Pricing of Credit Risk Derivatives with Stochastic Interest Rate

This paper deals with a credit derivative pricing problem using the martingale approach. We generalize the conventional reduced-form credit risk model for a credit default swap market, assuming that the firms' default intensities depend on the default states of counterparty firms and that the stochastic interest rate follows a jump-diffusion Cox-Ingersoll-Ross process. First, we derive the joint Laplace transform of the distribution of the vector process (r(t), R-t) by applying piecewise deterministic Markov process theory and martingale theory. Then, using the joint Laplace transform, we obtain the explicit pricing of defaultable bonds and a credit default swap. Lastly, numerical examples are presented to illustrate the dynamic relationships between defaultable securities (defaultable bonds, credit default swap) and the maturity date.