Credit Rating Dynamics and Markov Mixture Models

Abstract

Despite overwhelming evidence to the contrary, credit migration matrices, used in many credit risk and pricing applications, are typically assumed to be generated by a simple Markov process. In this paper we propose a parsimonious model that is a mixture of (two) Markov chains. We estimate this model using credit rating histories and show that the mixture model statistically dominates the simple Markov model and that the differences between two models can be economically meaningful. The non-Markov property of our model implies that the future distribution of a firm's ratings depends not only on its current rating but also on its past rating history. Indeed we find that two firms with identical credit ratings can have substantially different transition probability vectors.

Keywords: Risk management, credit risk, credit derivatives