Estimating and Validating Long-Run Probability of Default With Respect to Basel II Requirements

45 Pages Posted: 2 Nov 2007

See all articles by Peter Miu

Peter Miu

McMaster University - DeGroote School of Business

Bogie Ozdemir

Standard & Poor's

Date Written: October 2007


Basel II adopting banks estimate and validate Long-Run Probability of Default (LRPD) for each of their Internal Risk Ratings (IRRs). In this study, we examine alternative methodologies in estimating and validating LRPD. We propose the maximum likelihood estimators incorporating both cross-sectional 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 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 LRPDs, we also examine alternative ways of establishing confidence intervals (CIs). For most of the cases, the use of the CIs 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.

Keywords: Basel II, Long-Run Probability of Default, Asset Correlation, Stress Condition, Validation, Confidence Interval, Hypothesis Test

Suggested Citation

Miu, Peter and Ozdemir, Bogie, Estimating and Validating Long-Run Probability of Default With Respect to Basel II Requirements (October 2007). Available at SSRN: or

Peter Miu (Contact Author)

McMaster University - DeGroote School of Business ( email )

1280 Main Street West
Hamilton, Ontario L8S 4M4
905-525-9140 ext 23981 (Phone)

Bogie Ozdemir

Standard & Poor's ( email )

130 King Street West
Suite 1100, PO Box 486
Toronto, Ontario M5X 1E5

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