Modeling Credit Risk by Affine Processes

In this paper, the treasury rates and the credit migrations are jointly modeled by multi-dimensional affine processes. In order to capture the entire information, including credit migrations and default events, we construct non-conservative regular affine processes to model credit migrations and characterize the default by the death of the processes. In particular, two specific cases: purely jump affine models and affine diffusion models with potentials, are discussed. This affine approach not only produces the explicit formulas for the prices of corporate bonds and other credit derivatives, but also directly incorporates the credit rating information as a parameter into the pricing formulas. Moreover, our affine models allow to consider the joint credit migrations within an analytically tractable framework in order to capture the correlations of credit movements between firms. Finally, the empirical testing results of a simple affine model are presented to support the effectiveness of our models.