Using structural models for credit default swaps has been difficult. Existing models all adopt shortcuts as approximations. In this article, we provide an accurate and efficient solution to the price of the credit default swap. The main result is a Theorem in section 2. In an empirical study, we show how our model can properly capture credit default swap exposure to interest rate volatility and asset volatility. Furthermore, we apply the new model to study (1) the interactions among market, credit, and interest risks; (2) the consistency with the reduced-form credit risk models; and (3) implications to capital structure arbitrage.