Counterparty Risk and CVA

Transcription

1 Counterparty Risk and CVA Stephen M Schaefer London Business School Credit Risk Elective Summer 2012 Net revenue included a $1.9 billion gain from debit valuation adjustments ( DVA ) on certain structured and derivative liabilities, resulting from the widening of the Firm s credit spreads. This was partially offset by a $691 million net loss, including hedges, from credit valuation adjustments ( CVA ) on derivative assets within Credit Portfolio, due to the widening of credit spreads for the Firm s counterparties. JP Morgan, 3 rd Quarter Results 2001 Counterparty Risk and CVA 2

2 Counterparty Risk and the Growth of OTC Derivatives The OTC derivatives market has grown enormously in terms of notional amounts outstanding creates substantial exposure to default of counterparties Counterparty risk increased significantly due to practice of offsetting rather than unwinding derivative trades Since crisis both regulators and banks currently paying much more attention to assessing counterparty risk valuing counterparty exposure (CVA) $US Trillion Total IR and currency Credit default swaps Counterparty Risk and CVA 3 The Basic Idea: Exposure as replacement cost Suppose bank A has entered an OTC contract (e.g., a fixed-floating interest rate swap not necessarily a credit derivative) with a bank B Value of swap: Initiation In future (before maturity) At maturity Zero Positive or negative Zero If bank B defaults during life of swap: if PV to bank A negative: bank A pays PV to creditors of bank B (assuming bank A is solvent) if PV to bank A positive: bank A has claim on bank B and loses (1-R) x market replacement cost of contract Exposure measured in terms of replacement cost Counterparty Risk and CVA 4

3 Counterparty exposure: Exposure Definitions the larger of (i) zero and (ii) the market value of the portfolio of derivatives that would be lost if the counterparty were to default = (1-R) x replacement cost Current exposure (CE) current value of the counterparty exposure Potential future exposure (PFE) highest level of exposure at a given future date expected with a particular (typically high) degree of statistical confidence (e.g., 95%) analogous to VaR Counterparty Risk and CVA 5 Exposure Definitions, contd. Maximum potential future exposure (MPFE) the maximum (peak) value of PFE over life of portfolio Expected exposure (EE) the average value of the counterparty exposure on a given future date. Expected Loss expected exposure x (1 R) Right-way / wrong-way exposure relation between level of exposure and credit quality of counterparty inverse: wrong way positive: right way Counterparty Risk and CVA 6

4 Methods of Mitigating Counterparty Risk Netting agreements Collateral agreements safe harbour rule for derivatives Clearing houses Diversification Early termination agreements Counterparty Risk and CVA 7 Counterparty risk exposure Example: fixed/floating interest rate swap Counterparty Risk and CVA 8

5 Example A Single Fixed Floating Interest rate Swap Value of swap contract (e.g., receiving fixed) at: inception: zero (typically) future time t (after inception): where; ( S S ) A( t, T ) 0 t, T - S 0 is the contract swap rate; - S t,t is the market swap rate at time t for a swap that matures at T; and - A(t,T) is the market value of an annuity at time t that matures at T. Value of swap exposed to variation in swap rate Counterparty Risk and CVA 9 Swap example: Simulated Paths for Future Swap Rates Current Swap Rate 5% Maturity 10 Ann Vol of swap rate 1.00% Recovery Rate 40% Nominal amount 100 Swap Rate 14% 12% 10% 8% 6% 4% 2% 0% Time Method for simulating future interest rates comes from term structure modelling should be consistent with current term structure Counterparty Risk and CVA 10

6 25 20 Value of Swap Contract Swap value A Simulated Paths for Contract Value and Future Swap Rates Sw wap value % 12% Time If future swap rate is lower than contract rate (e.g., heavy blue line A ), value of contract to party receiving fixed is positive Swap Rate 10% 8% Swap Rates 6% 4% 2% 0% Time A Counterparty Risk and CVA 11 Counterparty exposure Counterparty Exposure A Simulated Paths for Exposure and Contract Value Contract Value A Time 0 Counterparty Exposure is maximum of contract value and zero Swap value Time Counterparty Risk and CVA 12

7 Expected Exposure and Potential Future Exposure (95%) 20 Expected Exposure PFE Counterparty Risk and CVA 13 Valuing Counterparty Exposure (CVA) Counterparty Risk and CVA 14

8 Valuation of Counterparty Credit Exposure: Credit (or Counterparty) Value Adjustment (CVA) Consider a portfolio of contracts under which Bank B (the counterparty) makes payments to Bank A the value to Bank A of these contracts is reduced by the possibility that Bank B may default The CVA is the difference between the value of the portfolio when there is : a. no possibility of default by the counterparty (Bank B); and b. a positive probability of a default by the counterparty We compute this (as in our analysis of CDS) by computing the discounted risk-neutral expected value of the expected loss. Counterparty Risk and CVA 15 Calculation of Credit value Adjustment (CVA) For each future period expected loss is EE t (expected exposure) x (1- R). Value of counterparty losses is then T Exepcted exposure 0.0 t ( t 1 t ) t (1 R) EE Q Q D t= Expected Exposure Where Q t is the risk-neutral survival probability of the counterparty to time t. Tim e Counterparty Risk and CVA 16

