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

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. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

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. They presented a closed-form solution for the probability of default and the default correlation using the characteristic function, which can substantially improve computational efficiency for the problem.