Counterparty Risk Citi

1Evan Picoult, February, 2008

Counterparty Credit Risk and Contingent Credit Default Swaps

PRMIA Credit Risk Forum

Evan Picoult

Citi Risk Oversight


Table of Contents

51Summary of methods to hedge counterparty credit risk9

47Decomposing and dynamically hedging counterparty credit risk8

38Contingent credit default swaps (CCDS) as a hedge of counterparty credit risk 7.

35Credit default swap (CDS) as a hedge of counterparty credit risk6.

32Mitigating counterparty credit risk5.

23Economic capital: Economic loss perspective and the CVA for counterparty risk4.

14Economic capital for counterparty credit risk: Default only perspective3.

10Economic capital for loans2.

3Measuring counterparty credit exposure: Portfolio Simulation1.

BASIC QUESTION: WHAT ARE THE CONSEQUENCES OF CREDIT EXPOSURE DEPENDING ON THE UNCERTAIN POTENTIAL FUTURE STATE OF MARKET RATES?


1. Measuring counterparty credit exposure: Portfolio Simulation


� The potential exposure profile over time of a single OTC derivative is uncertain. It is contingent on the path market rates follow over time.

Random path of forward FX rate for a fixed settlement date, over life of forward transaction in scenario 1.

Profile of market value of forward FX transaction over its life, for scenario 1.

Exposure Profile of transaction for scenario 1.

We only have exposure when the contract has a positive value to us.

Example 1: Forward FX, We buy GBP and sell US$ for settlement in two years at 1.5000 US$/GBP.

Random Scenario 1 for Forward FX Rate

1.250

1.375

1.500

1.625

1.750

0 3 6 9 12 15 18 21 24

Time (months)

Fo

rward

E

xch

an

ge

Rate

Forward FX Replacement Cost for Scenario 1

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

0 3 6 9 12 15 18 21 24

Time (Months)

Re

pla

ce

me

nt

Co

st

(%

N

oti

on

al)

Forward FX Exposure Under Scenario 1

0%

5%

10%

15%

20%

0 3 6 9 12 15 18 21 24

Time (months)

Po

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(%

No

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Counterparty credit exposure – single transaction


Counterparty credit exposure

Example 2: Three year Fixed/Floating LIBOR Interest Rate Swap

Profile of IR Swap Value

-2%

0%

2%

4%

6%

0 6 12 18 24 30 36

Time (Months) P

ote

nti

al E

xp

osu

re

(% N

otio

na

l)

Random Rate Scenario

3%

4%

5%

6%

7%

8%

0 6 12 18 24 30 36

Time (months)

Inte

res

t R

ate

IR Swap Exposure Profile

0%

2%

4%

6%

0 6 12 18 24 30 36

Time (Months)

Po

ten

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l E

xp

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(%

No

tio

nal)

� If we simulate thousands of paths of the market we can represent the potential exposure profile of a contract at a specified confidence level:

99% CL Profile

97.7% CL Profile

Expected Profile

Int. Rate Swap Exposure Profiles

at Three Confidence Levels

0%

1%

2%

3%

4%

5%

6%

7%

0 6 12 18 24 30 36

Time (Months)

Ex

po

su

re P

rofi

le (

%

No

tio

na

l)

99.0% CL Profile.

97.7% CL Profile.

Expected Profile

Forward FX Exposure Profiles


0%

10%

20%

30%

40%

50%

60%

0 3 6 9 12 15 18 21 24

Time (Months)

Ex

po

su

re P

rofi

le (

% N

oti

on

al)


� Two methods for measuring counterparty exposure (CE) of counterparty with multiple transactions :

Simple “Add-On” method for each transaction

CE TRANSACTION = Current MTM + “Worst case” potential increase in value

= Current MTM + Notional Principal * Credit exposure factor

CE CP PORTFOLIO = Σ Σ Σ Σ CE TRANSACTION

Portfolio simulation method:

CE CP PORTFOLIO = THE EXPOSURE PROFILE OF COUNTERPARTY

COUNTERPARTY EXPOSURE PROFILE

0

25

50

75

100

125

150

0 6 12 18 24 30 36 42 48 54 60

TIME (months)

PO

TE

NT

IAL

RE

PL

AC

EM

EN

T C

OS

T

($m

m)

Potential Exposure For A Counterparty With Multiple Transactions

Potential increase in value per unit of notional principal given transaction’s features.

Potential exposure to a counterparty, at a high C.L., over lifetime of transactions with counterparty.

Assumes:

- No additional transactions

- Contractual cash flows set and settle over time.

- All legally enforceable riskmitigant agreements are taken into account.


O DETAILED CONTRACT TERMS AND CONDITIONS.

Credit

Admin O TABLES OF LEGAL AGREEMENTS- NETTING

- MARGIN

O COLLATERAL

Credit

Admin O TABLES OF DEFAULT TRANSACTION PROFILES

COUNTERPARTY’S:

- TRANSACTION DETAILS.

- RISK MITIGANT DATA.

COUNTERPARTY’S:EXPOSURE PROFILE.

CE SERVER(analytical engine)

ANALYTICALENGINE

Tables of historical or implied volatilities

and correlations

Daily feeds of current market data

MARKET DATA

COUNTERPARTYCREDIT DATA BASE

FX FX DEBT I.R. EQ. COMM. COLLATERAL PRODUCT PROCESSOROPT SEC. DER. DER. DER. SYSTEM SYSTEMS

Detailed T&C

of Transaction

Counterparty Exposure Portfolio Simulation


1) Simulate a path, p, of market rates over time, M(t)P

- Start with current market rates.

