Risk Neutral versus Objective Loss Distribution and CDO Tranches Valuation

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Risk Neutral versus Objective Loss Distribution and CDO Tranches Valuation

by Roberto Torresetti of Banca IMI,
Damiano Brigo of Banca IMI, and
Andrea Pallavicini of Banca IMI

April 13, 2007

Abstract: We consider the risk neutral loss distribution as implied by index CDO tranche quotes through a "scenario default rate" model as opposed to the objective measure loss distribution based on historical analysis. The risk neutral loss distribution turns out to privilege large realizations of the loss with respect to the objective distribution, thus implying the well-known presence of a risk premium. We quantify this difference numerically by pricing CDO tranches and indices under the two distributions. En passant we analyze the implied risk neutral default rate distributions calibrated from April-2004 throughout April-2006, pointing out its distinctive "bump feature" in the tail.

JEL Classification: G13.

Keywords: Default Rate distribution, CDO, CDO tranches, Implied Copula, Transition Matrices, Rating Classes, Risk Premium, Recovery Rate.

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