Stochastic Migration Models with Application to Corporate Risk

In this article we explain how to use rating histories providedby the internal scoring systems of banks and rating agenciesin order to predict the future risk of a set of borrowers. Themethod is developed following the steps suggested by the BasleCommittee. To introduce both migration correlation and non-Markovianserial dependence, we consider rating histories with stochastictransition matrices. We develop the methodology to estimateboth the number and dynamics of the factors influencing thetransitions and we explain how to use the model for prediction.As an illustration, the ordered probit model with unobservabledynamic factor is estimated from French data on corporate risk.