The Bayesian approach to default risk: A guide

A Bayesian approach to default rate estimation is proposed and illustrated using a prior distribution assessed from an experienced industry expert. The principle advantage of the Bayesian approach is the potential for coherent incorporation of expert information - crucial when data are scarce or unreliable. A secondary advantage is access to efficient computational methods such as Markov Chain Monte Carlo. After a preliminary discussion of elicitation of expert beliefs, all steps in a thorough Bayesian analysis of a default rate are illustrated. Using annual default rate data from Moody's (1999-2009) and a prior elicited from an industry expert, we estimate three structural credit models in the asymptotic single risk factor (ASRF) class underlying the Basel II framework (Generalized Linear and Generalized Linear Mixed Models), using a Markov Chain Monte Carlo technique.