A factor contagion model for portfolio credit derivatives

Abstract

We propose a factor contagion model with the Marshall-Olkin copula for correlated default times and develop an analytic approach for finding the kth default time distribution based on our model. We combine a factor copula model with a contagion model under the assumption that the individual default intensities follow contagion processes, and that the default times have a dependence structure with the Marshall-Olkin copula. Then, we derive an analytic formula for the kth default time distribution and apply it to compute the price of portfolio credit derivatives, such as kth-to-default swaps and single-tranche CDOs. To test efficiency and accuracy of our formula, we compare the theoretical prediction with existing methods.