Pricing Credit Default Swaps when Interest Rate Process and Hazard Rate Process are Stochastic

This paper models the dynamics of the building blocks for a plain vanilla credit default swap. We use a normal process for the interest rate (Vasicek model) to model the price of zero-coupon bonds (or the discount factor) and a log-normal process for the hazard rate to model the survival probabilities in a java applet. Model-generated data are used to calculate a fair market price for such a contract once survival probabilities and values of the discount function have been estimated using stochastic models. The article concludes by presenting numerical results from the models. Combining a constant interest rate and a stochastic hazard rate process, this one-factor model shows that the level of hazard rate rather than the volatility affecting the change in CDS spreads the most. With a constant survival probability and a stochastic interest rate, a lower CDS spread is associated with a higher spot rate due to the protection buyer's higher opportunity cost on the premium payments. Results also show that a higher survival probability of the reference entity indicates a lower CDS spread as expected. A two-factor model gives a much higher CDS price than the one-factor model especially when the drift parameters are higher in the credit events process