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Collateralized Debt Obligations Pricing and Factor Models: A new methodology using Normal Inverse Gaussian distributions

by Dominique Guegan of Ecole Normale Supérieure de Cachan, and
Julien Houdain of Ecole Normale Supérieure de Cachan & Fortis Investments

June 2005

Abstract: The reported "correlation smile" in the CDO market is proof that the spreads of CDOs tranches are not consistent when we use the widely-known Gaussian one-factor model for the pricing. We introduce a new methodology in which non-standard tranches such as bespoke single tranches can be valued. The underlying idea of our framework is to use the tranches' price quotes available in the market to determine the implied distribution of the common factor for a given correlation level. In our methodology the estimated correlation between the underlying assets of a CDO's underlying portfolio becomes an input. We propose an improvement to the market standard model by using Normal Inverse Gaussian distributions and we show that our approach is theoretically and empirically more accurate.

JEL Classification: G12, G13.

Keywords: CDO pricing, correlation smile, implied correlation, implied distribution, loss distribution, factor model, NIG distributions, conditional default probability.

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