- Simulate a scenario (or path) of market rates at many future dates, over many years,

using tables of volatilities and correlations.

General method to simulate counterparty’s exposure profile:

4) After simulating thousands of potential paths of market rates, M(t)p

Calculate exposure profile of counterparty: the potential exposure at some high confidence level, at a set of forward dates

2) For simulated path, p, measure the potential market value over time of each transaction withcounterparty K.

- Start with feed of transaction details and legal information.

- For each simulated scenario, calculate the potential market value of each contract

at many future dates, using the contract’s terms and conditions, revaluation formula and

the simulated state of the market.

- For each simulated scenario, at each future point in time, transform the

potential market value of each contract into the potential exposure of the portfolio

through aggregation rules that take risk mitigants and legal context into account.

- i.e. For the counterparty K, for path M(t)P derive Exposure(t)K,P

3) Then for simulated path, p, derive counterparty K’s potential exposure over time

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Counterparty credit exposure

� The potential exposure profile of a counterparty with many transactions is contingent on all the market factors that effect the value of those transactions as well as any legally enforceable risk mitigation agreements, such as netting or margin.

� It is complex to model because of the need to take into account the effect of legally enforceable risk mitigation agreements like netting and margin.

� If we simulate thousands of paths of the market we can represent the potential exposure profile of a portfolio of contracts at a specified confidence level:

99%CL

Expected Positive Exposure

(EPE)

A Counterparty's Exposure Profile

0

25

50

75

100

125

150

0 6 12 18 24 30 36 42 48 54 60

Time (Months) ==>

Po

ten

tial

Exp

osu

re (

$M

M)

Potential exposure profile of a counterparty, at two confidence levels, over the lifetime of the transactions with the counterparty:

Assumes:

• No additional transactions

• Contractual cash flows are set and settle over time.

• All legally enforceable risk mitigation agreements are taken into account


2. Economic Capital for loans


Probability Distribution of Potential Credit Loss

for a Portfolio of Many Obligors

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

0-20-40-60-80-100-120-140-160

Potential Credit Loss ($mm)

Pro

bab

ilit

y o

f C

red

it L

oss

EC Definition

� Economic Capital (also called “Economic Risk Capital” or “Risk Capital”) is a measure of risk.

� Risk in this context means the potential unexpected loss of economic value over one year, calculated at a very high confidence level (99.97% CL).

� Thus EC measures risk from an insolvency or debt holders perspective (potential loss of value) rather than from an equity investment perspective (undiversified volatility of returns).

� Here is an example of EC for a loan portfolio:

Expected LossLoss at high CL

Economic Capital

Economic capital

= Unexpected Loss

= Loss at very high CL– Expected loss.

Expected loss should be covered by reserves and/or pricing.

• Finally, need to allocate total EC to the EC per loan as a function of risk characteristics of obligor, loan facility and risk concentration


ASSUME SOURCE OF CREDIT RISK IS DEFAULT AND RECOVERY ONLY.

• Factors needed to simulate total loss distribution:

- Credit exposure per obligor

- Probability distribution of exposure at default, for contingent credit.

- Probability of default and correlations of probability of default

- Probability distribution of loss given default (LGD) (i.e. 1 – recovery%).

• A robust method will model and capture the relative degree of risk

diversification or risk concentration in the portfolio.

• Also need a method for allocating the total EC across all obligors to each

loan facility, as a function of risk characteristics of obligor and loan facility.

• There are several very different ways of modeling the potential loss

distribution due to default and recovery and of allocating total EC to each

credit facility.

Economic Loss - Loan Portfolio - Default Only Analysis


- Probability distribution of migration of PD (internal risk rating).

- Volatilities and correlations of change in spread, given rating.

- Potential change in idiosyncratic spread.

ASSUME SOURCE OF CREDIT RISK IS ECONOMIC LOSS

• Factors needed to simulate loss distribution:

- Credit exposure per obligor

- Probability distribution of exposure at default, for contingent credit.

- Probability of default and correlations of probability of default.

- Probability distribution of loss given default (LGD).

• There are several very different ways of modeling the potential loss

distribution due to economic loss.

Components of default only perspective

Component of long term simulation of obligor’s spread

Economic Loss - Loan Portfolio – Economic Loss Analysis


3. Economic Capital for counterparty credit risk:Default only perspective


Default

and

recove

ry

scenarios

Overview Of Analysis

Potential Loss

Distribution

Set of Transactions

Set of Legally Enforceable Risk Mitigation Agreements

Simulated paths of market

Exposure Profile of CP N at x% CL

. . .Exposure Profile of CP 2 at x%CL

Exposure Profile for CP 1 at x%CL

Exposure Profile of Portfolio of Transactions with Counterparty at x%CL

Path M

. . .. . .. . .. . .. . .

. . .. . .. . .. . .Path 2

Exposure profile of CP N for path 1

. . .Exposure profile of CP 2 for path 1

Exposure profile of CP 1 for path 1

Path 1

Counterparty

N

. . . Counterparty

2

Counterparty

1

SIMULATION OF COUNTERPARTY

EXPOSURE PROFILE

. . . Default/Recovery Scenario J

Default/Recovery Scenario 2

Default/Recovery Scenario 1

Simulation of exposure profile

Full Simulation of Economic Capital:

Joint simulation of exposure, default and recovery


– EC For Counterparty Risk vs. EC For Loan Risk From A Default Only Perspective.

Economic Loss - Counterparty Risk - Default Only Analysis

√√√√Inter-counterparty portfolio w.r.t. exposure

√√√√√√√√Inter-counterparty portfolio w.r.t. default.

