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

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Abstract

In single-obligor default risk modeling, 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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Authors and Affiliations

  1. ETH Zurich, D-MATH, Rämistr. 101, 8092, Zurich, Switzerland

    Philippe Ehlers & Philipp J. Schönbucher

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  1. Philippe Ehlers
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  2. Philipp J. Schönbucher
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Correspondence to Philippe Ehlers.

Additional information

Financial support by the National Centre of Competence in Research “Financial Valuation and Risk Management” (NCCR FINRISK) is gratefully acknowledged. NCCR FINRISK is a research program supported by the Swiss National Science Foundation (SNSF).

The authors would like to thank Monique Jeanblanc and two anonymous referees for their helpful comments and suggestions. Parts of this paper were presented at RiskDay 2006, Zurich. All remaining errors are our own. Comments and suggestions are very welcome.

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Ehlers, P., Schönbucher, P.J. Background filtrations and canonical loss processes for top-down models of portfolio credit risk. Finance Stoch 13, 79–103 (2009). https://doi.org/10.1007/s00780-008-0080-x

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