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Implied Multi-Factor Model for Bespoke CDO Tranches and other Portfolio Credit Derivatives

by Igor Halperin of JP Morgan

October 14, 2009

Abstract: This paper introduces a new semi-parametric approach to the pricing and risk management of bespoke CDO tranches, with a particular attention to bespokes that need to be mapped onto more than one reference portfolio. The only user input in our framework is a multi-factor model (a "prior" model hereafter) for index portfolios, such as CDX.NA.IG or iTraxx Europe, that are chosen as benchmark securities for the pricing of a given bespoke CDO. Parameters of the prior model are fixed, and not tuned to match prices of benchmark index tranches. Instead, our calibration procedure amounts to a proper reweightening of the prior measure using the Minimum Cross Entropy method. As the latter problem reduces to convex optimization in a low dimensional space, our model is computationally efficient. Both the static (one-period) and dynamic versions of the model are presented. The latter can be used for pricing and risk management of more exotic instruments referencing bespoke portfolios, such as forward-starting tranches or tranche options, and for calculation of credit valuation adjustment (CVA) for bespoke tranches.

JEL Classification: G13, C14, C63.

Keywords: CDO, bespoke tranches, implied distribution, factor model.

Published in: Journal of Credit Risk, Vol. 6, No. 3, (Fall 2010), pp. 3-52.

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