Dynamic CDO Term Structure Modelling

Mathematical Finance, Forthcoming

21 Pages Posted: 9 Jul 2009

See all articles by Damir Filipović

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Ludger Overbeck

University of Giessen

Thorsten Schmidt

University of Freiburg

Date Written: April 14, 2009

Abstract

This paper provides a unifying approach for valuing contingent claims on a portfolio of credits, such as collateralized debt obligations (CDOs). We introduce the defaultable $(T,x)$-bonds, which pay one if the aggregated loss process in the underlying pool of the CDO has not exceeded $x$ at maturity $T$, and zero else. Necessary and sufficient conditions on the stochastic term structure movements for the absence of arbitrage are given. Background market risk as well as feedback contagion effects of the loss process are taken into account. Moreover, we show that any exogenous specification of the volatility and contagion parameters actually yields a unique consistent loss process and thus an arbitrage-free family of $(T,x)$-bond prices. For the sake of analytical and computational efficiency we then develop a tractable class of doubly stochastic affine term structure models.

Keywords: affine term structure, collateralized debt obligations, loss process, single tranche CDO, term structure of forward spreads

JEL Classification: G13, C60

Suggested Citation

Filipovic, Damir and Overbeck, Ludger and Schmidt, Thorsten, Dynamic CDO Term Structure Modelling (April 14, 2009). Mathematical Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1431316

Damir Filipovic (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

HOME PAGE: http://people.epfl.ch/damir.filipovic

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Ludger Overbeck

University of Giessen ( email )

Institut of Mathematics
Giessen, 35394
Germany

Thorsten Schmidt

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

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