Estimating Probabilities of Default

Abstract:     
In this paper we conduct a systematic comparison of confidence intervals around estimated probabilities of default (PD) using several analytical approaches from large sample theory as well as bootstrapped small-sample confidence intervals. We do so for two different PD estimation methods, cohort and duration (intensity), using 22 years of credit ratings data. We find that the bootstrapped intervals for the duration based estimates are surprisingly tight when compared to the more commonly used (asymptotic) Wald interval. We find that even with these relatively tight confidence intervals, it is impossible to distinguish notch-level PDs for investment grade ratings, e.g. a PD(AA-) from a PD(A+). However, once the speculative grade barrier is crossed, we are able to distinguish quite cleanly notch-level estimated default probabilities. Conditioning on the state of the business cycle helps: It is easier to distinguish adjacent PDs in recessions than in expansions.

Number of Pages in PDF File: 36

Keywords: Risk management, credit risk, bootstrap, confidence intervals

JEL Classification: G21, G28, C16

working papers series