
31
Centralized Risk Management

To make a long story short, pricing is a question of forecasting future fixed, floating or conditional flows in a given currency and discounting them consistently with a funding level in this currency (in order to avoid arbitrage opportunities).
For a single flow we can formally write:
Time t value of the future flow in a given currency
V t f 
B f
 

F t
Time t forecasted value of the future flow in the given currency
Time t value of a unit of currency paid at T
According to a funding level
In case of collateral agreement, additional flows are to be taken into account in the valuation process.
Indeed, to be posted a collateral has to be funded and remunerated with the funding rate , on the other hand, the collateral posted is remunerated with a given collateral rate described within the collateral agreement.
The additional flows are all differentials of interest generated by the difference between funding and collateral rates applied to the collateral amount posted.
These additional flows have to be funded and their price is straightforward as soon as we know their forecasted value.
3

Coming back on the case of a single flow, additional flows linked to a collateral agreement depend upon the collateral amount paid at each period:
4 t
0 t
1 t
2
Collateral-linked flow paid at t
4 equal to the differential of interest of collateral
Remuneration posted at t
3
C
 
3

 r f t
3 r c
:
   
3

 
3 t
3 t
4 t
5 t
6
Future derivative value
In general, the collateral amount to be posted is directly deduced from the value of the collateralized derivative i.e. including additional interest flows, say V c , which is different from the value of the unsecured derivative ( V f ).
Hence, the value of a collateralized derivative depends upon this value: we’re facing an implicit problem .

In case of bilateral collateral agreement, we have:
C
 

V t c
In this special case, under model assumptions, one can show that the price of a collateralised contract is obtained by discounting with the collateral remuneration rate instead of the funding rate.
For a single flow, we can formally write:
Time t value of the future flow in a given
Currency including collateral additionaml flows
V t c 
B c t ,

F t
Time t forecasted value of the future flow in the given currency
Time t value of a unit of currency paid at T according to the collateral remuneration rate
Note that in this case, the value of the collateralized contract doesn’t depend any more upon the funding rate .
Note also that if a given derivative pays flows in a given currency but is collateralized in another currency then its collateralized value will depend upon FX-Term Changes .
5

Many other possibilities exist in practice. For instance the unilateral collateral agreement can be written as follows:
C


V


t c
In this case, the collateral impact remains implicit but cannot be explicitly solved like in the standard case.
To treat the general case, one has to solve a high dimensional optimal control problem .
This is generally not do-able in practice but it is well approximated by Monte Carlo simulation method
Market data are diffused on simulated paths
On each node of the simulation the Mark-to-Market of each product included in the collateral agreement are approximated
The collateral amount to be posted on each node can then be deduced
Additional flows resulting from collateral agreement can then be evaluated on each node
The average of their present value approximate the LVA impact
Note that the collateral impact crucially depends upon the global portfolio within the collateral contract and cannot be treated on a stand alone basis. A contribution to the global adjustment can be computed.
6

Pre-crisis
Bor rates were market convention for discounting all trades, independently on the counterparty, CSA, etc …
Implicit assumptions
If the counterparty was uncollateralised, CA-CIB could lend/borrow (unsecured) @ Bor flat
If the counterparty was collateralised, it meant the interest paid on the collateral posted/received was Bor (which is consistent with interest - mainly OIS as defined in the CSA)
Historically
Access to liquidity was taken as granted
EONIA, 3m Euribor 6m Euribor: historical values *
Basis were tight
6%
These assumptions were verified 5%
4%
3%
2%
1%
2000 2001 2002 2003 2004 2005 2006 2007
Eonia
3m Euribor
6m Euribor
Source: Bloomberg
7

During and post crisis
Liquidity crisis
Drying up of lending/borrowing between banks
Creditworthiness of banks questioned
Pre-crisis funding assumptions no longer hold
Unsecured funding much more expensive
Interest paid on collateral (usually OIS) significantly diverged from Bor rates
3M EONIA/Euribor spread (LHS)
5Y 3m EONIA/Euribor basis (LHS)
5Y 3m/6m Euribor basis (RHS) EONIA, 3m Euribor 6m Euribor: historical values *
6%
5%
4%
3%
2%
1%
0%
2007 2008 2009 2010 2011 2012 2013
Eonia 3m Euribor 6m Euribor
200
150
100
50
0
25
20
15
10
5
-50 0
2007 2008 2009 2010 2011 2012 2013
8

