Collateralized Debt Obligations

This chapter discusses how to model and price Collateralized Debt Obligation (CDO) tranches. The price of a CDO tranche is a function of many things: the probability of default of the underlying of the CDSs in the reference portfolio, their recovery values in case of default, the current interest rate environment and, most importantly, the default dependency between the assets in the reference portfolio. The chapter also discusses Lévy Base Correlation (BC) and makes comparison of several Lévy models with the classical Gaussian case. Lévy BC is a straightforward generalization of the classical Gaussian BC. It differs only in the underlying one-factor model. As the introduction of the one-factor Gaussian copula model for pricing synthetic CDO tranches, correlation is seen as an exogenous parameter used to match observed market quotes. Therefore, a CDO position can also be seen as a correlation trade: an equity tranche investor can be shown to be long the default correlation between the credits in the underlying CDS index while a senior tranche investor is short this default correlation.