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Dynamic CDO Term Structure Modelling

by Damir Filipović of the University of Vienna & Vienna University of Economics and Business Administration,
Ludger Overbeck of the University of Giessen, and
Thorsten Schmidt of Chemnitz University of Technology

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.

Published in: Management Science, Vol. 21, No. 1, (January 2011), pp. 53-71.

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