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Recovering Portfolio Default Intensities Implied by CDO Quotes

Rama Cont

Imperial College London; CNRS; Norges Bank Research

Andreea Minca

Cornell University

January 1, 2008

Columbia University Center for Financial Engineering, Financial Engineering Report No. 2008-01

We propose a stable non-parametric algorithm for the calibration of pricing models for portfolio credit derivatives: given a set of observations of market spreads for CDO tranches, we construct a risk-neutral default intensity process for the portfolio underlying the CDO which matches these observations, by looking for the risk neutral loss process 'closest' to a prior loss process, verifying the calibration constraints. We formalize the problem in terms of minimization of relative entropy with respect to the prior under calibration constraints and use convex duality methods to solve the problem: the dual problem is shown to be an intensity control problem, characterized in terms of a Hamilton-Jacobi system of differential equations, for which we present an analytical solution. Given a set of observed CDO tranche spreads, our method allows to construct an implied intensity process consistent with the observed spreads. We illustrate our method on ITRAXX index data: our results reveal strong evidence for the dependence of loss transitions rates on the past number of defaults, thus offering quantitative evidence for contagion effects in the risk-neutral loss process.

Number of Pages in PDF File: 32

Keywords: CDO, portfolio credit derivatives, model calibration, default risk, inverse problem

JEL Classification: G13, C51

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Date posted: March 13, 2008 ; Last revised: October 2, 2010

Suggested Citation

Cont, Rama and Minca, Andreea, Recovering Portfolio Default Intensities Implied by CDO Quotes (January 1, 2008). Columbia University Center for Financial Engineering, Financial Engineering Report No. 2008-01 . Available at SSRN: https://ssrn.com/abstract=1104855 or http://dx.doi.org/10.2139/ssrn.1104855

Contact Information

Rama Cont (Contact Author)
Imperial College London ( email )
London, SW7 2AZ
United Kingdom
HOME PAGE: http://www3.imperial.ac.uk/people/r.cont
CNRS ( email )
Laboratoire de Probabilites & Modeles aleatoires
Universite Pierre & Marie Curie (Paris VI)
Paris, 75252
HOME PAGE: http://rama.cont.perso.math.cnrs.fr/
Norges Bank Research ( email )
P.O. Box 1179
Oslo, N-0107
Andreea Minca
Cornell University ( email )
222 Rhodes Hall
Ithaca, NY NY 14853
United States
HOME PAGE: http://people.orie.cornell.edu/acm299/
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