The Pricing of Credit Default Swap under Stochastic Liabilities

The credit default swap is an important credit derivative. Based on the basic principle of the credit default swap, this paper analyses the value of a credit default swap in terms of its cash flow. Furthermore, the arbitrage-free principle and structural approaches are used to price the credit default swap under stochastic liabilities, and we get a basic model of the swap. The function of default probability density is obtained by the distribution of the minimum of a Brown motion with a drift, and then we obtain the pricing formula to a credit default swap by above results.