Pricing Corporate Bonds With Credit Risk Under Jump Diffusion Model

Default probability plays a critical role in pricing corporate bonds and credit derivatives under structural credit risk model.However,generally there is no closed form solution for the default probability in jump diffusion model.Kou and Wang (2003) give the explicit solutions to the Laplace transform of the default time under. double exponential jump diffusion model,then obtain the numerical solution of default probability.This paper assumes both the firm value and the firm debt are exponential jump diffusion model,and uses "common shock" to describe the dependence of counting process of claim number.We give the closed form solutions to the Laplace transforms of default time when the jump part of the firm value and the firm debt are both double exponential distributions,and obtain both the numerical solutions of default probability and the value of corporate bonds using Gaver-Stehfest algorithm.Further we give the sufficient condition under which the explicit solutions to the Laplace transforms of default time exists,and show the impact of the dependence on the default probability and the value of corporate bonds.