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Confidence Intervals for Probabilities of Default

Samuel Gregory Hanson

Harvard Business School

Til Schuermann

Oliver Wyman

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.

Number of Pages in PDF File: 44

Keywords: Risk management, credit risk, bootstrap

JEL Classification: G21, G28, C16

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Date posted: August 5, 2005  

Suggested Citation

Hanson, Samuel Gregory and Schuermann, Til, Confidence Intervals for Probabilities of Default (July 2005). Available at SSRN: https://ssrn.com/abstract=766345 or http://dx.doi.org/10.2139/ssrn.766345

Contact Information

Samuel Gregory Hanson
Harvard Business School ( 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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