Abstract
From 2001 the trade volume of credit default swaps is increasing and it is necessary to develop other derivatives based on credit default swaps （CDS）. This article provides the models to price forward CDS and CDS options. The way to price forward CDS and CDS options is based on Hull and White (2003) but we use the transition matrix of credit rating to estimate the probability of default and volatility of CDS. When there are no transactions of CDS, this way is simple and easy to price these derivatives. In this way, we also can get the step-function of probability of default which is similar to Hull and White（2003）and modify the problem of large volatility. Then, we assume the CDS rate follow HJM stochastic process when there are the CDS trading data. By constructing CDS rate tree and simulation, we can get the price of CDS option and avoid the inconsistency assumption of Hull and White（2003）. This article provides the numerical result of first part using the credit rating data of Moody’s and TCRI, the result of second part using the same data as Hull and White（2003）, and illustrates the effects of the variables in these models.