Study on the pricing of credit default swap with affine jump-diffusions processes

The article deduced the closed form solution of credit default swap´s at-market rate by assuming that interest rate r and default intensity lambda are the affine jump-diffusions process, and intensities are independent (risk-neutrally) of interest rates. Then the article studied how the coefficients of random process and the maturity of the contract influence the price. Later, with the initial conditions the article calculated the market credit-swap spread for a one-year CDS, and analyzed the influences on spreads imposed by the varying interest rates and intensities after half a year passed. The main conclusions include: (1) The coefficients of jump-diffusion process have a notable influence on the price of CDS at the beginning; (2) And the spreads rise with the increases of default intensity, decrease with the increases of interest rates. But the effect of intensity is more significant than that of interest rate. So the spreads still rise even with the same increase of interest rates and intensities