Stochastic Migration Models with Application to Corporate Risk

In this paper we explain how to use rating histories provided by the internal scoring systems of banks and by rating agencies in order to predict the future risk of a set of borrowers. The method is developed following the steps suggested by the Basle Committee. To introduce both migration correlation and non- Markovian serial dependence, we consider rating histories with stochastic transition matrices. We develop the methodology to estimate both the number and dynamics of the factors inuencing the transitions and we explain how to use the model for prediction. As an illustration the ordered Probit model with unobservable dynamic factor is estimated from French data on corporate risk.