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Limiting dependence structures for tail events, with applications to credit derivatives

Part of: Distribution theory Multivariate analysis Applications

Published online by Cambridge University Press:  14 July 2016

Arthur Charpentier  and
Alessandro Juri
Arthur Charpentier*
Affiliation:
ENSAE/CREST
Alessandro Juri*
Affiliation:
UBS AG, Zürich
*
∗Postal address: Laboratoire de Finance et Assurance, ENSAE/CREST, Timbre J120, 3 avenue Pierre Larousse, FR-92245 Malakoff Cedex, France. Email address: arthur.charpentier@ensae.fr
∗∗Postal address: Credit Risk Control, UBS AG, PO Box, CH-8098 Zürich, Switzerland. Email address: alessandro.juri@ubs.com
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Abstract

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Dependence structures for bivariate extremal events are analyzed using particular types of copula. Weak convergence results for copulas along the lines of the Pickands-Balkema-de Haan theorem provide limiting dependence structures for bivariate tail events. A characterization of these limiting copulas is also provided by means of invariance properties. The results obtained are applied to the credit risk area, where, for intensity-based default models, stress scenario dependence structures for widely traded products such as credit default swap baskets or first-to-default contract types are proposed.

Keywords

Copulacredit riskdependent defaultsdependent risksextreme value theoryregular variationtail dependence

MSC classification

Primary: 62E20: Asymptotic distribution theory
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.) 62P05: Applications to actuarial sciences and financial mathematics
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 2 , June 2006 , pp. 563 - 586
Copyright
© Applied Probability Trust 2006 

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