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
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: Suggested Citation