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.

Autorentext

D. Gray is an instructor of Mathematics and Statistics at the University of Liberia. He received his B.Sc. in Mathematics from the University of Liberia and M.Sc. in Regional planning from the University of Liberia, also obtained a second M.Sc. in Statistics from the Obafemi Awolowo University, Nigeria. Presently a PhD candidate.

Klappentext

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.