Recovering Portfolio Default Intensities Implied by CDO Quotes

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

32 Pages Posted: 13 Mar 2008 Last revised: 2 Oct 2010

See all articles by Rama Cont

Rama Cont

University of Oxford; CNRS

Andreea Minca

Cornell University

Multiple version iconThere are 2 versions of this paper

Date Written: January 1, 2008

Abstract

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.

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

JEL Classification: G13, C51

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

Rama Cont (Contact Author)

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

HOME PAGE: http://https://www.maths.ox.ac.uk/people/rama.cont

CNRS ( email )

LPSM
Sorbonne University
Paris
France

HOME PAGE: http://rama.cont.perso.math.cnrs.fr/

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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