Structural credit risk modelling with Hawkes jump diffusion processes

To describe the unexpectedness of default and especially default clustering in the framework of Merton’s structural default, we propose a novel jump diffusion model for the firm’s value. In this model, the jumps, which reflect the systematic risk common to all firms and an idiosyncratic risk, arrive dependently and they are described by self-exciting Hawkes processes rather than the classical Poisson processes. Some classical models are the special cases of the proposed model. The analytical solution to the value of the firm is derived. Numerical analysis shows that Hawkes jump diffusion model can better explain the behavior of default clustering than Poisson jump diffusion model.