9 Suppose: Risk-Neutral Default Probability CDS curve for counterparty is flat and equal to bps Recovery rate is 40% Then one-year RN conditional default probability is constant and equal to 1.64% (and independent of the zero curve!) Counterparty Risk and CVA 17 Exampl le, contd. Expected Exposure D(t) Q(t) CVA Calc Total Counterparty Risk and CVA 18

10 CVA CVA in this case is (per 100 nominal) or 22.4 bps This assumes no collateralisation and no netting. Cost of counterparty default will affect price at which bank should be prepared to enter deal. In fact, counterparty risk in swaps is two sided and so, while counterparty default risk reduces portfolio value, own default risk increases it. Counterparty Risk and CVA 19 Mitigating Counterparty Risk Counterparty Risk and CVA 20

11 Counterparty Risk Mitigation I: Aggregation of Counterparty Risk and Netting For counterparty risk, we first have to aggregate at the level of a given counterparty (e.g., all our exposures to Bank of America, Deutsche Bank etc.) In doing this we aggregate only over positions with positive exposure and so do NOT benefit from hedging between different positions with that counterparty unless we have a netting agreement in place (usually, there will be) Contracts with Counterparty X Netting can substantially reduce counterparty exposure Cross-product netting highly desirable Potential problem with legal entities Exposure Contract Value No Netting With Netting a b c d e Counterparty Risk and CVA 21 Aggregation and Comparison with VaR Analysis of uncertainty in future contract value is similar to analysis of value-at-risk (VaR) For VaR bank needs to aggregate across all positions in a business unit at various levels of aggregation, such as: a trading desk (e.g., a particular corporate bond desk, a particular equity derivatives desk etc.) a geographical region/business area (e.g., European Fixed Income) and.. the bank as whole (global basis) In VaR we aggregate all positions and benefit from positions with offsetting exposures (hedging); and diversification Counterparty Risk and CVA 22

12 Counterparty Risk Mitigation II: Collateral A second contractual mechanism that reduces counterparty risk is the use of collateral. Banks will increasingly use a legally binding margin agreement that requires one or both parties to post collateral when the uncollateralised exposure exceeds a given threshold. In addition to the threshold level the agreement will also specify the call period, i.e., the frequency at which collateral is monitored and called for. The use of collateral to mitigate counterparty risk is subject to operational risk. Derivatives benefit from a safe harbour provision that means that, in the event of default by one counterparty, the other is able to realise collateral without having to go through the bankruptcy process. Counterparty Risk and CVA 23 Risk Mitigation III: Diversification Having aggregated all exposures to a given counterparty (not only derivative exposures but, for example, bonds issued by the counterparty held in inventory, equity in the counterparty etc.) counterparty risk is reduced by diversification across counterparties. One simple mechanism employed by banks to achieve this is to impose a maximum exposure to each counterparty (equivalent to a credit line). Counterparty Risk and CVA 24

13 Risk Mitigation IV: Early Termination Optional Early Termination (OET) agreements give each party the right to seek termination (at the current market price and without giving a reason). used when, e.g., an interest rate swap has 10-years to maturity but counterparty has credit line for only 5 years mitigates risk in the event that counterparty credit quality deteriorates. Mandatory Early Termination (MET) agreements example: 20-year interest rate swap with mandatory termination in 5 years (at market prices) why do banks do this? Because banks want the exposure to the 20-year rate but do not want 20-year counterparty exposure used less than OETs. Counterparty Risk and CVA 25 Right-way / wrong way exposure Calculation of CVA on previous slide assumes no correlation between counterparty risk exposure and credit quality of counterparty.. But actual correlation between risk-neutral probability of default (RN-p) and exposure may be non-zero: right-way exposure: if RN-p low when exposure is high then this reduces value (cost) of counterparty credit risk wrong-way exposure: if RN-p high when exposure is high then this increases value (cost) of counterparty credit risk Examples: right way exposure: holding forward contract to buy oil from BP at fixed price: low oil price means BP default risk high when and contract value low (negative) wrong way exposure: holding a put option on Lehman written by.. Lehman!! Counterparty Risk and CVA 26

14 Another example of right way / wrong way risk Variance Swaps Jan-90 Cumulative returns -- VIX - Realised Var - Fixed Qauntity of exposure File: Realised Vol & VIX Jan-92 Jan-94 Jan-96 Jan-98 Jan-00 Jan-02 Jan-04 Jan-06 Jan-08 Jan-10 Variance swap is contract where one side pays fixed and the other pays realised variance of returns (e.g., on S&P) On average high risk premium (implied vol. > realised vol. on average) but in crisis realised vol. was huge. SELLER of variance faces right-way risk.. will pay out in crisis and receive in normal times Counterparty Risk and CVA 27 Summary Size of notional outstanding in derivatives market means that management of counterparty risk is a major issue for banks and many other types of financial institution. Key concepts: exposure expected exposure (EE) potential future exposure (PFE) Methods of managing counterparty risk netting collateral diversification early termination Valuation of counterparty exposure: credit value adjustment (CVA) Counterparty Risk and CVA 28