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Background Filtrations andCanonical Loss Processes for Top-Down Models of Portfolio Credit Risk

Author

Listed:
  • Philippe Ehlers

    (ETH Zurich, D-MATH)

  • Philipp J. Schoenbucher

    (ETH Zurich, D-MATH)

Abstract

In single-obligor default risk modelling, using a background filtration in conjunction with a suitable embedding hypothesis (generally known as H-hypothesis or immersion property) has proven a very successful tool to separate the actual default event from the model for the default arrival intensity. In this paper we analyze the conditions under which this approach can be extended to the situation of a portfolio of several obligors, with a particular focus on the so-called top-down approach. We introduce the natural H-hypothesis of this setup (the successive H-hypothesis) and show that it is equivalent to a seemingly weaker one-step H-hypothesis. Furthermore, we provide a canonical construction of a loss process in this setup and provide closed-form solutions for some generic pricing problems.

Suggested Citation

  • Philippe Ehlers & Philipp J. Schoenbucher, 2007. "Background Filtrations andCanonical Loss Processes for Top-Down Models of Portfolio Credit Risk," Swiss Finance Institute Research Paper Series 07-07, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp0707
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    Cited by:

    1. Nicole El Karoui & Monique Jeanblanc & Ying Jiao, 2013. "Density approach in modelling multi-defaults," Working Papers hal-00870492, HAL.
    2. Nicole El Karoui & Monique Jeanblanc & Ying Jiao, 2017. "Dynamics of multivariate default system in random environment," Post-Print hal-01205753, HAL.
    3. Biagini, Francesca & Mazzon, Andrea & Oberpriller, Katharina, 2023. "Reduced-form framework for multiple ordered default times under model uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 1-43.
    4. Ying Jiao, 2009. "Multiple defaults and contagion risks," Papers 0912.3132, arXiv.org.
    5. Jakob Sidenius & Vladimir Piterbarg & Leif Andersen, 2008. "A New Framework For Dynamic Credit Portfolio Loss Modelling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 163-197.
    6. El Karoui, Nicole & Jeanblanc, Monique & Jiao, Ying, 2017. "Dynamics of multivariate default system in random environment," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3943-3965.
    7. Ernst Eberlein & Zorana Grbac & Thorsten Schmidt, 2010. "Discrete tenor models for credit risky portfolios driven by time-inhomogeneous L\'evy processes," Papers 1006.2012, arXiv.org, revised Apr 2013.
    8. Ying Jiao, 2009. "Multiple defaults and contagion risks," Working Papers hal-00441500, HAL.

    More about this item

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    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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