Liquidity & credit risk issues are more and more actively managed by banks.
The main trend is a clear shift towards growing use of CSA as collateralization remains among the most widely used methods to mitigate counterparty credit risk in the OTC derivatives market.
Growth of value of total collateral (USD billions) Growth of collateral agreements
9
Source: ISDA Margin Survey 2011

Each CSA determines the collateralization terms between counterparties: bilateral or unilateral, type of collateral, currency, haircut, threshold, minimum transfer amount and all other details are stipulated in the CSA. The amount of margin posted and the margin interest – and consequently the valuation of the structure – will depend on the CSA terms.
10
CSA determines the range of assets that may be posted as a collateral – cash in different currencies , government bonds or corporate or mortgage backed securities
The choice of collateral currency will alter the expected return as the cash funding terms are tied to the corresponding currency’s overnight rate (need of cross currency swap if the collateral currency is not the same as the deal currency)
For cash-only CSA’s, the funding curve corresponds to the specified collateral interest rate
The threshold level will determine how much of the exposure is collateralized. Margin transfers will be made only if the minimum transfer amount is exceeded.
Bilateral CSA collateral profile
PV
+
Counterparty posts collateral and receives interest
-
Bank posts collateral and receives interest

Margin transfer form
Unilateral – only one way transfers – CA CIB posts a collateral but the counterparty dos not (required by some supranational entities )
Bilateral
– symmetric transfer terms
Margin call frequency
Daily margin call is frequency required (becoming a market standard). Longer than daily margin call frequency can be practical for markets and assets that are not volatile
Threshold
This is the exposure amount below which collateral is not required (the threshold represents an amount of uncollateralized exposure).
A threshold of zero implies that any exposure is collateralized
Minimum transfer amount
The smallest amount of collateral that can be transferred.
It is used to avoid the workload associated with a frequent transfer of insignificant amounts of collateral
11

Bilateral margin transfer form: symmetric transfer terms for both parties
Daily margin call frequency (weekly can be also accepted as standard)
No threshold – up to 5M threshold is considered as reasonable
Cash and G7 bonds (haircuts – 0%-2% on short term maturities and 5-10% on longer term maturities)
In EUR or in USD, remunerated at EONIA
FLAT or Fed Funds FLAT
No CSA
Unilateral CSA (can be unilateral in our favour; often supranational institutions require an unilateral CSA in their favour)
CSA with very high threshold – 50-100M threshold will impact pricing
CSA with rating triggers (example: CA-CIB needed to post an independent amount to EIB due to the S&P rating action)
Sub-optimal CSAs – negative spreads on cash collateral, securities received that can’t be re-hypothecated
12

The Credit Value Adjustment appears in the pricing framework when a credit risk is taken into account.
Formally, one can explicit this risk by multiplying each payment flow by the following function:
F
T
T
F
T

T
In case of a counterparty default at time T , the key question is to measure the exposure .
A priori, the exposure is the sum of all positive mark to market of each transaction remaining at time T with this counterparty.
In case of netting agreement with the counterparty, the exposure becomes the sum of all netted positive mark to market of each set of transactions within each netting agreement contract.
A classical CVA formula can be expressed as the amount of discounted future Expected Losses
CVA

LGD *
Maturity t


0
PD t

1 , t
* EPE t
* DF t
Loss Given Default Default Probability Exposure at Default (Discounted)
14

Expected Positive Exposure (EPE)
Calculated via simulations process (Monte Carlo…)
Computation including netting and collateral agreements
Involves only the Positive Exposures in case of Counterparty Default
Definition of Exposure linked to the mark to market of transaction
Evaluated Contingent on the default of the counterparty
– including right way / wrong way risks
CSA or break clause have a huge impact on EPE
Default Probability
Implied from CDS spreads (market-implied) or,
Historical default probabilities
Loss Given Default / Recovery Rate
Market Implied (where possible) : LGD
Market
Internal Recovery measure : LGD
Internal
Market CDS Curve
15

