A review of non-Markovian models for the dynamics of credit ratings

This survey reviews the growing literature on Markovian and non-Markovian models for modeling the dynamics of credit ratings. Credit rating is a measure of the creditworthiness of a firm, i.e., it is an evaluation of its likelihood of default. The level of credit ratings varies with respect to time due to random credit risk and thus need to be modeled by an appropriate stochastic process. Models based on Markov chains have been proposed in the literature and are widely used due to mathematical simplicity. However, many empirical evidences suggest the non-suitability of the Markov process to model rating dynamics. To overcome the limitations of Markovian models, several non-Markovian models based on semi-Markov process and Markov regenerative processes have been proposed in the literature. In this article, we give a review of the models proposed in the literature. Further, empirical applications on the real data are presented to compare various modeling approaches.