Dynamic Models of Portfolio Credit Risk

Abstract

Valuing portfolio credit derivatives, such as CDO tranches based on a broad portfolio of credits, like the CDX.NA.IG index portfolio with 125 investment grade names, remains a very difficult problem. Only approximate and imperfect solutions are available so far. The industry standard Gaussian copula model has several known shortcomings, including the fact that it is a static model which does not offer a clear way to tie together valuation for CDO tranches with different maturities, and it doesn't generate wide enough spreads to match market prices for the supersenior tranches. Efforts to make the default hazard rate dynamic by modeling it as a diffusion run into the second difficulty when the models are calibrated to market prices. This article introduces a dynamic process for the cumulative hazard rate for a credit portfolio, that allows discrete jumps with jump size increasing in the number of jumps. This approach ties together the market quotes for CDO tranches of different maturities into a unified valuation framework. It also can generate large enough default intensity once several defaults have occurred to produce default risk on the senior and supersenior tranches of the magnitude that the market seems to be incorporating into their prices.