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

Yu Xing, Wei Wang and Xiaonan Su

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 6, 1813-1835

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.

Date: 2025
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DOI: 10.1080/03610926.2024.2349715

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