This paper discusses the pricing problem of credit default swap in the fractional Brownian motion environment. As credit default swap is exposed to both the interest rate risk and the default risk, we assume that the default intensity of a firm depends on the stochastic interest rate and the default states of counterparty firms. The interest rate risk is reflected by the fractional Vasicek interest rate model. We model the firm's default intensity under the looping default model and derive the pricing formulas of risky bonds and credit default swap.

We present an intensity-based model with counterparty risk. We assume the default intensity of firm depends on the stochastic interest rate driven by the jump-diffusion process and the default states of counterparty firms. Furthermore, we make use of the techniques in Park (2008) to compute the conditional distribution of default times and derive the explicit prices of bond and CDS. These are extensions of the models in Jarrow and Yu (2001).

This paper mainly discusses the pricing of credit default swap (CDS) in the fractional dimension environment. We assume that the default intensity of a firm depends on the default states of counterparty firms and the term structure of interest rates, but the contagious impact of the counterparty firm is decreasing over time, until disappears. The interest rate risk is reflected by the fractional Vasicek interest rate model. We model the firm's default intensity in the looping default framework and derive the pricing formulas of risky bonds and credit default swap.

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