Before revision: In this work we define a multivariate semi-Markov process. We derive an explicit expression for the transition probability of this multivariate semi-Markov process in the discrete time case. We apply this multivariate model to the study of the counterparty credit risk , with regard to correlation in a CDS contract.
After revision: We consider the problem of constructing an appropriate multivariate model for the study of the counterparty credit risk , with regard to correlation in a CDS contract.