Probabilistic prediction of credit ratings: a filtering approach

In a financial market, to analyze the credit quality of firms, this note proposes a dynamical model. The population of firms is divided into a finite number of classes, depending on their credit status. The cardinality of the population can increase during the time, since new firms can enter in the market. Due to changes in credit quality and to the defaults, each firm can move from a class to another, or can go to the class of the defaulted firms. Different rating agencies are considered, each of them defines its own partition of the population. Aim of this note is to find the probabilistic prediction of the actual partition of the population, and of the conditional distribution of the distance to defaults. In a partial observing setting, this topic is discussed using stochastic filtering techniques.