Bayesian Migration in Credit Ratings Based on Probabilities of Default

The advent of models for computing probabilities of default (PD) has provided a supplementary measure of default likelihood in addition to credit ratings. Credit ratings are a coarser measure of default likelihood, and embed the same information as PDs plus a modicum of human judgment. Rating transitions tend to occur less frequently than PD changes, since the human judgment involved overrides temporary spikes in state variables driving PDs.We have developed a Bayesian model based on PD changes to mimic rating changes. The free parameters in the model are tuned to historical data to fit the human judgment element in rating transitions.The model is easy to implement. We generate a simulation-fitted transition matrix that mimics the historical empirical one closely. This lends support to the often-made argument that PDs may be used as sufficient statistics for rating changes. Rating agencies may use this model as a basis for proposing rating changes to credit analysts, and finally, portfolio managers may use the model to obtain forecasts of rating changes, based on the observed historical time series of firm PDs