Credit risk dependence modeling with dynamic copula: An application to CDO tranches

We have developed a new family of Archimedean copula processes for modeling the dynamic dependence between default times in a large portfolio of names and for pricing synthetic CDO tranches. After presenting a general procedure for constructing these processes, we focus on a specific one with lower tail dependence as in the Clayton copula. Using CDS data as on July 2005, we show that the base correlations given by this model at the standard detachment points are very similar to those quoted in the market for a maturity of 5 years.