Issues in Counterparty Credit Risk

1. Issues in Counterparty Credit Risk David Lynch Federal Reserve Board Presentation to Quant Congress USA 2008 The views expressed in this presentation are those of the presenter and do not represent the views of the Board of Governors of the Federal Reserve System

2. Background and Outline • Background • In 2005 the BCBS adopted changes to Basel II capital requirements for counterparty credit risk that allowed firms to use expected positive exposure as the basis for regulatory capital requirements • Expected positive exposure is the average over time of the forecast of the mean exposure to a counterparty at various horizons over the next year • Outline • Explanation of IMM Capital Charge. • EPE vs EEPE • Rollover then aggregate • Risk neutral or historical distributions to calculate EE. • CDS to cover counterparty credit risk

3. An Explanation of the Counterparty Credit Risk Charge Using the Internal Models Method. • In Basel II IRB formula for credit risk use: • EAD =1.4 x EEPE (“Effective Expected Positive Exposure”) • Theory: Developed by Canabarro, Picoult, and Wilde in a series of papers and documented in ISDA-LIBA-TBMA compendium of Papers (2004). • EPE (“Expected positive exposure”) is the loan equivalent (deterministic) amount to use for stochastic exposures in a portfolio credit risk model.

4. Expected positive exposure • Expected positive exposure (EPE) is the basis for calculating EAD in Basel II (actually uses effective EPE). Steps to find EPE: • Find the Distribution of Market Values for trades with a counterparty • For many future dates find the probability distribution of net market values of transactions within a netting set for some future date given the realized market value of those transactions up to the present time. • Find the Distribution of Exposures • Adjust the probability distribution of market values for each of those future dates by setting cases of negative net market values equal to zero within the distribution (this takes account of the fact that, when the bank owes the counterparty money, the bank does not have an exposure to the counterparty). • Find the Expected Exposure • For each date find the mean (average) of the distribution of exposures at any particular future date before the longest-maturity transaction in the netting set matures. An expected exposure value is typically generated for many future dates up until the longest maturity date of transactions in the netting set. • Find Expected Positive Exposure (EPE) • Take the weighted average over time of expected exposures where the weights are the proportion that an individual expected exposure represents of the entire time interval. When calculating the minimum capital requirement, the average is taken over the first year or over the time period of the longest-maturity contract in the netting set.

5. Under Basel II, loans in the banking book use the remaining unpaid balance for the exposure at default in determining capital. The theory is that Counterparty Credit Risk exposures use Expected Positive Exposure for exposure at default. The Chart shows the exposure values for an amortizing loan of $150,000 that cannot be prepaid. Unpaid balance is $150,000 Expected Positive Exposure is $149,170 To reconcile the loan exposure and CCR exposure (by accounting for rollover in the CCR charge) use Effective EPE which is the average over time of effective expected exposure (EEEt); EEEt = Max (EEEt-1, EEt) Use of EEPE adjustment reconciles Loan and CCR capital charges Unpaid balance= EEPE= $150,000 EEPE vs. EPE

6. Rollover then Aggregate? • Industry has raised the issue of whether banks should aggregate exposures across netting sets (add EEt’s of netting sets) before rollover (EEEt = max(EEEt-1, EEt)) or account for rollover before aggregating netting sets • BCBS documents specify rollover then aggregating netting sets • BCBS is considering the issue but has formed no conclusion

7. EEPE at the Netting set level EEPE at the counterparty Level Netting Set A EEEA EEA EEA EEB = EEEB EEB Netting Set B EEEA+EEEB EEPE EPE=EEPE Combined Netting Sets EPE Graphical depiction of rollover before netting issue

8. Risk Neutral vs. “Real World” modeling of EPE • Real World EPE model based on historic diffusion: • Current exposure (CE) does not always equal modeled current exposure (EE0) since pricing is done with historic volatility • Modeled drift is same as actual drift • Risk Neutral EPE model based on risk neutral model: • Current exposure is the same as modeled current exposure • Risk neutral drift is different than real world drift $ $ EE Real world EE EE Risk Neutral EE EE0 EE0=CE CE CE CE Time Time Basel Committee does not specify which to use, nor does US implementation, The Choice is left to the firm. Regardless of choice, the firm should know “CE”, what a counterparty would owe the bank if it defaulted today

9. CDS to cover counterparty credit risk • CDS may be used to hedge counterparty risk • Other ways to hedge CVA have not been addressed • Contingent CDS are CDS that reference a derivative underlying • How should CDS be incorporated into Counterparty credit risk metrics? • Substitution approach – subtract the underlying reference obligation of the CDS from the netting set of the reference entity of the CDS (even if there is not an offsetting identical transaction) and add the underlying obligation to the netting set of the protection provider.

10. CCDS Capital treatment-simple example • US rules allows substitution of exposures, note that there is an additional benefit • If CCDS protection provider has a lower PD than the original counterparty

11. Modeling multiple forms of collateral • Explicit modeling of collateral agreements in a counterparty credit risk model is envisioned by Basel rules. This is straightforward when collateral is in the form of cash • It is much more difficult to model collateral agreements when the counterparty can deliver other forms of collateral What kind of collateral is delivered at this time when the collateral threshold is met? exposure Collateral threshold time