In this paper, we study the credit default swap (CDS) pricing with counterparty risk in a reduced form model. The default jump intensities of the reference firm and counterparty are both assumed to follow the mean-reverting CIR processes with independent jumps respectively and a common jump. The approximate closed-form solutions of the joint survival probability density and the probability density of the first default can be obtained by using the PDE method. Then with the expressions of the probability densities, we can get the formula for the CDS price with counterparty risk in a reduced form model with a common jump. In the numerical analysis part, we find that the default of the reference asset has a greater impact on the CDS price than that of the default of counterparty after introducing the common jump process.

在本文中，我们在简化模型中研究了具有交易对手风险的信用违约互换 (CDS) 定价。参考公司和交易对手的默认跳跃强度均假定遵循分别具有独立跳跃和共同跳跃的均值回归 CIR 过程。联合生存概率密度和第一违约概率密度的近似封闭形式的解可以通过使用PDE方法得到。然后根据概率密度的表达式，我们可以在具有共同跳跃的简化形式模型中得到具有交易对手风险的CDS价格的公式。在数值分析部分，引入共同跳跃过程后，我们发现参考资产违约对CDS价格的影响大于交易对手违约。