Estimating Default Correlations from Short Panels of Credit Rating Performance Data

Abstract

When models of portfolio credit risk are calibrated to historical ratings performance data, parameters that capture cross-obligor dependence can be (and often are) fit directly to estimated default correlations. The accuracy of our measures of credit value-at-risk therefore rests on the precision with which default correlations can be estimated. In practice, data are always scarce. The rating system may cover many obligors, but performance data span, at most, two or three decades. Nonetheless, the moments-based estimators commonly used by practitioners make minimal use of parameter restrictions. In this paper, we demonstrate that these estimators perform quite badly on the sample sizes typically available, and generally produce a large downward bias in estimated default correlations. Models calibrated in this manner are thus likely to understate value-at-risk quite significantly. Our main theme concerns the trade-off between precision and robustness in the calibration of default correlation parameters. We show how economically meaningful assumptions about the unobserved process that determines when obligors default can be used to generate natural restrictions on cross-obligor default correlations. We demonstrate how these restrictions can be imposed when maximum likelihood methods are used to calibrate parameters to historical ratings performance data, and then assess the associated improvements in small sample behavior of the estimators. We apply our various estimators to Moody’s and S&P ratings performance data.

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