TYPES OF DIVERSIFICATION BENEFITS

DRIVERS OF WIDTH OF LOSS DISTRIBUTION

√√√√Intra-counterparty portfolio

w.r.t. exposure

√√√√Variable exposure

√√√√√√√√Default and recovery

COUNTERPARTY CREDIT RISK

LOAN PORTFOLIO

– Full simulation of EC from a default only perspective:

� For a given path of the market over time, the risk free value of each contract and the corresponding conditional exposure of each counterparty can be fully specified.

� For each path we can therefore simulate thousands of scenarios of default and recoveries, exactly as we would for a loan portfolio from a default only perspective.

� We can then loop over thousands of potential scenarios of changes in market rates.

IncreasesRisk

DecreasesRisk


1) SIMULATE A PATH, P, OF MARKET RATES OVER TIME M(t)P

Same as for Exposure Profile.

EC BY FULL SIMULATION: GENERAL METHOD, FIVE STEPS

5) AFTER SIMULATING THOUSANDS OF POTENTIAL PATHS OF MARKET RATES, M(t)P

CALCULATE FULL LOSS DISTRIBUTION AND DERIVE THE FULL SIMULATION ECONOMIC

CAPITAL FOR COUNTERPARTY RISK.

2) FOR SIMULATED PATH P, MEASURE THE POTENTIAL MARKET VALUE OVER TIME OF EACH TRANSACTION WITH EACH COUNTERPARTY K. Same as for Exposure Profile.

3) FOR SIMLUATED PATH P, DERIVE COUNTERPARTY K’S POTENTIAL EXPOSURE OVER TIME.

i.e. For each counterparty K, for path M(t)P derive Exposure(t)K,P Same as for Exposure Profile.

Lo

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nd

s o

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ath

s P

.

4) USING THE SET OF EXPOSURE PROFILES {Exposure(t)K,P } FOR EACH AND EVERY COUNTERPARTY K, GENERATED BY MARKET PATH P:

CALCULATE THE POTENTIAL LOSS DISTRIBUTION BY SIMULATING THOUSANDS OF SCENARIOS OF DEFAULT AND RECOVERY FOR THE SET OF COUNTERPARTIES K.


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s

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fau

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ve

ry.


� Is it possible to define a “loan equivalent” for counterparty exposure?

– A “Loan Equivalent” is the fixed exposure profile, per counterparty, that would generate the same economic

capital as obtained by full simulation of changes in market rates, default and recovery.

� How good an approximation is the expected exposure profile as a loan equivalent? In what context, if any, is it a good approximation?

Note:

– There is no actual scenario of market rates that corresponds to each counterparty having an exposure equal to its average potential positive exposure. In fact, for a large derivative trader there will be no scenario for which every counterparty will have positive exposure at the same time. Nonetheless, the loan equivalent is a valid and very useful method to assess the total Economic Capital due to counterparty risk, across all counterparties.

� Why does question arise?

– In Basel II: Risk Weighted Asset = EAD * RW(PD, LGD, M) where RW is the risk weight function. Therefore to

calculate the RW for counterparty risk we need to measure the EAD for counterparty risk (i.e. the loan

equivalent) and M (the effective maturity).

– Internally, transactors need an easy method for evaluating EC and return on EC. Therefore they need to have

the loan equivalent (EAD in Basel II) and the effective maturity (M in Basel II) as parameters to input into EC

tables or EC analytic functions (as in Basel II).



a) Simulate a path, P, of market rates over time M(t)P

EC using expected positive exposure profile as a loan equivalent:

3) Calculate the economic capital from the loss distribution derived from each counterpartry’s expected exposure profile.

b) For simulated path, P, measure the simulated market value over time of each transaction with counterparty K.

c) For simulated path, P, derive counterparty exposure over time.

i.e. For the counterparty K, for path M(t)P , derive Exposure(t)K,P

Lo

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nd

s

of

pa

ths

P.

2) Use the set of expected positive exposure profiles {EPE (t)k} for every counterparty

Calculate the potential loss distribution by simulating thousands of scenarios of default and recovery for the set of counterparties K.

1) Calculate the expected positive exposure profile, EPE(t)k , of each counterparty K

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.Economic Loss - Counterparty Risk - Default Only Analysis

d) Derive each counterparty’s expected positive exposure profile EPE(t)K


� Shortcut to full simulation of exposure, default and recovery: EAD = αααα * EPE

– Define a portfolio parameter alpha: αααα

Capital Economic

Capital Economic

ONLY DEFAULT SIM;FIXED_EPE_

ONLY DEFAULT FULL_SIM; =αααα

– Where the denominator of the ratio is defined as the economic capital measured by assuming that the exposure profile of each counterparty can be expressed as a constant exposure whose magnitude is EPEK , the average of the EPEK(T) profile over a one year horizon.

– EPEK = Σ Σ Σ Σ EPEK(tj) / (tj - tj-1)

– For a large trading desk, αααα ≅≅≅≅ 1.1 to 1.2 (e.g. see Canabarro, Picoult, Wilde; Risk, Sept. 2003)

� For each counterparty, to a very good approximation, the economic capital per counterparty can be calculated by treating the counterparty exposure as if it were a fixed exposure of magnitude:

– EAD (Exposure at Default) = αααα * EPE

where EPE is the average of the EPE(t) profile over one year.

– Note: In a default only analysis, the effective maturity of the exposure is one year.


EC using EPE * αααα as a loan equivalent:


� Create test portfolios and calculate α α α α as a function of the characteristics of the portfolio:

� Effective number of counterparties

� Effective number of market factors

� Probability of default of counterparties

� Correlation of default.

