Bayesian Migration in Credit Ratings Based on Probabilities of Default

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Abstract
There is no theoretical or empirical model in the literature that posits a stochastic model of rating changes based directly on the joint process of probabilities of default (PD), although it is natural that ratings should be based on default intensity. The authors propose such a model that is simple and practical to implement. Changes in PDs are related to changes in ratings, and a modified Bayesian model may be used to calibrate the historical time series of PD changes to historical rating transition matrices. Rating agencies could use the model to predicate rating changes based on the stochastic process for probabilities of default.