Estimating Probabilities of Default

36 Pages Posted: 28 Jul 2004

See all articles by Samuel Gregory Hanson

Samuel Gregory Hanson

Harvard University - Business School (HBS)

Til Schuermann

Oliver Wyman

Date Written: July 2004


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.

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

JEL Classification: G21, G28, C16

Suggested Citation

Hanson, Samuel Gregory and Schuermann, Til, Estimating Probabilities of Default (July 2004). Available at SSRN: or

Samuel Gregory Hanson

Harvard University - Business School (HBS) ( email )

Soldiers Field Road
Morgan 270C
Boston, MA 02163
United States

Til Schuermann (Contact Author)

Oliver Wyman ( email )

1166 6th Avenue
New York City, NY
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Abstract Views
PlumX Metrics