� Initial MTM of counterparties’ portfolios.

� Other factors.

� Initial Proposal: …………………………………………Evan Picoult, Citigroup

� Simulations of Stylized Portfolios:…………………..Eduardo Canabarro, GS (now Morgan Stanley)

� Analytical Calculations:………………………………..Tom Wilde, CSFB

� Measurement of a for Real Portfolios:………………Several Firms

� SUMMARY CONCLUSION: For Large Market Makers αααα ≈ 1.1

See: - ISDA web site, Papers on Counterparty Risk to Basel Committee, June 2003

- Risk Magazine, (Canabarro, Picoult, Wilde) September, 2003

� Later, additional calculations were done:

� For “general wrong way risk”: For Large Market Maker αααα ≈ 1.2

but some banks have portfolios with mostly “general right way risk”.

ISDA TESTS



αααα across various portfolio characteristics

Correlation

Current

exposure

Number of

risk factors

Number of

ctpt'ies

Prob of

default Percentile

M-Carlo

(Eduardo)

Analytic

(Tom)

M-Carlo

(Eduardo)

M-Carlo

(Marcus)

Analytic

(Tom)

Base case

22% 1.36 3 200 0.30% 99.90% 1.09 1.08 1.12 1.21 1.15

Sensitivity to credit correlation

0% 1.36 3 200 0.30% 99.90% 1.43 1.43 1.43

12% 1.36 3 200 0.30% 99.90% 1.21 1.15 1.23 1.29 1.22

24% 1.36 3 200 0.30% 99.90% 1.08 1.07 1.10 1.17 1.14

50% 1.36 3 200 0.30% 99.90% 1.02 1.02 1.05 1.09 1.09

Sensitivity to current exposure level

22% 0 3 200 0.30% 99.90% 1.35 1.33 1.69 1.47 1.58

22% 1 3 200 0.30% 99.90% 1.14 1.12 1.24 1.28 1.25

22% 2 3 200 0.30% 99.90% 1.05 1.04 1.02 1.12 1.07

22% 3 3 200 0.30% 99.90% 1.03 1.02 1.01 1.07 1.03

Sensitivity to number of market risk factors

22% 1.36 1 200 0.30% 99.90% 1.10 1.09 1.42 1.42 1.38

22% 1.36 5 200 0.30% 99.90% 1.08 1.08 1.16 1.15 1.12

22% 1.36 10 200 0.30% 99.90% 1.07 - 1.09 - 1.09

22% 1.36 50 200 0.30% 99.90% 1.07 - 1.06 - 1.08

Sensitivity to number of counterparties

22% 1.36 3 20 0.30% 99.90% 1.26 1.31 1.35 1.32 1.39

22% 1.36 3 50 0.30% 99.90% 1.22 1.20 1.35 1.28 1.28

22% 1.36 3 100 0.30% 99.90% 1.10 1.13 1.23 1.28 1.20

22% 1.36 3 500 0.30% 99.90% 1.04 1.04 1.12 1.11 1.11

Sensitivity to probability of default

22% 1.36 3 200 0.10% 99.90% 1.17 1.12 1.22 1.31 1.20

22% 1.36 3 200 0.50% 99.90% 1.07 1.06 1.09 1.18 1.14

22% 1.36 3 200 1.00% 99.90% 1.06 1.05 1.08 1.13 1.12

22% 1.36 3 200 5.00% 99.90% 1.05 1.04 1.07 1.13 1.12

Sensitivity to confidence level

22% 1.36 3 200 0.30% 99.00% 1.07 1.10 1.04 1.10 1.13

22% 1.36 3 200 0.30% 99.50% 1.10 1.09 1.08 1.15 1.13

Alpha with Wrong-Way Risk

(Rsq = 20%)

Alpha

Key to names

• Eduardo =

Eduardo

Canabarro

was at Goldman

now at Lehman

• Tom =

Tom Wilde

CSFB

• Marcus =

Marcus Fleck

Dresdner Bank

Data slide originally from Eduardo Canabarro, now at Morgan Stanley.



4. Economic Capital for counterparty credit risk:Economic Loss Perspective and the CVA


� First Question:

– What should be the effect of credit spreads / risk rating on derivative valuation?

– If all derivatives are (and should be) marked-to-market by discounting expected future cash flows at LIBOR bid/offer midpoint, then valuation would be:

• Independent of counterparty’s risk rating and

• Independent of counterparty’s credit spread.

– If that were the case, changes in risk rating or spreads would not cause a change in economic value. Default only and economic loss analysis would be the same.

Economic Loss - Counterparty Risk - Economic Loss Analysis


� What is the credit risk premium for OTC derivatives?

� Let us first review the credit risk premium for a loan:

Bond/Loan Value = PV of cash flows discounted at Risk Free Rate – RISK Premiumloan/Bond

= PV of cash flows discounted at (Risk Free Rate + SPREAD)

∴∴∴∴ Risk Premium Loan/bond ≅≅≅≅ PVRisk Free * Duration * Average SpreadLoan/bond (from simple math)

� Let us try to apply the same logic to calculate the credit risk premium of a derivative:

– Derivative Value = PV of cash flows discounted at Risk Free Rate – Risk Premium

� However, the context for ascertaining the credit risk premium of derivatives is material different than it is for loans because of the different nature of their respective credit exposures. We need to:

– Perform a portfolio analysis of exposure

– Take into account the uncertain future exposure

– Evaluate significance, if any, of bilateral nature of exposure

� In general, at any future date

• Obligor could owe us (asset) or

• We could owe obligor (liability)

� Therefore how should we take the potential bilateral nature of exposure into account?

