The Pricing of Credit Default Swap Based on Credit Rating

Abstract:

In this paper study the pricing of Credit Default Swap(CDS), and its reference bond has the structure of credit ranks. Considering bond can jump from one credit ranks to another, which might lead to a fact that the default probability and recovery rate are always changing, we construct a conditional expectation with respect to rank and time to maturity in order to price CDS’s premium and value by using transition matrix and recovery vector. Then by reducing the conditional expectation, we obtain two ODE systems corresponding to coupon leg and default leg, respectively. Furthermore, both explicit solution of ODE system are given to determine the premium of CDS. Finally numerical analysis is given to show effectiveness of the proposed model.