Peak Exposure : Maximum of the MtM of the transaction over its lifespan, given a high confidence level (VaR
95%)
Loan Equivalent: Average EPE over time (measure to determine risk equivalent in terms of loan for economic capital calculation)
Tail Credit Risk (CVaR): average of 5% maximum potential losses
10y EUR IRS CA-CIB Receives Fixed 2.3%
16

Measure of Expected Loss
Use of Historical Default Probabilities
Inactive Risk Management (Acceptance to ‘carry’ the Credit Risk)
No Market Hedges in Place (IR, FX or Credit)
CVA as a Mark to Market Adjustment
Market Cost of Dynamically Hedging Counterparty Risk
Use of Market Implied Default Probabilities (implied from CDS)
Active Risk Management Strategy in place
Local Sensitivities
Jump to Default Risks
Concentrations / Wrong Way risks
Market Hedges in place (IR, FX and Credit)
Credit Risk transferred to a centralised CVA desk
17

CVA is a fair market adjustment to the derivatives portfolio
CVA charges are there to offset losses in the global CVA portfolio due to new trades
Incremental impact on the portfolio
CVA P&L is flat provided the cash transfers take place
CVA hedges are initiated in order to offset future CVA P&L volatility for CA-CIB
Due to portfolio MTM movements (IR, FX, Credit Hedges)
Due to counterparty CDS Spread Changes (Credit Hedges)
At inception: CVA P&L is flat, Hedge P&L is flat:
1. CDS spreads increase: CVA increases (Loss) versus Hedge P&L (Gain)
2. CDS spreads decrease: CVA decrease (Gain) versus Hedge P&L (Loss)
3. CDS spreads stay static: Negative carry on Hedge (Loss) is offset against positive carry of CVA (Gain)
CVA Credit Hedges also provide
Jump to default risk management
Basel III capital reductions
Debit Value Adjustment ( DVA ) is the CVA seen from the counterparty. To take it into account allows symmetrical views on the shared portfolio.
18

The Credit Support Annex is a key tool for credit risk mitigation
EPE computation includes netting and collateral agreements
EPE is calculated up to the threshold
Above threshold, mark to market drift is calculated on margin call period + collateral lag period (10days)
CSA features are built into EPE simulations and consequently have an impact on CVA
Trade description
Collateral features
Start date:
Maturity:
Notional:
CA-CIB receives:
CA-CIB pays:
10 Apr 2012
10Y
EUR 100M
2.30% (SA, act/360)
6M Euribor (SA, 30/360
Unilateral vs Bilateral
Threshold
Frequency
Currency
Minimum Transfer Amount (MTA)
Counterpart:
5Y cds:
Internal rating:
XXX
143bps
B
20

No collateral agreement in place
Peak exposure:
Market CVA:
Historical CVA:
9 508 071
137 124 (1.49 bps p.a)
9 942
(0.11 bps p.a)
Market CVA ~ hedging cost of loan lquivalent on cds market
Risk exposure is maximal for CA-CIB
EPE Credit Risk Loan equivalent
10,000,000
9,000,000
8,000,000
7,000,000
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
0
20
12
20
13
20
14
20
15
20
16
20
17
20
18
20
19
20
20
20
21
CSA agreement in place
CSA in place
Bilateral
Frequency: daily
Threshold: 0
MTA: 0
Currency: EUR
Peak exposure: 1 378 356
Market CVA: 27 948
(0.30 bps p.a)
Historical CVA: 1 850 (0.02 bps p.a)
Sharp decrease of risk profile due to CSA risk mitigation
EPE Credit risk
1,600,000
1,400,000
1,200,000
1,000,000
800,000
600,000
400,000
200,000
0
20
12
20
13
20
14
20
15
20
16
20
17
Loan equivalent
20
18
20
19
20
20
20
21
21

