The Pricing Of CDS With Counterparty Risk In A Markov Copula Model

Credit risk is one of the most important risk in the financial industry.Credit De-fault Swaps (CDS) are the most important tool of credit risk management. CDS arebilateral financial contracts between credit protection buyers (risk sellers) and creditprotection sellers (risk buyers) which purpose is to provide insurance for the loss ofsome reference assets. They are essential contracts of insurance for risk of defaultableassets.To efectively play the function of managing credit risk，the key is whether CDSare priced reasonablly. Currently, the main pricing theories are structural models basedon Black-Scholes option pricing formula,reduced models based on defaultable inten-sity and mixtural models.However, due to some characteristics of credit risk, there aremany theoretical difculties in pricing CDS.Therefore, we need to invest more atten-tion to study it.We study the pricing of CDS with counterparty risk in a Markov Copula Modelunder postponed-payments. We first state few preliminary results about pricing of aCDS with counterparty risk under postponed-payments in a general set-up.We then in-troduce a Markov Copula model in which the correlation of counterparty risk and ref-erence assets risk is represented by the possibility of joint defaults between them. Thenunder the framework,the discounted cash flow is dealt with the martingale method. Un-der the case of postponed-payments,the pricing functions of special and ordinary CDSare deduced and the fee rates are also obtained.We also solve the pricing functions andfee rates under the case of instant payments.Finally,model calibration is made simpleby the Markov Copula property and numerical results show the behavior of pricingfuctions and fee rates in the model with stylized features.