Risk Neutral Versus Objective Loss Distribution and CDO Tranches Valuation

15 Pages Posted: 14 May 2006

See all articles by Roberto Torresetti

Roberto Torresetti

Banco Popolare

Damiano Brigo

Imperial College London - Department of Mathematics

Andrea Pallavicini

Banca IMI; Imperial College London - Department of Mathematics

Date Written: May 15, 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.

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

JEL Classification: G13

Suggested Citation

Torresetti, Roberto and Brigo, Damiano and Pallavicini, Andrea, Risk Neutral Versus Objective Loss Distribution and CDO Tranches Valuation (May 15, 2007). Available at SSRN: https://ssrn.com/abstract=900784 or http://dx.doi.org/10.2139/ssrn.900784

Roberto Torresetti (Contact Author)

Banco Popolare ( email )

Milan
Italy

Damiano Brigo

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/damiano.brigo

Andrea Pallavicini

Banca IMI ( email )

Largo Mattioli 3
Milan, MI 20121
Italy
+39 02 7261 (Phone)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

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