The CDS Option Pricing Research Under The Cox Process Within The HJM Framework

In recent years, as a tool of credit risk management, credit default swaps have become increasingly popular among market participators. Now many finan-cial professors and financial engineers have carried out theoretical research and practice application for them. The paper provides the Cox process within the HJM framework in a probability setting equipped with a subfiltration structure, and also we use this model to evaluate the Credit Default Swaps and Options pricing research. In this process, the default event is modelled using the Cox pro-cess where the stochastic intensity represents the credit spread. This default time is the first default. A simulation approach for defaultable forward yield curves term structure is developed within the Heath-Jarrow-Morton framework. Then, we deduce the Credit Default Swaps and Options pricing formula by combining the Cox Process with the HJM model.