Stress Testing Banking Book Positions Under Basel II

by Paul Kupiec

Comments by Matt PritskerThe views represent my own and not those of the Federal Reserve Board or

other members of its staff.

Summary

1. Documentation of ASFM deficiencies. Based on panel regression evidence.

2. Enhancements for ASFM. 1. Stochastic default barrier2. Stochastic correlation 3. Stochastic EAD and LGD.

3. Message: Stress tests should be based on ASFM with realistic enhancements.

Why stochastic correlations and default boundaries: Intuition from Structural Models

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dV

Process for firm value in Merton-like model:

DVi )1(

Default occurs if:

Intuition Continued

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)(5.))0(ln()ln()1()1(

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The default condition reduces to:

Default correlations and the default boundary in the Vasicek model both change with risk exposures in the Merton Model.

More Intuition

• If and if then default correlations and the default boundary both change.

• Default occurs if:

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)(5.))0(ln()ln(1

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Main Policy Message: Why do we need stress tests?

• Positions with changing risk exposures.– Positions with significant optionality.– Positions which go from fixed to floating payments.

• Positions which are sensitive to time-varying volatility of macro-fundamentals.

• Positions which are subject to time-varying funding risk.

• Time-varying LGD and EAD• Restrictive assumptions about factor structure,

PD, and default correlation in Basel II.

Comment / Suggestion 1

• Comment: The model is too black box.

• Suggestion: Use a structural model with a real world example to illustrate the importance of time-varying correlations and default boundaries for economic capital.

Comment 2: Econometrics of the Panel Regression

• Panel regression is clever, but constant ρ assumption is problematic.

• Small N Problem

– Moody’s data is sometimes sparse in some ratings categories. (2 observations in some ratings categories based on data from post 1970).

– Occasional data sparsity will have undue influence on fixed effects and time effects in panel regression.

• Estimation techniques that condition on data sparsity may help.

Example: Non-linear panel regression with as dependent variable.

WLS will be asymptotically pivotal and variance stabilized and may be more reliable.

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Suggestion 2: Estimate by Maximum Likelihood

• Likelihood for Ki,t defaults for rating class i at time t conditional on em,t:

• Likelihood of all the data:

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Suggestion 2: Continued

• Systematic shocks are not i.i.d. due to through the cycle ratings.

• Fit a time-series process to em,t.

– This will simultaneously introduce time-varying default boundaries ( a big plus)

– But they will be perfectly correlated, so it may not help the ASFM enough.

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Conclusion

• I learned a lot from reading this paper(s).• Suggestions:

– More work quantifying the severity of the weaknesses in ASFM---with a concrete example (mortgages?).

– More work documenting the failure of the ASFM model to fit the data.