CSA agreement in place
CSA in place
Bilateral
Frequency: weekly
Threshold: 0
MTA: 0
Currency: EUR
Weekly frequency: drift is computed on one week +
10 days collateral lag
Peak exposure: 1 704 987
Market CVA: 33 938 (0.37 bps p.a)
Historical CVA: 2 252 (0.02 bps p.a)
EPE Credit risk
1,800,000
1,600,000
1,400,000
1,200,000
1,000,000
800,000
600,000
400,000
200,000
0
20
12
20
13
20
14
20
15
20
16
20
17
Loan equivalent
20
18
20
19
20
20
20
21
CSA agreement in place
CSA in place
Bilateral
Frequency: daily
Threshold: 0
MTA: 0
Currency: EUR
Peak exposure: 1 378 356
Market CVA: 27 948 (0.30 bps p.a)
Historical CVA: 1 850 (0.02 bps p.a)
EPE Credit risk Loan equivalent
1,600,000
1,400,000
1,200,000
1,000,000
800,000
600,000
400,000
200,000
0
20
12
20
13
20
14
20
15
20
16
20
17
20
18
20
19
20
20
20
21
22

CSA agreement in place
CSA in place
Bilateral
Frequency: daily
Threshold: 500K
MTA: 0
Currency: EUR
Peak exposure: 1 878 356
Market CVA: 43 346 (0.47 bps p.a)
Historical CVA: 3 263 (0.024 bps p.a)
EPE Credit risk Loan equivalent
2,000,000
1,800,000
1,600,000
1,400,000
1,200,000
1,000,000
800,000
600,000
400,000
200,000
0
20
12
20
13
20
14
20
15
20
16
20
17
20
18
20
19
20
20
20
21
CSA agreement in place
CSA in place
Bilateral
Frequency: daily
Threshold: 0
MTA: 0
Currency: EUR
Peak exposure: 1 378 356
Market CVA: 27 948 (0.30 bps p.a)
Historical CVA: 1 850 (0.020 bps p.a)
EPE Credit risk
1,600,000
1,400,000
1,200,000
1,000,000
800,000
600,000
400,000
200,000
0
20
12
20
13
20
14
20
15
20
16
20
17
20
18
Loan equivalent
20
19
20
20
20
21
23

Trade description
Start date:
Maturity:
Notional:
EURUSD:
CA-CIB pays:
CA-CIB receives:
Notional exchange:
10 Apr 2012
10Y
EUR 100M
1.3091
6M Euribor (SA, act/360)
USD 2.25% (SA, act/360)
Beg and end
Name:
5Y cds:
Internal rating:
Counterparty
XXX
143bps
B
Collateral features
Unilateral vs Bilateral
Threshold
Frequency
Currency
Minimum Transfer Amount (MTA)
24

No collateral agreement in place
Peak exposure: 94 738 968
Market CVA:
Historical CVA:
1 718 224
192 376
(18bps p.a)
(2 bps p.a)
CSA agreement in place
CSA in place
Bilateral
Frequency: daily
Threshold: 0
MTA: 0
Currency: EUR
100,000,000
90,000,000
80,000,000
70,000,000
60,000,000
50,000,000
40,000,000
30,000,000
20,000,000
10,000,000
0
20
12
20
13
Risk exposure is maximal for CA-CIB
EPE Credit Risk Loan equivalent
20
14
20
15
20
16
20
17
20
18
20
19
20
20
20
21
CSA drastically minimizes risk exposure on cross-currency
25
Peak exposure: 4 181 994
Market CVA:
Historical CVA:
227 864
22 381
(2.40 bps p.a)
(0.24 bps p.a)
4,500,000
4,000,000
3,500,000
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
0
20
12
20
13
20
14
EPE
20
15
Credit risk
20
16
20
17
20
18
Loan equivalent
20
19
20
20
20
21

In the new pricing framework, market prices remain of course a central source of information but one has to interpret them consistently .
A price is at least dependent with the CSA of the product priced and when one observe the price of an OTC product on a screen the question of the implicit CSA of this price has to be solved.
To fix this problem, a standardization of market practice arise
Standard swap are assumed cleared with a collateral in the currency of the swap with a collateral remuneration at
OIS rate.
Multi-currency products are often assumed collateralized in USD with a collateral remuneration at USDOIS rate.
Physical settlement swaption quotation often assumes the underlying swap to be a standard swap and quotes a forward premium in order to avoid the LVA impact on the discounted premium.
Once the implicit CSA question is answered, it becomes possible to strip from market prices cleaned market data (IR curves per tenor, FX forward, default probabilities, inflation forward, liquid volatilities, etc)
Our own funding level will also intervene in the new pricing framework even if its monetisation isn’t straightforward.
From the CVA point of view, some new deal information are to be taken into account like break clause .
Lastly, the main new information type to input and which will impact all quotations is all information related to the client (CSA, netting agreement, rating, …)
27

