A comprehensive Analysis of Advanced Pricing Models for Collateralised Debt Obligations

The subject of this paper is the single tranche portfolio credit default swap or synthetic single tranche CDO, which has received a great deal of interest in recent years. Unlike single name CDS, tranche portfolio products depend on the joint default behavior of the underlying credits or in other words their default correlation.The Gaussian copula has emerged as a market standard for modeling the dependence structure and pricing CDOs. The introduction of credit indices has made it possible to compute a market implied correlation, which for the Gaussian copula results in a smile similar to the volatility smile for the Black and Scholes model in the equity options market. The smile is inconsistent with the model and causes problems for pricing bespoke CDOs. Therefore a lot of research has been devoted to develop extensions to the Gaussian copula and/or alternative pricing models that are better able to explain the correlation smile. In this thesis we will review and compare the performance of a number of advanced pricing models for collateralised debt obligations which were recently suggested, including the Base Correlation framework, the double t copula, the NIG copula and two extensions to the normal copula comprising random recovery rates and random factor loadings. The models are assessed in terms of how well they are able to replicate/explain the correlation skew in the index market. The performance of the models is tested over time for both the iTraxx and CDX 5 year index. Unlike previous research which focused on particular points in time we tested the models on a monthly basis between January 2005 and May 2006.