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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Volume (Year): 13 (2009)
Issue (Month): 1 (January)
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- 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, 02.
- Sanjiv Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2006. "Common Failings: How Corporate Defaults are Correlated," NBER Working Papers 11961, National Bureau of Economic Research, Inc.
- 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..
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195.
- 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. Full references (including those not matched with items on IDEAS)
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