Valuing credit default swap in a non-homogeneous semi-Markovian rating based model

In this paper, we use a discrete time non-homogeneous semi-Markov model for the rating evolution of the credit quality of a firm C (see D’Amico, Janssen, and Manca Proceedings of the II international workshop in applied probablity, 2004a) and we determine the credit default swap spread for a contract between two parties, A and B that, respectively, sell and buy a protection about the failure of the firm C. We work both in the case of deterministic and stochastic recovery rate. We also highlight the link between credit risk and reliability theory.