### Abstract

Any portfolio credit risk model that is to be used to calculate a loss distribution associated with defaults and changes in rating must address the challenge of modelling dependent defaults and dependent rating migrations. Most industry models (such as KMV, CreditMetrics, CreditRisk+) incorporate mechanisms for modelling this dependence, generally by assuming conditional independence of defaults and migrations given common economic factors. However, the calibration of these mechanisms is often quite ad hoc, despite the fact that the tail of the portfolio loss distribution is extremely sensitive to small changes in the parameters governing dependence.

We consider the problem of making formal statistical inference for such models based on historical default and rating migration data. In the solution we propose portfolio credit models are represented as generalized linear mixed models (GLMMs) and inference is made using Markov chain Monte Carlo (MCMC) techniques. This general framework allows quite complex models with a latent random effects structure to represent unobserved common factors that influence default and migration.