Credit default swap pricing with counterparty risk in a reduced form model with Hawkes process

Abstract.

In this article, we investigate the pricing of credit default swaps (CDS) while taking into account counterparty risk. We adopt a reduced form model with a self-exciting Hawkes process that allows for clustering in the default intensity. By solving the partial differential equations, we derive semi-analytical formulas for the joint survival probability density and the first default probability density. To obtain the numerical solutions for CDS pricing, we use the Runge-Kutta numerical method. Through our numerical analysis, by comparing the CDS pricing under the Poisson process, we find that the CDS pricing model under the Hawkes process provides a more general and richer structure and better describes the default risk of contagion.

Keywords:

• CDS pricing
• counterparty risk
• Hawkes process

Disclosure statement

The authors declare no conflict of interest.

Additional information

Funding

This work was supported by Philosophy and Social Science Research in Colleges and Universities of Jiangsu Province (2022SJYB0365) and Open Project of Jiangsu Key Laboratory of Financial Engineering (NSK2021-13, NSK2021-15).