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

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.