In addition to market data and client data, we have seen that most of xVA are linked to global portfolio measures based on Monte Carlo simulations .
Once the diffusion model is defined, its calibration can partly be implicit (calibration on a set of market prices) but will mainly linked to historical market behaviour.
Like for any diffusion model design for structured derivatives pricing, the calibration process is dependent with the sophistication of the diffusion process (from a theoretical point of view) and availability of implicit and historical information .
A key point to focus on is the joint behaviour between all class of market risks (let’s say correlation to simplify) implicitly defined in the diffusion process. It is indeed well known that this point will drive market risk netting from the global portfolio point of view.
For a great number of counterparties there is no quoted CDS .
The CVA needs information on default probabilities and LGD for any counterparty. This information is to be forecasted .
Based on all internal works on counterparty risk management (sector classification, internal ratings, historical recovery rates, …), it becomes possible to map any counterparty on market information.
28

By definition, the “stand alone” price of a product is its value independent with the portfolio of deals
Raw
Market Data
Stripping under CSA assumptions
Cleaned
Market Data
Calculation Engines
Data Forecasting
Engine
29
Internal
Client
Data
Internal
Client
Portfolio
Product Description
(Termsheet) t
0 t
1 t
2 t
3
4 t t
5 t
6
Client
Bilateral
CSA Input
Global Simulation
Engine
Stand-Alone
Pricing Engine
Portfolio adjustment
(CVA, DVA, FVA, non standard LVA)
Stand alone Price

Generally speaking, portfoliolinked adjustments aren’t linear i.e. the value adjustment of a given deal depends upon the portfolio (and market data) at the moment the valuation.
Same trade with two counterparties, with different credit profiles or portfolio visà-vis the bank, will have different market prices .
Example: Client receives Fixed on 10y Swap
Mid Market 10y Swap Rate = 2.31%
– Client 1: Rated Areceives 2.27%
– Client 2: Rated B+ receives 2.23%
4bp CVA charge
8bp CVA charge
In practice, an incremental portfolio value adjustment relating to the new trade is used. It corresponds to the differential of portfolio value adjustment with and without the deal.
This incremental value can either be positive or negative and a pricing policy is to be defined .
30
The global portfolio value adjustment is made with several sources of risks (credit, liquidity, funding) and with several market data qualities (pure market data versus forecasted data).
To look into these, it is meaningful to evaluate the global portfolio value adjustment breakdown based on those different sources of risk and data qualities.
Similarly, this breakdown can be computed for incremental portfolio value adjustments at the deal level .

A priori, the stand-alone product value can be hedged trading desk per trading desk without particular need of centralisation.
Nevertheless, the multiplicity of CSA may induce “not so material” additional sources of risks for trading desks
(like cross-currency basis swap margin risks) which can pollute trading desk risk management and which could be centralised.
We have to keep in mind that any transaction has, from valuation and risk management point of view, a stand-alone part and a portfolio part . The implicit CSA of the standalone part of the deal isn’t necessarily the actual CSA of the deal.
Funding risk could in theory be managed on a standalone basis since this risk isn’t explicitly linked to the portfolio view.
But this risk can’t be directly risk managed in the market .
Hence, this risk has to be risk managed jointly with ALM . Indeed, the stake is the remuneration or the charge of this adjustment. This has to be made consistently with the way these remuneration/charge are monetised by ALM .
Global simulation tools can of course be very used to obtain a complete view of the distribution of funding needs at any future maturity (expectation, standard deviations, … of funding needs including collateral simulation).
32

By definition, this adjustment has to be centrally risk-managed . Indeed:
The value to risk manage make sense at the portfolio level only.
Global metrics to evaluate (EPE) are time consuming and depend upon a wide range of market data then standard complete local management is just numerically impossible and alternative risk management strategies has to be developed.
Some adjustments are based on forecasted/mapped data which as to be specifically risk managed
At the centralized level, impacts of global events like defaults, CSA changes, Funding changes can be anticipated , studied and quantified .
Conversely, a centralized desk can be pro-active on all portfolio-linked risks :
CSA change
Waives/Further discounted counterparties (to take into account liquidity providers or to be aligned with the Banks business strategy.
Wrong way / Right way risk.
RWA management
A centralised desk ensure a unique and consistent FO view internally and externally.
33

