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Doubly Stochastic CDO Term Structures

  • Damir FilipovićEmail author
  • Ludger Overbeck
  • Thorsten Schmidt
Conference paper
Part of the Progress in Probability book series (PRPR, volume 63)

Abstract

This paper provides a general framework for doubly stochastic term structure models for 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 exceededx at maturityT, and zero else. Necessary and sufficient conditions on the stochastic term structure movements for the absence of arbitrage are given. Moreover, we show that any exogenous specification of the forward rates and spreads volatility curve actually yields a 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 affine term structure models.

Keywords

Affine term structure collateralized debt obligations loss process single tranche CDO term structure of forward spreads 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Damir Filipović
    • 1
    Email author
  • Ludger Overbeck
    • 2
  • Thorsten Schmidt
    • 3
  1. 1.Swiss Finance InstituteEcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.Department of MathematicsUniversity of GiessenGiessenGermany
  3. 3.Department of MathematicsChemnitz University of TechnologyChemnitzGermany

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