Before revision:  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. The age state dependency, typical of the semi-Markov environment, allow us to insert the correlation in a dynamical way. In particular, suppose that A is a default-free bondholder and C is the relative firm. The bondholder buy protection against C's default by another defaultable subject, say B the protection seller. Our model describe the evolution of the credit rating of the couple B and C. We admit for simultaneus default of C and B, the single default of C or single default of B .
After revision:  In the our model, we describe the evolution of credit rating of the financial subjects like a multivariate semi-Markov chain model. Methods are given for computing the transition probabilities, reliability functions and the price of a risky Credit Default Swap .