Exponential Power Jump Diffusion Model Applied to Credit Risk

This study formulated a model for the evolution of a firm’s value obtained the probability of a firm’s default under the formulated model. More precisely based on the structural approach to credit risk modeling the dynamics of the value of the firm is assumed to be a combination of a diffusion process and a jump process driven by an exponential power distribution. Within the framework of structural models of credit risk the Nikkie 225 asset value was modelled by a jump-diffusion process. A compound Poisson process driven by an exponential power distribution was used as the jump component to construct a jump diffusion model for the Nikkie 225 asset value and the diffusion component was modelled by a geometric Brownian process. The Ito’s formula for a jump-diffusion process was used to establish the solution to the proposed model. The distribution of the jump-diffusion process together with the assumption that default on the debt contract can only occur at maturity was used to obtain the probability of default of the firm.