Pricing defaultable bonds under Hawkes jump-diffusion processes

In this paper, we propose a reduced-form model for the embedded credit risk in corporate bonds. We specify the default hazard rate as an affine function of a series of influential variables. To capture the clustering property in some extreme situations, Hawkes jump-diffusion processes are adopted to model the variables. We derive the semi-analytical pricing formula for defaultable bonds. The empirical results from U.S. bond market illustrate the significance of jump clustering when pricing low credit-rating bonds.