Mixed copula model with stochastic correlation for CDO pricing

This paper deals with the problem of pricing credit derivatives portfolio—CDO. The article assumes that the systematic factor and idiosyncratic factors subject to the fat-tailed mixed G-VG distribution instead of the traditional Gaussian distribution in the framework of factor model. Thus, the G-VG copula model is established. Stochastic correlation is also incorporated to account for the correlation skew problem. The semi-analytical expressions for conditional default probability, cumulative loss distribution function and expected tranche loss are explicitly derived in the G-VG copula models under large homogeneous portfolio approximation. Thus the CDO price can be determined. The numerical analysis is carried out and the properties of the new models with those of the traditional models are compared. Results show that new models not only provide a closer fit to the market quotes, but also bring more flexibility into the dependence structure.