Confidence Intervals for Probabilities of Default

44 Pages Posted: 5 Aug 2005

See all articles by Samuel Gregory Hanson

Samuel Gregory Hanson

Harvard University - Business School (HBS)

Til Schuermann

Oliver Wyman

Multiple version iconThere are 2 versions of this paper

Date Written: July 2005


In this paper we conduct a systematic comparison of confidence intervals around estimated probabilities of default (PD) using several analytical approaches as well as parametric and nonparametric bootstrap methods. We do so for two different PD estimation methods, cohort and duration (intensity), with 22 years of credit ratings data. We find that the bootstrapped intervals for the duration based estimates are relatively tight when compared to either analytic or bootstrapped intervals around the less efficient cohort estimator. We show how the large differences between the point estimates and confidence intervals of these two estimators are consistent with non-Markovian migration behavior. Surprisingly, even with these relatively tight confidence intervals, it is impossible to distinguish notch-level PDs for investment grade ratings, e.g. a PDAA- from a PDA+. However, once the speculative grade barrier is crossed, we are able to distinguish quite cleanly notch-level estimated PDs. 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

JEL Classification: G21, G28, C16

Suggested Citation

Hanson, Samuel Gregory and Schuermann, Til, Confidence Intervals for Probabilities of Default (July 2005). 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

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