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

by Philippe Ehlers of ETH Zurich, and
Philipp J. Schönbucher of ETH Zurich

January 2009

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.

JEL Classification: G13.

AMS Classification: 60G35, 91B28, 91B30.

Keywords: Credit risk, Default correlation, Point processes, Generalized Cox processes, Hypothesis ℍ.

Published in: Finance and Stochastics, Vol. 13, No. 1, (January 2009), pp. 79-103.

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