Paths and Indices of Maximal Tail Dependence

ASTIN Bulletin: The Journal of the International Actuarial Association, Forthcoming

20 Pages Posted: 6 May 2014 Last revised: 17 Jul 2016

See all articles by Edward Furman

Edward Furman

York University - Department of Mathematics and Statistics

Jianxi Su

Purdue University - Department of Statistics

Ricardas Zitikis

Western University

Date Written: June 19, 2015

Abstract

We demonstrate both analytically and numerically that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with the new paradigm of prudent risk management. This phenomenon holds in the context of both symmetric and asymmetric copulas with and without singularities. As a remedy, we introduce a notion of paths of maximal (tail) dependence and utilize it to propose several new indices of tail dependence. The suggested new indices are conservative, conform with the basic concepts of modern quantitative risk management, and are able to distinguish between distinct risky positions in situations when the existing indices fail to do so.

Keywords: multivariate distribution; copula; tail dependence; maximal dependence; fatal shock; multivariate Pareto; enterprise risk management.

JEL Classification: C02, C51

Suggested Citation

Furman, Edward and Su, Jianxi and Zitikis, Ricardas, Paths and Indices of Maximal Tail Dependence (June 19, 2015). ASTIN Bulletin: The Journal of the International Actuarial Association, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2433347 or http://dx.doi.org/10.2139/ssrn.2433347

Edward Furman

York University - Department of Mathematics and Statistics ( email )

4700 Keele Street
Toronto, M3J 1P3
Canada

Jianxi Su (Contact Author)

Purdue University - Department of Statistics ( email )

West Lafayette, IN 47907
United States

Ricardas Zitikis

Western University ( email )

1151 Richmond Street
Suite 2
London, Ontario N6A 5B8
Canada

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