Pricing CDOs with Correlated Variance Gamma Distributions

In this article, we propose a method for synthetic CDO pricing with Variance Gamma processes and distributions. First, we extend a structural model proposed by Luciano and Schoutens [2005] by allowing a more general dependence structure. We show that our ex-tension leads to a correlation smile as observed in liquid index tranches. Since this method is not adequate for practical purposes, we extract the dependence structure into a factor approach based on Variance Gamma distributions. This approach allows for an analytical solution for the portfolio loss distribution. The model fits to prices of liquid CDS index tranches. It can be used to price bespoke CDOs in a consistent way. 1