Method for calculating risk

premium may depend on the

purpose of the calculation:

- Pricing

- Cost of credit



� Let us call the credit risk premium of the counterparty’s portfolio its CVA.

CVA = Credit value adjustment for counterparty’s credit risk

� Therefore, the market value of derivative portfolio with a counterparty is:

= ΣΣΣΣ MARKET VALUE (discounted at risk free rate) - COUNTERPARTY RISK PREMIUM

= ΣΣΣΣ MARKET VALUE (discounted at risk free rate) - CVA

� Measuring the cva of a counterparty: Modification of a proposal by Bollier & Sorensen.

Two perspectives on cva: a unilateral and a bilateral perspective.

Unilateral CVA: CVACOUNTERPARTY K, UNILATERAL = CVA+

CNTPY K

Bilateral CVA: CVACOUNTERPARTY K, BILATERAL = CVA+

CNTPY K - CVA–

CNTPY K

Credit premium of own firm’s expected asset from derivatives

Credit premium of CP’s expected asset from derivatives.

Calculated on a portfolio basis, taking into account potential future exposure

Economic Loss - Counterparty Risk - Economic Loss AnalysisDefining a unilateral and a bilateral CVA


Defining a unilateral and a bilateral CVA

A Counterparty's Expected Positive Exposure Profile

0

15

30

45

60

75

0 6 12 18 24 30 36 42 48 54 60

Time (Months)

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($

MM

)

A Counterparty's Expected Negative Exposure Profile

0

15

30

45

60

75

0 6 12 18 24 30 36 42 48 54 60

Time (Months)

Po

ten

tial E

xp

osu

re (

$M

M)

CVA+

CNTPY K (Credit premium of own’s firm potential asset due to CP K)

CVA-

CNTPY K (Credit premium of CP K’s potential asset due to own firm)

Market Value CP Portfolio = ΣΣΣΣ MVCP Portfolio (risk free) - CVA CP Portfolio

CVA CP Portfolio_Unilateral = CVA+

CNTPY

CVA CP Portfolio_Bilateral = CVA+

CNTPY - CVA-

CNTPY

Expected amount CP will owe to own firm.

Expected amount own firm will owe to CP.

Calculate and sum over each forward period J, for CP K.

Calculate and sum over each forward period J, for CP K

)*** JJJ,KJ,K dftSpread CP ForwardExposure Expected ( J

∆∑∑∑∑++++====

)*** JJJJ,K dftSpreads Firm' Own ForwardExposure Expected( J

∆∑∑∑∑−−−−====



Market Value CP Portfolio = Σ MVCP Portfolio (risk free) - CVA CP Portfolio

CVA CP Portfolio_Bilateral = CVA+

CNTPY - CVA-

CNTPY (bilateral perspective)

CVA CP Portfolio_Unilateral = CVA+

CNTPY (unilateral perspective)

Examples

Example 1:

• Assume:

– Only One Swap With Counterparty

– Counterparty And Own Firm Have Same Risk Rating.

– Potential Change in Value Has Symmetric Shape For Pay or Receive Fixed Swaps.

(e.g. flat yield curve).

• Consequence for unilateral and bilateral CVA

Example 2:

• Assume:

– Only One Swap With Counterparty

– Counterparty Is BBB And Own Firm Is AA.

• Consequence for unilateral and bilateral CVA

Economic Loss - Counterparty Risk - Economic Loss AnalysisImplications of a unilateral and a bilateral CVA


Deriving Duration, M, for Unilateral CVA:

� For simplicity, let us define Spread = average spread for counterparty

EPE1 yr = Average EPE over one year horizon.

� Let us first assume that EPE stays constant but that spreads can change. We have:

∑∑∑∑

∑∑∑∑

====

======== Year 1

1 k

kkk

Maturity

1 k

kkk

dftEPE

dftEPE M

∆

∆

∑∑∑∑====

====portfolio of life Full

1k

kkk dftEPE * Spread CVA ∆

∑∑∑∑====


1k

kkk dftEPE * Spread CVA ∆∆∆

M * EPE * Spread CVA year1∆∆ ≡≡≡≡

� In analogy to the relationship between the change in the credit spread of a bond and its duration, we can define the effective M for the unilateral CVA by the equation:

� We therefore have the definition of M, from a unilateral perspective:

M is simply the ratio of:

The area under the full-lifetime discounted EPE curve divided by the area under the 1-year discounted EPE curve.

For fuller discussion including M for bilateral CVA, see Evan Picoult and David Lamb (2004) Economic Capital for Counterparty Credit

Risk, Chapter in Economic Capital: A Practitioner Guide, London, Risk Books

(Similar to: ∆∆∆∆Risk PremiumBond = ∆∆∆∆ SpreadBond * PVRisk Free * Duration)



Expected Exposure Profile and the EPE averaged over one year.

Example of expected positive exposure increasing in each forward period.

Expected Exposure Profile and the EPE averaged over one year.

Example of expected positive exposure increasing then decreasing over time.

As might occur for portfolio with short-dated transactions

Effective Expected Exposure Profile and the Effective EPE averaged over one year.

Effective Expected positive exposure is defined to never decrease over the first year.

