CDO pricing using single factor MG-NIG copula model with stochastic correlation and random factor loading

We consider the valuation of CDO tranches with single factor MG-NIG copula model, where the involved distributions are mixtures of Gaussian distribution and NIG distribution. In addition, we consider two cases for stochastic correlation and random factor loadings instead of constant factor loadings. We analyze the unconditional characteristic function of accumulated loss of the reference portfolio, and derive the loss distribution through the fast Fourier transform. Moreover, using the loss distribution and semi-analytic approach, we can get the CDO tranches spreads.