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Background filtrations and canonical loss processes for top-down models of portfolio credit risk



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.
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Suggested Citation

  • Philippe Ehlers & Philipp Schönbucher, 2009. "Background filtrations and canonical loss processes for top-down models of portfolio credit risk," Finance and Stochastics, Springer, vol. 13(1), pages 79-103, January.
  • Handle: RePEc:spr:finsto:v:13:y:2009:i:1:p:79-103
    DOI: 10.1007/s00780-008-0080-x

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    References listed on IDEAS

    1. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    2. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195.
    3. Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007. "Common Failings: How Corporate Defaults Are Correlated," Journal of Finance, American Finance Association, vol. 62(1), pages 93-117, February.
    4. Christophette Blanchet-Scalliet & Monique Jeanblanc, 2004. "Hazard rate for credit risk and hedging defaultable contingent claims," Finance and Stochastics, Springer, vol. 8(1), pages 145-159, January.
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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. Ying Jiao, 2009. "Multiple defaults and contagion risks," Papers 0912.3132,
    4. repec:wsi:ijtafx:v:11:y:2008:i:02:n:s0219024908004762 is not listed on IDEAS
    5. repec:eee:spapps:v:127:y:2017:i:12:p:3943-3965 is not listed on IDEAS
    6. Ernst Eberlein & Zorana Grbac & Thorsten Schmidt, 2010. "Discrete tenor models for credit risky portfolios driven by time-inhomogeneous L\'evy processes," Papers 1006.2012,, revised Apr 2013.
    7. Ying Jiao, 2009. "Multiple defaults and contagion risks," Working Papers hal-00441500, HAL.

    More about this item


    Credit risk; Default correlation; Point processes; Generalized Cox processes; Hypothesis ℍ; G13; 60G35; 91B28; 91B30;

    JEL classification:

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


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