Effective EEk = max(Effective EEk-1, EEk)

Expected Exposure Profile

0

0.5

1

1.5

2

2.5

0 3 6 9 12 15 18

Time (months)

Ex

pe

cte

d E

xp

os

ure Expected Exposure Profile

EPE averaged over one year

Expected Exposure Profile

-0.5

0

0.5

1

1.5

2

2.5

0 3 6 9 12 15 18

Time (months)

Ex

pe

cte

d E

xp

os

ure Expected Exposure Profile

EPE averaged over one year

Effective Expected Exposure Profile

-0.5

0

0.5

1

1.5

2

2.5

0 3 6 9 12 15 18

Time (months)

Ex

pe

cte

d E

xp

os

ure Effective Expected Exposure Profile

Effective

EPE averaged over one

year

Expected

Exposure

Profile

In Basel II EAD = α α α α * Effective EPE What is Effective EPE?




0

25

50

75

100

125

150

0 6 12 18 24 30 36 42 48 54 60

Time (Months) ==>

Po

ten

tial

Exp

osu

re (

$M

M)

140.7 dftEPEportfolio of life Remaining

1 k

kkk ====∑∑∑∑====

∆


0

25

50

75

100

125

150

0 6 12 18 24 30 36 42 48 54 60

Time (Months) ==>

Po

ten

tial

Exp

osu

re (

$M

M)

EPE 75.9 dftEPE Year 1

Year 1

1 k

kkk ========∑∑∑∑====

∆

Therefore M = (140.7/75.9) yrs

= 1.85 yrs

= 22.2 months

Lifetime area under discounted curve

One year area under discounted curve

For Basel II calculation of M:

Need to use Effective EPE over the first year in numerator and denominator rather than EPE

∑∑∑∑

∑∑∑∑ ∑∑∑∑

====

≤≤≤≤

==== >>>>

++++

==== Year 1

1 kkkk

yr1

1 k

portfolio oflife Remaining

yr1 k

kkk

dftEPEEffective

df dftEPEtEPEEffective

M

kkk

∆

∆∆



5. Mitigating Counterparty Credit Risk


Growth of OTC Derivative Market

� OTC Derivative Market continues to grow exponentially, measured by notional outstanding:

� Because counterparty credit exposure is contingent on market rates:

– Counterparty credit exposure is more difficult to measure than lending exposure.

– Counterparty credit risk is more difficult to measure and hedge than lending risk.

GROWTH OF OTC DERIVATIVE MARKET All Currencies

(ISDA) (all dates end-of-yr, but 2007 is as of mid-year)

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,0001

98

7

19

89

19

91

19

93

19

95

19

97

19

99

20

01

20

03

20

05

20

07

Year End

NO

TIO

NA

L P

RIN

CIP

AL

($

bn

)

EquityDerivatives

CreditDefaultSwaps

Total IR andCurrency


Methods for reducing counterparty credit risk� Comparison of different methods for reducing or hedging counterparty credit risk.

� Low costs to enter into.

� Moderate cost to build process to accurately calculate portfolio exposure profile.

Costs

� Widely used.

� Usually weak impact.

� Widely used in interbank market.

� Strong impact

� Reduces exposure if counterparty has transactions with offsetting market values:

– Oppositely positioned transactions.

– Or, potential benefit for a large set of transactions on different, not perfectly correlated, underlying market factors.

Netting

Corporate end-user Usage and Impact

Interbank Usage and Impact

Requirements to be an effective risk mitigant

Method

� Relatively high infrastructure costs and liquidity impact.

� Rarely used because corporations don’t have infrastructure and don’t want liquidity risk.

� Widely used in interbank market.

� Very strong impact when used.

� None – other than a low minimum threshold.

Margin

� Big need� Not needed when there are margin agreements.

Hedge Counterparty Credit Risk

Re

du

ce

co

un

terp

art

y e

xp

os

ure

Re

du

ce

PD


CVA

� Market Value CP Portfolio = ΣΣΣΣ MVCP Portfolio (risk free) - CVACP Portfolio

� Two choices:

– Credit Risk Perspective

� CVA is treated as part of credit risk. This bifurcation of counterparty risk into a) market risk and b) credit risk is identical to what occurs under accrual accounting, where the risk of a loan portfolio is bifurcated into a) accrual interest rate risk and b) credit risk.

� From this perspective hedging counterparty risk is done by buying a CCDS from a third party, in the same way that the credit risk of a loan is hedged by buying a CDS or a Guarantee from a third party

– Full Market Risk Perspective:

� CVA is treated as part of market risk, in the same way that the spread of a bond is treated as part of market risk.

� Dynamically delta hedging CVA is equivalent to transforming counterparty credit risk to market risk and hedging it like market risk.

.


Hedging counterparty credit risk

� Alternative means of hedging counterparty risk (i.e. reducing the PD of counterparty default)

� Credit Risk Perspective: Reduce the effective exposure to the original counterparty

– CDS: Credit Default Swap

� Fixed Notional hedge

– CCDS: Contingent Credit Default Swap

� Variable notional hedge, where notional amount is determined by a referenced derivative.

� Market Risk Perspective: Treat CVA as market risk and hedge it.

– Dynamic Delta Hedging:

� Transform counterparty credit risk into market risk by decomposing and dynamically hedging the CVA (Credit Value Adjustment) of counterparty credit risk.

– CCDS: Contingent Credit Default Swap

� CCDS would have to be analyzed in terms of same factor sensitivities as the CVA


6. Credit Default Swap (CDS) As Hedge of Counterparty Risk


CDS

� A Credit Default Swap (CDS) is a bilateral contract between two parties to isolate and separately trade the credit risk of at least one third party referenced entity:

– The buyer of credit protection pays a periodic fee to the seller in exchange for a contingent payment, on the occurrence of a specified credit event to the referenced entity.

– Upon the trigger of the credit event to the referenced entity, the seller must pay the buyer either:

� The par amount of a referenced asset (e.g. defaulted bond) in exchange for its physical delivery to the seller.

