Pricing CDO tranches with stochastic correlation and random factor loadings in a mixture copula model

In this paper, we introduce a mixture distribution of Gaussian and Variance Gamma distribution. Then we use the one-factor double mixture copula model to solve the problem of CDO pricing. Two cases of stochastic correlation and random factor loadings are considered. In each case, the unconditional characteristic function of accumulated loss is calculated and the loss distribution can therefore be derived by using the fast Fourier transform. The loss distribution of a large homogeneous portfolio is also derived. Furthermore, we analyze the numerical results.