Capital CCR only covers default risk: MtM + standardized add-on based on issuer type, underlying and maturity
No capital requirement for MTM loss due to change in counterparty credit spread
34
Capital CCR only covers default risk
Internal Ratings-Based approach: Internal assessment of default risk via internal probability of default and LGD
No capital requirement for MTM loss due to change in counterparty credit spread
EPE: counterparty exposure estimated using non-stressed market data, on a 1Y horizon
Basel III Capital CCR = Capital Default (Basel II) + Capital CVA
Capital CVA: additional Capital requirement for MtM loss due to change in counterparty credit spread
Capital CVA : Market Risk capital charge estimated using stressed VaR on credit instruments
EPE: counterparty exposure estimated under stressed parameters on the full maturity
CVA VaR is calculated Net of Eligible Hedges
Other adjustments:
– Assuming a higher correlation between financial institutions in the supervisory formula
–
Extending the collateral lag period from 10 days to 20 days

Changing Landscape
CVA VaR now a key component in Return on Capital calculations for New Trades
DVA not an allowable offset under Basel III, so competitors using DVA for pricing must consider capital usage
Active CDS Hedging encouraged  Influences CDS pricing and volatility
Innovation needed to help reduce RWA costs
Cost of Novations / Intermediations now closely scrutinised
Need for CVA Pricing Tools to consider Basel III impacts
CVA Capital Methodology linked more closely to Market Dynamics
Regulatory Methodology is entirely Market Based --> No reliance on Historical Default Measures
Basel III extends maturity of Exposure at Default to the Full EPE Profile (previously 1y EPE under Basel II)
Capital Relief provided by Eligible Hedges
Includes Single name CDS, CDS index, CCDS and other hedges that directly reference the Counterparty
Hedging a CVA portfolio releases Capital
35

Centralise and risk manage FO derivatives counterparty and portfolio-linked risk
Minimise xVA P&L impact for FO through:
Systematic Macro hedging of the overall xVA P&L impact
Single Name default hedging (where practical)
Active participation in RWA management
Target business model is to incentivise Sales Force not only on revenue generation but also on RWA and liquidity consumption
Sales recognition methodology has to be consistently defined
Establish a Pricing Policy aligned with the internal xVA methodology
Educate and train sales and support functions in xVA related issues
Involvement in Regulatory Discussions / Decisions affecting xVA
Involvement in ISDA / CSA discussions affecting xVA.
Need to remain Competitive in Pricing …
Must remain business-focused and incentivise the right types of trades:
– Waiver / Exemption for Target Clients / Businesses
– Additional Charge for Wrong Way trades
– Benefits for Right Way Trades / Unwinds / Portfolio Diversifications
– Need for feedback from clients relating to current market practices
– Encourage risk mitigation (eg negotiation of Credit Support Annex (CSA ) with counterparties)
36

Central Desk is there to Support the Business:
In accurately pricing Credit and Liquidity into new trades, and
To manage the credit risk of derivatives portfolio through dynamic CVA hedging
To achieve this Central Desk needs:
Active Dialogue with Trading / Sales / Structuring on new trades, and existing portfolio (risk reduction opportunities)
Involvement in Complex Trades , especially where replacement costs in default are hard to define
Clear Understanding of all key components of the trades
Identification of potential risk mitigants - break clauses, legal details (CSA, netting), etc
Feedback from Clients !
... and on problem names
To ‘wall cross’ the CVA team in case non-public information needs to be shared. To check PV details in front/back office systems.
Involve Legal team to ensure appropriate modus operandi is followed
Goal is to streamline process
Revised guidelines for involvement of Central desk in trade analysis (e.g. where CVA > 50k EUR, ... thresholds to be discussed/revised)
Improvement of CVA / LVA pricing tools (including capital costs/usage)
Clear communication is critical
... and to Adapt to Change
Methodology is dynamic and intended to support business initiatives
37

38
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