Modeling of CDO Squareds

Abstract

This article is an extract of a more complete and detailed work on a specific class of credit derivatives, namely Collateralized Debt Obligations made out of Collateralized Debt Obligations, widely known as CDO Squareds (CDO2). This asset class has become quite popular in recent years as it deserves investors' appetite for higher credit spread via leverage when investing in bonds. This article focuses more on the modeling aspects of plain vanilla structures than on factors which would allow for tailoring a CDO2 for specific investors' risk appetites. First we give a brief introduction to CDO2 and recall important specifies which have to be taken into account for modeling. The following section intends to put John Hull's ideas of pricing CDO2 which he proposed during the ICBI Global Derivatives Conference of May 2005 in concrete and formal mathematical terms. First, we will model the total loss conditional on the market factor on the respective underlying portfolios via a double-t factor copula model. This allows us to calculate the correlation between these underlying entities and to put the values into a correlation matrix. We will refer to this step as “capturing the second dimension, i.e. the cross dependence structure”. With the help of this matrix, it is now possible to calculate—conditional on the commonality factor—the total loss distribution of the CDO2 via a one-factor Gaussian Copula Model and numerical methods. The obtained CDO2 loss distribution is used for pricing a CDO2 tranche inspired by Credit Default Swap (CDS) pricing methods.