On cox processes and credit risky securities

A framework is presented for modeling defaultable securities and credit derivatives which allows for dependence between market risk factors and credit risk. The framework reduces the technical issues of modeling credit risk to the same issues faced when modeling the ordinary term structure of interest rates. It is shown how to generalize a model of Jarrow, Lando and Turnbull (1997) to allow for stochastic transition intensities between rating categories and into default. This generalization can handle contracts with payments explicitly linked to ratings. It is also shown how to obtain a term structure model for all different rating categories simultaneously and how to obtain an affine-like structure. An implementation is given in a simple one factor model in which the affine structure gives closed form solutions.