Modeling dependencies between rating categories and their effects on prediction in a credit risk portfolio

The internal-ratings based Basel II approach increases the need for the development of more realistic default probability models. In this paper we follow the approach taken in McNeil and Wendin (2006) by constructing generalized linear mixed models for estimating default probabilities from annual data on companies with different credit ratings. The models considered, in contrast to McNeil and Wendin (2006), allow parsimonious parametric models to capture simultaneously dependencies of the default probabilities on time and credit ratings. Macro-economic variables can also be included. Estimation of all model parameters are facilitated with a Bayesian approach using Markov Chain Monte Carlo methods. Special emphasis is given to the investigation of predictive capabilities of the models considered. In particular predictable model specifications are used. The empirical study using default data from Standard and Poor gives evidence that the correlation between credit ratings further apart decreases and is higher than the one induced by the autoregressive time dynamics.