Measuring non-exchangeable tail dependence using tail copulas

TL;DR

This paper introduces two new measures, MTCM and ATCM, for quantifying non-exchangeable tail dependence using tail copulas, addressing limitations of the traditional tail dependence coefficient in risk management.

Contribution

The paper proposes novel tail dependence measures that capture non-exchangeable dependence, with analytical forms and real data application demonstrating their effectiveness.

Findings

Revealed significant tail dependence in stock indices during financial distress.

Demonstrated non-exchangeability in tail dependence using the new measures.

Provided analytical formulas for the proposed measures across various copulas.

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.