具信用等级迁移风险的信用违约互换定价

In this paper, we consider pricing a Credit Default Swap (CDS) which is based on a corporation bond with credit rating migration risks. Under the structure framework, we establish the pricing model for the CDS, which is expressed by a partial differential equation system coupled by an additional condition at the rating migration boundary. The default probability is obtained by solving the PDE in semi-closed form. Then, with this probability, the CDS spread is obtained from the standard CDS pricing formula. At last, by the pricing formula, a numerical simulation shows the relationship between default probability, CDS premium and parameters in the model.