Estimating and validating long-run probability of default with respect to Basel II requirements

Peter Miu and Bogie Ozdemir

Journal of Risk Model Validation

Abstract: ABSTRACT Basel II adopting banks estimate and validate long-run probability of default (LRPD) for each of their internal risk ratings. In this study, we examine alternative methodologies in estimating and validating LRPD. We propose the maximum likelihood estimators incorporating both crosssectional and serial asset correlations while being consistent with the economic model underlying the Basel II capital requirement formulation. We first adopt Basel’s infinitely-granular portfolio assumption and propose a LRPD estimation methodology for regulatory capital estimation. We then relax this assumption to examine alternative estimation methodologies and their performances for a finite number of borrowers. Simulation-based performance studies show that the proposed estimators outperform the alternatives in terms of their accuracies even under a number of small sample settings. Using the simple average of default rates as an estimator is found to be prone to underestimation of LRPD. For the purpose of validating the assigned LRPD, we also examine alternative ways of establishing confidence intervals (CI). For most of the cases, the use of the CI constructed based on the proposed maximum likelihood estimators results in fewer errors in hypothesis tests. We show that the proposed method enables the use of external default rate data to supplement internal default rate data in attaining a more accurate and representative estimate of LRPD.

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