Comparing and quantifying tail dependence

TL;DR

This paper introduces a new stochastic order for tail dependence, extends existing measures, and demonstrates its application in analyzing stock market data to better understand extreme co-movements.

Contribution

It proposes a novel stochastic order for tail dependence and extends classical measures, providing a more comprehensive framework for analyzing extreme co-movements.

Findings

New stochastic order for tail dependence introduced

Extended tail dependence measures that are monotone in the order

Empirical analysis shows improved understanding of stock tail dependence

Abstract

We introduce a new stochastic order for the tail dependence between random variables. We then study different measures of tail dependence which are monotone in the proposed order, thereby extending various known tail dependence coefficients from the literature. We apply our concepts in an empirical study where we investigate the tail dependence for different pairs of S&P 500 stocks and indices, and illustrate the advantage of our measures of tail dependence over the classical tail dependence coefficient.