Bivariate Semi-Markov Process for Counterparty Credit Risk

We consider the problem of constructing an appropriate multivariate model to study counterparty credit risk in the credit rating migration problem. For this financial problem different multivariate Markov chain models were proposed. However, the Markovian assumption may be inappropriate for the study of the dynamics of credit ratings, which typically show non Markovian-like behavior. In this article, we develop a semi-Markov approach to study the counterparty credit risk by defining a new multivariate semi-Markov chain model. Methods are given for computing the transition probabilities, reliability functions and the price of a risky Credit Default Swap.