基于信用等级迁移的信用违约互换定价

The Pricing of Credit Default Swap Based on Credit Rating

摘要:

研究了参考债券具有信用等级结构的信用违约互换的定价。考虑债券处于不同的等级，且债券的违约强度和回收率随着债券在等级间的迁移，不断变化，基于转移矩阵和回收率向量，构建了常微分方程(ODE)来求解信用违约互换(CDS)的或有赔付和保费支付的价值，并给出了其解析解，从而确定了CDS保费费率和CDS的价值，最后通过数值分析验证理论结果。

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.