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Measuring non-exchangeable tail dependence using tail copulas

Published online by Cambridge University Press:  28 February 2023

Takaaki Koike Open the ORCID record for Takaaki Koike [Opens in a new window] ,
Shogo Kato  and
Marius Hofert Open the ORCID record for Marius Hofert [Opens in a new window]
Takaaki Koike*
Affiliation:
Graduate School of Economics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan
Shogo Kato
Affiliation:
Risk Analysis Research Center, Institute of Statistical Mathematics, Tachikawa, Tokyo 190-8562, Japan
Marius Hofert
Affiliation:
Department of Statistics and Actuarial Science, Faculty of Science, The University of Hong Kong, Pokfulam, Hong Kong
*
*Corresponding author. E-mail: takaaki.koike@r.hit-u.ac.jp
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Abstract

Quantifying tail dependence is an important issue in insurance and risk management. The prevalent tail dependence coefficient (TDC), however, is known to underestimate the degree of tail dependence and it does not capture non-exchangeable tail dependence since it evaluates the limiting tail probability only along the main diagonal. To overcome these issues, two novel tail dependence measures called the maximal tail concordance measure (MTCM) and the average tail concordance measure (ATCM) are proposed. Both measures are constructed based on tail copulas and possess clear probabilistic interpretations in that the MTCM evaluates the largest limiting probability among all comparable rectangles in the tail, and the ATCM is a normalized average of these limiting probabilities. In contrast to the TDC, the proposed measures can capture non-exchangeable tail dependence. Analytical forms of the proposed measures are also derived for various copulas. A real data analysis reveals striking tail dependence and tail non-exchangeability of the return series of stock indices, particularly in periods of financial distress.

Keywords

Copulatail copulatail dependencetail dependence coefficienttail dependence functiontail non-exchangeabilityC01C02C40G11
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 53 , Issue 2 , May 2023 , pp. 466 - 487
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The International Actuarial Association

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