� Or the difference between the par amount and the market value of the referenced asset.

� The terms and conditions of the CDS specify:

– The referenced entity.

– The referenced asset of the referenced entity and its fixed par amount.

– The definition of the credit event

– The tenor of the contract

– The periodic fee.

Periodic payment

Buyer Seller

Contingent payment

Payment is triggered by occurrence of credit event to referenced entity,

and will be of one of two forms:

Either: a) Par amount in exchange for physical delivery of referenced asset

Or: b) Difference between par and market value of referenced asset.


Ineffectiveness of CDS for hedging counterparty credit risk

� Example:

– 3yr pay-fixed/receive floating USD LIBOR IRS;

– Notional principal of $100mm

� How much notional CDS should one buy?

� Statistical picture of exposure over time at different confidence levels

99% CL Profile

97.7% CL Profile

Expected Profile

Int. Rate Swap Exposure Profiles


0%

1%

2%

3%

4%

5%

6%

7%

0 6 12 18 24 30 36

Time (Months)

Exp

os

ure

Pro

file

(%

No

tio

nal)

� If the assumptions about future volatility are accurate than at the 99%CL, the CDS notional would be set at $6mm (6%*100mm).

� But this means one would be over hedged more than 99% of the time. Even for the 99%CL profile, the exposure is at $6mm only for a fraction of the three year period.

� This is an inefficient hedge.


7. Contingent Credit Default Swap (CCDS) As Hedge of Counterparty Risk


CCDS

� A Contingent Credit Default Swap (CCDS) is a form of a CDS.

� Its distinguishing characteristic is that the par amount of the referenced asset that must be delivered to the seller is specified by the market value of a referenced derivative.

– As a consequence, the par amount of the referenced asset is contingent on the state of the market.

� Definition:

– A CCDS is a bilateral contract between two parties to isolate and separately trade the Counterparty Credit Risk of at least one third party referenced entity:

– The buyer of credit protection pays a periodic fee to the seller in exchange for a contingent payment, on the occurrence of a specified credit event to the referenced entity.

– Upon the trigger of the credit event to the referenced entity:

� The par amount of the referenced asset is set to the current market value of the referenced derivative, discounted at LIBOR flat.

� The seller must pay the buyer either:

� The par amount of a referenced asset (e.g. defaulted bond) in exchange for its physical delivery to the seller.

� Or the difference between the par amount and the market value of the referenced asset.

Note: The specific terms and conditions of CCDS will evolve and broaden as market grows.


CCDS

� The terms and conditions of the CDS specify:

– The referenced entity.

– The referenced asset of the referenced entity

– The referenced derivative (whose market value determines the par amount of the referenced asset) and the method for valuing the referenced derivative.

– The definition of the credit event

– The tenor of the contract

– The periodic fee.


Ex. 1 Exposure Profile of 5 Yr. Swap

0

2

4

6

8

10

12

14

0 12 24 36 48 60

Time (Months)

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l R

ep

lac

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t C

os

t

($m

m)

CCDS� Example 1: CCDS which fully hedges a derivative.

– Underlying transaction that needs to be hedged:

� A $100mm, 5 year IRS with counterparty A.

� Counterparty A pays LIBOR and receives fixed semi-annually

– CCDS hedge with counterparty B

� Referenced entity: Counterparty A

� Referenced asset: Five year fixed rate bond of counterparty A that is pari passu, in the event of default, with an unsecured derivative with counterparty A.

� Referenced derivative: $100mm, 5 year fixed/floating LIBOR IRS.

� Credit Event: Default by A.

99% CL Profile

Profile for a random

path.

Exposure Profile of underlying swap Profile of Par Amount of CCDS Hedge=

EPE Profile

Ex. 1 Profile of Par Amount of CCDS Hedge

0

2

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6

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0 12 24 36 48 60

Time (Months)

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l R

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lac

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t C

ost

($m

m)


CCDS

� Example 1 continued

Original exposure to

Counterparty A

Hedged Exposure Residual Exposure to Counterparty A

a

Use either:

• Substitution approach

– Substitute PD of seller of CCDS for PD of underlying counterparty.

– Allowed under Basel.

• Double Default approach

• Calculate joint probability of default of underlying obligor (A) and seller of CCDS (B).

• Basel II has its own double default formula that applies in narrow contexts.

• No residual exposure in this example.

• If there were residual exposure, it would simply be treated as unhedged exposure to the underlying counterparty.


CCDS� Example 2: CCDS which partially hedges a derivative.

– Underlying transaction that needs to be hedged:

� A $100mm, 5 year IRS with counterparty A, with 50% extra notional principal the first 2 years.

� Counterparty A pays LIBOR and receives fixed semi-annually

– CCDS hedge with counterparty B

� Referenced entity: Counterparty A

� Referenced asset: Five year fixed rate bond of counterparty A that is pari passu, in the event of default, with an unsecured derivative with A.

� Referenced derivative: $100mm, 5 year fixed/floating LIBOR IRS.

� Credit Event: Default by A.

Example 2: Comparison of 99%CL Exposure Profile ofUnderlying Swap vs. Par Amount of CCDS Hedge

Ex. 2 Comparison of 99%CL Exposure Profile of

Swap vs. CCDS Hedge

0

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t C

os

t ($

mm

)

In this example, the exposure profile of the referenced derivative (a plain vanilla swap) is not identical to that of the underlying swap during the first 2 years of the 5 year tenor..

Underlying swap

CCDS Hedge


CCDS� Example 2: CCDS which partially hedges a derivative.

