Dealing with double default under Basel II

1. Dealing with double default under Basel II Erik HeitfieldBoard of Governors of the Federal Reserve System 20th and C Street, NW Washington, DC 20551 USA Erik.heitfield@frb.gov

2. Today’s Talk • Basel II’s credit risk capital model for unhedged exposures • The substitution approach for hedged exposures • The ASRF/Merton model for hedged exposures • Example calibrations • A simple alternative to the ASRF/Merton Model • Conclusions

3. Basel II “[Basel II] is intended to align regulatory capital requirements more closely with underlying risks, and to provide banks and their supervisors with several options for the assessment of capital adequacy.” -- William McDonough

4. Basel II’s Credit Risk Capital Rule • Capital charges are designed to satisfy a portfolio-level solvency target (VaR rule) • Charges must be assessed on a loan-by-loan basis

5. The ASRF Framework • In general, a VaR capital rule cannot be applied on a loan-by-loan basis because the marginal contribution of a single exposure to portfolio risk depends on its correlation with all other exposures • Gordy (2003) shows that under stylized assumptions a simple, decentralized capital rule satisfy a VaR solvency target • Collectively these assumptions are called the asymptotic-single-risk-factor (ASRF) framework

6. ASRF Assumptions • Cross-exposure correlations in losses are driven by a single systematic risk factor • The portfolio is infinitely-fine-grained (i.e. idiosyncratic risk is diversified away) • For most exposures loss rates are increasing in the systematic risk factor

7. ASRF Capital Rule • The th percentile of X is • Set capital to the th percentile of L to ensure a portfolio solvency probability of  • Plug the th percentile of X into c(x)

8. Merton Model Obligor i defaults if its normalized asset return Yi falls below the default threshold . where

9. IRB Risk Weight Function • The conditional expected loss function for exposure i given X is • Plugging the 99.9th percentile of X into ci(x) yields the core of the Basel II capital rule

10. Credit Risk Mitigation Basel II will provide some capital relief to account for the risk-mitigating effects of credit hedges • Financial guarantees • credit default swaps Bank Obligor Guarantor

11. Joint Default Probabilities Joint default probability is generally much lower than either marginal default probability ρog = 60%

12. The Substitution Approach “[C]redit risk mitigation in the form of derivatives and financial guarantees must not reflect the effects of double default.” --CP3 paragraph 270 Under the substitution approach a bank can substitute the PD and LGD of the guarantor for those of the obligor if this would result in a lower risk weight

13. Substitution Approach

14. Substitution Approach • Shortcomings of the substitution approach • Provides no incentive to hedge high quality exposures • Not risk sensitive for low-quality hedged exposures • Lacks theoretical foundation • Solution • The same ASRF framework used to derive capital charges for unhedged loans can be used to derive capital charges for hedged loans

15. ASRF/Merton Approach • A Merton model describes default by both the obligor (o) and the guarantor (g) • Two risk factors drive default correlations • X affects all exposures in the portfolio • Z affects only the obligor and the guarantor

16. ASRF/Merton Approach • Model allows for • Guarantors with high sensitivity to systematic risk • “Wrong way” risk between obligor and guarantor • Three correlation parameters

17. ASRF/Merton Approach Plugging the 99.9th percentile of X into the conditional expected loss function for the hedged exposure yields an ASRF capital rule

18. Base Case • Treats guarantors in a manner symmetric with corporate obligors • Guarantor asset correlation is the same as asset correlation for corporate obligors • ρg declines from 24% to 12% • No extra “wrong-way” risk

19. Base Case

20. Substitution Approach

21. Base Case • The base case represents the least conservative possible calibration of the ASRF/Merton model • Generates capital charges that are significantly lower than the substitution approach for any combination of obligor and guarantor PDs

22. Wrong-way Risk • Guarantor asset correlation is the same as asset correlation for corporate obligors • ρg declines from 24% to 12% • Obligor and guarantor are exposed to common shocks beyond those associated with systematic risk • ρog = 50%

23. Wrong-way Risk Case

24. Substitution Approach

25. Wrong-way Risk • Produces capital charges that lie between the base case and the substitution approach • When ρo = ρg, as ρog approaches 100% the ASRF/Merton capital charges approach those of the substitution approach

26. Guarantor Systematic Risk • Guarantor exposure to systematic risk is greater than for typical corporate obligors • ρg = 50% • No extra “wrong-way” risk

27. Guarantor Systematic Risk Case

28. Substitution Approach

29. Guarantor Systematic Risk • For exposures to high-PD obligors ASRF/Merton capital charges may exceed those of the substitution approach • For exposures to low-PD obligors ASRF/Merton capital charges remain well below those of the substitution approach • As ρg approaches 100% ASRF/Merton capital charges approach capital charges for unhedged exposures

30. Conservative Case • Imposes conservative assumptions about correlation parameters • Guarantors are more sensitive to systematic risk than corporate obligors • ρg = 50% • There is significant wrong-way risk • ρog = 50%

31. Conservative Case

32. Substitution Approach

33. Conservative Case • Capital charges rise quickly with the obligor and guarantor PDs • ASRF/Merton capital charges may be either higher or lower than under the substitution approach • ASRF/Merton capital charges for exposures to low-PD obligors remain much lower than those generated by the substitution approach

34. A Simpler Approach • Applying the ASRF approach directly would add complexity to the Accord • Uses a bivariate normal CDF • Relies on three asset correlation parameters • A simpler alternative would be to rescale the unhedged risk weight function • The scaling function would depend on the PD of the guarantor • The scaling function would be fit to the ASRF/Merton model

35. A Simpler Approach CP3 Risk Weight Function

36. Conclusions

37. Drawbacks of theSubstitution Approach • The substitution approach is not risk sensitive • Provides little incentive to hedge low PD credits • Not sensitive to PDs of high PD credits • The substitution approach has been widely criticized because it lacks a theoretical foundation

38. ASRF vs. Substitution • ASRF provides incentive to hedge risk for all types of obligors • ASRF is more risk-sensitive for both high and low quality obligors and guarantors • ASRF may or may not generate lower capital charges than substitution

39. Advantages of the ASRF Approach • The ASRF approach is more risk sensitive than the substitution approach • The ASRF approach is derived from the same model used to construct risk-weight function for unhedged exposures • The simplified ASRF approach would not add much additional complexity to the Accord

40. References • Available on the Federal Reserve Board’s web-sitehttp://www.federalreserve.gov/generalinfo/basel2/default.htm • “Third consultative paper on the New Basel Capital Accord” • “Risk Based Capital Guidelines; Implementation of the New Basel Capital Accord” Advance Notice of Proposed Rulemaking • “Treatment of Double-Default and Double-Recovery Effects under Pillar I of the New Basel Capital Accord” Federal Reserve White Paper • Additional References • Gordy, M. (2003), “A risk-factor model foundation for ratings-based bank capital rules,” Journal of Financial Intermediation 12(3), pp. 199-232 • Heitfield, E. (2003), “Using guarantees and credit derivatives to reduce credit risk capital requirements under the new Basel Capital Accord,” in Credit Derivatives: the Definitive Guide, J. Gregory (Ed.), Risk Books