A note on the calculation of default probabilities in “Structural credit risk modeling with Hawkes jump–diffusion processes”

Abstract

Ma and Xu (2016) proposed a Hawkes jump–diffusion model for the firm’s value to describe the unexpectedness of default and default clustering in the framework of Merton’s structural default. However, the authors resorted to Monte-Carlo simulations for the calculation of the default probability and the default correlation, as no other solution method was available in the literature. In this note, we present a closed-form solution for the probability of default and the default correlation using the characteristic function. Our new solution can substantially improve the computational efficiency for the problem.