Extreme Tails for Linear Portfolio Credit Risk Models

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Extreme Tails for Linear Portfolio Credit Risk Models

by André Lucas of the Tinbergen Institute Amsterdam,
Pieter Klaassen of Vrije Universiteit,
Peter Spreij of the University of Amsterdam, and
Stefan Straetmans of Maastricht University

May 28, 2002

Abstract: We consider the extreme tail behavior of the CreditMetrics model for portfolio credit losses. We generalize the model to allow for alter-native distributions of the risk factors. We consider two special cases and provide alternative tail approximations. The results reveal that one has to be careful in applying extreme value theory for computing extreme quantiles efficiently. The applicability of extreme value theory in characterizing the tail shape very much depends on the exact distributional assumptions for the systematic and idiosyncratic credit risk factors.

JEL Classification: G21, G33, G29, C19.

Keywords: portfolio credit risk, extreme value theory, tail events, tail index, CreditMetrics, second and higher order expansions.

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