Using distortions of copulas to price synthetic CDOs

This paper demonstrates how to use distorted Gaussian copula functions to produce a heavy tailed portfolio loss distribution in the context of synthetic Collateralized Debt Obligations (CDOs). Distortion functions have not previously been used in this area. Hence, we demonstrate that it is possible to simulate realistic tranche prices by incorporating distorted copula functions within a well established CDO pricing system, such as that of JP Morgan. Furthermore, we only require a single dependence parameter for the entire portfolio rather than one per tranche. Thus, we are providing practitioners with a simpler and more flexible alternative to current CDO pricing methods.