Bayesian Estimation of Probabilities of Default for Low Default Portfolios
Journal of Risk Management in Financial Institutions 6 (3), 302-326, 2013
28 Pages Posted: 30 Apr 2012 Last revised: 22 Jan 2014
Date Written: April 5, 2012
The estimation of probabilities of default (PDs) for low default portfolios by means of upper confidence bounds is a well established procedure in many financial institutions. However, there are often discussions within the institutions or between institutions and supervisors about which confidence level to use for the estimation. The Bayesian estimator for the PD based on the uninformed, uniform prior distribution is an obvious alternative that avoids the choice of a confidence level. In this paper, we demonstrate that in the case of independent default events the upper confidence bounds can be represented as quantiles of a Bayesian posterior distribution based on a prior that is slightly more conservative than the uninformed prior. We then describe how to implement the uninformed and conservative Bayesian estimators in the dependent one- and multi-period default data cases and compare their estimates to the upper confidence bound estimates. The comparison leads us to suggest a constrained version of the uninformed (neutral) Bayesian estimator as an alternative to the upper confidence bound estimators.
Keywords: Low default portfolio, probability of default, upper confidence bound, Bayesian estimator
JEL Classification: C11, C13
Suggested Citation: Suggested Citation