An Improved Implied Copula Model and Its Application to the Valuation of Bespoke CDO Tranches

John Hull and Alan White

Volume 8, Number 3, Third Quarter 2010

In Hull and White (2006) we showed how CDO quotes can be used to imply a probability distribution for the hazard rate over the life of the CDO. This is known as the implied copula model. In this paper we develop a parametric version of the implied copula model and show how it can be used for valuing bespoke CDOs. A two-parameter version of the model is a simple and appealing alternative to the Gaussian copula model. One of the parameters in this model is used to match spreads. The other can be implied from tranche quotes and is much less variable across the capital structure than base correlation. Both homogeneous and heterogeneous versions of the model are presented and the differences between the results obtained from these two versions of the model are examined. Results are also presented for the situation where hazard rates are driven by more than one factor.