A structural approach to credit risk model using jump-diffusion process

Abstract

We study the evaluation of credit risk that is associated with the fluctuation in the firm value. The usual assumption that the firm value follows a Brownian motion is extended to the jump diffusion process having the jump amplitude of double exponential distribution. The key quantity in pricing corporate bonds and credit derivatives is the default probability. We utilize the well-known fact that the Laplace transform of the jump diffusion process with double exponential distribution can be obtained explicitly. We then obtain the default probability using the Gaver-Stehfest algorithm, which provides a fast and convenient numerical Laplace inversion. When a firm defaults, it is common that only a fraction of the liability, called the recovery rate, is paid. Given the recovery rate and the default probability, the value of the corporate bond and the credit spread are obtained. Lastly, we see the change of default probability and credit spread by reliable parameters from the real market.