Exposure Profile of underlying swap with A

Profile of Par Amount of CCDS Hedge

Profile of Unhedged Exposure to A

Ex. 2 Profile of Par Amount of CCDS Hedge

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($m

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Ex. 2 Exposure Profile of 5 Yr. Swap

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Time (Months)

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t

($m

m)

Ex. 2 Unhedged Exposure Proflie

at 99%CL and EPE

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0 12 24 36 48 60

Time (Months)

Po

ten

tia

l R

ep

lac

em

en

t C

os

t

($m

m)

99%CL

EPE


CCDS

� Example 2 continued

Original exposure to

Counterparty A

Hedged Exposure Residual Exposure to Counterparty A

a

Use either:

• Substitution approach

– Substitute PD of seller of CCDS for PD of underlying counterparty.

– Allowed under Basel.

• Double Default approach

• Calculate joint probability of default of underlying obligor (A) and seller of CCDS (B).

• Basel II has its own double default formula that applies in narrow contexts.

• This example has residual exposure to counterparty A..

• It will simply be treated as unhedgedexposure to the underlying counterparty.


CCDS

� Reference Derivative of CCDS will most likely be a plain vanilla, very liquid derivative.

– Transparency in pricing.

– Ease of delta hedging the CCDS by the seller of the CCDS.

� Questions

– What should be the characteristics of the referenced asset for it to function as an optimal hedge?

� Answer: The referenced asset should be pari passu with derivative it is hedging, so that the LGD will be the same.

– How effective is the CCDS as a credit risk mitigant under Basel II?

� Answer: Recognized by US implementation of Basel II, subject to approval by primary supervisor.

– What is the relationship between the CVA (Credit Value Adjustment) of a derivative (or of a portfolio of derivatives with a counterparty) and the value of the CCDS?

– What alternative means of hedging are there?

� Answers in the remaining sections.


8. Decomposing and dynamically hedging the CVA


Dynamically Hedging Counterparty Risk


Gives rise to market risk EC. Gives rise to counterparty credit risk EC.

∑∑∑∑====


1k

kkkUnilateral dftEPE * Spread CVA ∆

• For a specific portfolio of U.S. Dollar LIBOR interest rate swaps, the discounted area under the EPE curve, Σ(Σ(Σ(Σ(EPEk ∆∆∆∆tk dfk), will be a function of the terms and conditions of all the swaps and the term structure and volatility of the U.S. Dollar LIBOR yield curve.

) x, Mitigants; Risk Cs,&TContract (g * Spread

)x Mitigants; Risk Cs,&TContract (g * Spread

})σ{}r(t){ ; Mitigants Risk Cs,&TContract (g * Spread

df∆tEPE * Spread CVA

kk

kkk

portfolio of life Full

1k

σσ

====

====

====

==== ∑∑∑∑====

,

, kk

. . . x*Spread*xSpread

CVA * * Spread x*

x * Spread dftEPE * Spread CVA

2portfolio of life Full

1k

kkk ++++∂∂∂∂∂∂∂∂

++++++++∂∂∂∂

∂∂∂∂++++==== ∂∂∂∂∑∑∑∑

====

∆∆∆∆∆∆∆ σσσσδσδσδσδσ

δδδδCVACVA

• EPE of counterparty depends on Terms and conditions of contracts, legally enforceable risk mitigant agreements, yield curve and assumed volatilities and correlations.

• Represent interest rates by a single variable X and interest rate implied

vol by a single variable σ σ σ σ .


. . . x*Spread*xSpread

CVA * * Spread x*

x * Spread dftEPE * Spread CVA

2

k

portfolio of life Full

1k

k ++++∂∂∂∂∂∂∂∂

++++++++∂∂∂∂

∂∂∂∂++++==== ∂∂∂∂∑∑∑∑

====

∆∆∆∆∆∆∆ σσσσδσδσδσδσ

δδδδCVACVAk**

Dynamically Hedging Counterparty Risk

∑∑∑∑====


1k

kkk dftEPE * Spread CVA ∆

Delta hedge spread risk in proportional to discounted EPE curve.

Determines notional value of credit default swaps to buy.

Delta hedge potential changes in market rates (Interest rates and implied vol) in proportion to CP spread.

Determines notional value of interest rate option need to buy to hedge interest rate risk and implied vol risk (or more general hedges needed to hedge more general market risk).

Potential risk of correlation of change in spread and changes in market rates.

Determines sensitivity to correlation risk, which may not be possible to delta hedge.

Correlation can be right or wrong way.

Effectively have transformed counterparty credit risk into market risk.


9. Summary of alternative means of hedging counterparty credit risk


CVA


� Two choices:

– Full Market Risk Perspective:

� CVA is treated as part of market risk, in the same way that the spread of a bond is treated as part of market risk.

� Dynamically delta hedging CVA is equivalent to transforming counterparty credit risk to market risk and hedging it like market risk.

� A key market variable is the implied correlation between level of rates and spread. The value of a traded CCDS enables one to impute a market implied correlation to the transaction.

– Credit Risk Perspective

� CVA is treated as part of credit risk. This bifurcation of counterparty risk into a) market risk and b) credit risk is identical to what occurs under accrual accounting, where the risk of a loan portfolio is bifurcated into a) accrual interest rate risk and b) credit risk.

� From this perspective hedging counterparty risk is done by buying a CCDS from a third party, in the same way that the credit risk of a loan is hedged by buying a CDS or a Guarantee from a third party.

� US Regulators have indicated they are open to allowing a CCDS, whose reference derivative is plain vanilla, to be treated like a CDS or a Guarantee under Basel II.

Documents

Counterparty Risk Citi