Before revision:  In this regard, the study of the risk of default of the counterparty in any financial contract has become crucial in the credit risk . Many works has been done to trying to describe the counterparty risk in a CDS contract, but all this work are based on the Markovian approach to risk. In the our opinion this kind of model are too restrictive, because they require that the distribuction function of the waiting times has to be exponential or geometric, for discrete time. In the our model, we describe the evolution of credit rating of the financial subjects like a multivariate semi-Markov model, so we allow for arbitrarily distributed sojourn time.
After revision:  In this regard, the study of the counterparty credit risk by defining a new multivariate semi-Markov model, so we allow for arbitrarily distributed sojourn time.