Stochastic Migration Models with Application to Corporate Risk

In this paper we explain how to use the rating histories provided by theinternal scoring systems of banks and by rating agencies in order to predictthe future risk of a given borrower or of a set of borrowers. The method isdeveloped following the steps suggested by the Basle Committee. To intro-duce both migration correlation and non-Markovian serial dependence, weconsider rating histories with stochastic transition matrices. We develop thecomplete methodology to estimate both the number and dynamics of thefactors inßuencing the transitions. Further we explain how to use the sto-chastic migration model for prediction. As an illustration the ordered Probitmodel with unobservable dynamic factor is estimated from French data oncorporate risk.