Counterparty Risk Citi

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Counterparty Credit Risk and Contingent Credit Default SwapsPRMIA Credit Risk Forum

Evan Picoult Citi Risk Oversight

Evan Picoult, February, 2008

1

Table of ContentsBASIC QUESTION: WHAT ARE THE CONSEQUENCES OF CREDIT EXPOSURE DEPENDING ON THE UNCERTAIN POTENTIAL FUTURE STATE OF MARKET RATES? 1. 2. 3. 4. 5. 6. 7. 8 9 Measuring counterparty credit exposure: Portfolio Simulation Economic capital for loans Economic capital for counterparty credit risk: Default only perspective Economic capital: Economic loss perspective and the CVA for counterparty risk Mitigating counterparty credit risk Credit default swap (CDS) as a hedge of counterparty credit risk Contingent credit default swaps (CCDS) as a hedge of counterparty credit risk Decomposing and dynamically hedging counterparty credit risk Summary of methods to hedge counterparty credit risk 3 10 14 23 32 35 38 47 51

Evan Picoult, February, 2008

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1. Measuring counterparty credit exposure: Portfolio Simulation

Evan Picoult, February, 2008

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Counterparty credit exposure single transactionThe potential exposure profile over time of a single OTC derivative is uncertain. It is contingent on the path market rates follow over time.Example 1: Forward FX, We buy GBP and sell US$ for settlement in two years at 1.5000 US$/GBP. 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.

Random Scenario 1 for Forward FX Rate1.750

Forward FX Replacement Cost for Scenario 1 Replacement Cost (% Notional)20% 15% 10% 5% 0% -5% -10% -15% -20%

Forward FX Exposure Under Scenario 1 Potential Exposure (% Notional)20%

Forward Exchange Rate

1.625

15%

1.500

10%

5%

1.375

0% 0 3 6 9 12 15 18 21 24

1.250

0

3

6

9 12 Time (months)

15

18

21

24

0

3

6

9

12

15

18

21

24

Time (Months)

Time (months)

Evan Picoult, February, 2008

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Counterparty credit exposureExample 2: Three year Fixed/Floating LIBOR Interest Rate Swap

Random Rate ScenarioPotential Exposure (% Notional)

Profile of IR Swap ValuePotential Exposure (% Notional)

IR Swap Exposure Profile

8% Interest Rate 7% 6% 5% 4% 3% 0 6 12 18 24 30 36 Time (months)

6% 4% 2% 0% -2% 0 6 12 18 24 30 36

6% 4% 2% 0% 0 6 12 18 24 30 36

Time (Months)

Time (Months)

If we simulate thousands of paths of the market we can represent the potential exposure profile of a contract at a specified confidence level:Forward FX Exposure Profiles at Three Confidence LevelsExposure Profile (% Notional) 60%

Int. Rate Swap Exposure Profiles at Three Confidence Levels7% Exposure Profile (% Notional)99.0% CL Profile. 97.7% CL Profile.

50% 40% 30% 20% 10% 0% 0 3 6 9 12 15 18 21 24 Time (Months)

6% 5% 4% 3% 2% 1% 0% 0 6 12 18 24 30 36 Time (Months)99% CL Profile 97.7% CL Profile Expected Profile

Expected Profile

Evan Picoult, February, 2008

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Potential Exposure For A Counterparty With Multiple TransactionsTwo methods for measuring counterparty exposure (CE) of counterparty with multiple transactions : Simple Add-On method for each transaction CE TRANSACTION = = CE CP PORTFOLIO = Current MTM Current MTM + + Worst case potential increase in value Notional Principal * Credit exposure factor Potential increase in value per unit of notional principal given transactions features.

CE TRANSACTION

Portfolio simulation method: CECP PORTFOLIO

=

THE EXPOSURE PROFILE OF COUNTERPARTYCOUNTERPARTY EXPOSURE PROFILE150

POTENTIAL REPLACEMENT COST ($mm)

125 100 75 50 25 0 0 6 12 18 24 30 36 42 48 54 60

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 risk mitigant agreements are taken into account.

TIME (months)

Evan Picoult, February, 2008

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Counterparty Exposure Portfolio SimulationFX FX OPT DEBT SEC. I.R. DER. EQ. DER.COMM.

COLLATERAL SYSTEM

DER.

PRODUCT PROCESSOR SYSTEMS

Detailed T&C of TransactionO

DETAILED CONTRACT TERMS AND CONDITIONS.

Credit Admin

O

TABLES OF LEGAL AGREEMENTS-

NETTING MARGIN

COUNTERPARTY CREDIT DATA BASE

O

COLLATERAL

Credit Admin

O

TABLES OF DEFAULT TRANSACTION PROFILES

COUNTERPARTYS: - TRANSACTION DETAILS. - RISK MITIGANT DATA.

COUNTERPARTYS: EXPOSURE PROFILE.

CE SERVER (analytical engine)

ANALYTICAL ENGINE

Tables of historical or implied volatilities and correlations

Daily feeds of current market data

MARKET DATA

Evan Picoult, February, 2008

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General method to simulate counterpartys exposure profile:1)Loop over thousands of paths P.

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.

2)

For simulated path, p, measure the potential market value over time of each transaction with counterparty 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 contracts terms and conditions, revaluation formula and the simulated state of the market.

3)

Then for simulated path, p, derive counterparty Ks potential exposure over time- 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

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

Evan Picoult, February, 2008

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Counterparty credit exposureThe 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:Potential exposure profile of a counterparty, at two confidence levels, over the lifetime of the transactions with the counterparty: Assumes:Potential Exposure ($MM)125 100 75 50 25 0 0 6 12 18 24 30 36 42 48 54 60

A Counterparty's Exposure Profile150

No additional transactions Contractual cash flows are set and settle over time. All legally enforceable risk mitigation agreements are taken into account

99%CL Expected Positive Exposure (EPE)

Time (Months) ==>

Evan Picoult, February, 2008

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2. Economic Capital for loans

Evan Picoult, February, 2008

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EC DefinitionEconomic 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:

Probability Distribution of Potential Credit Loss for a Portfolio of Many Obligors

3.0%Probability of Credit Loss

Loss at high CL

Expected Loss

2.5% 2.0% 1.5% 1.0% 0.5% 0.0% -160

Economic capital= Unexpected Loss = Loss at very high CL Expected loss.

Economic Capital

-140

-120

-100

-80

-60

-40

-20

0

Potential Credit Loss ($mm)

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 concentrationEvan Picoult, February, 2008

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Economic Loss - Loan Portfolio - Default Only AnalysisASSUME 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 a