NHSMP Model for the Evaluation of Credit Default Swaps

This chapter focuses on the credit default swaps (CDSs). A non-homogeneous semi-Markov environment is used for the description of the rating model and consequently for the evaluation of a CDS contract. The valuation procedure of the CDS consists of determining the market value of the contract at a generic time. The chapter discusses the computation of the annuity and the value of the swap at generic time for a contract starting at time s in the case of constant recovery rate. In both the cases of deterministic recovery rate and stochastic recovery rate, the chapter expresses the price and the value of the swap contract as a function of the reliability and the failure rate of the firm C. The introduction of the time-reversed transition probabilities in a semi-Markov environment is tackled using a non-homogeneous semi-Markov backward process. The chapter presents a numerical example showing the theoretical results.