# On the Interrelation between Dependence Coefficients of Extreme Value Copulas

## TL;DR

This paper derives bounds for dependence coefficients of extreme value copulas with known upper tail dependence, identifying specific copulas that attain these bounds and enhancing understanding of their dependence structures.

## Contribution

It establishes pointwise bounds for dependence coefficients of extreme value copulas based on the upper tail dependence, identifying extremal copulas that attain these bounds.

## Key findings

- Lower bounds are attained on Marshall--Olkin copulas.
- Upper bounds are attained on copulas with piecewise linear dependence functions.
- Provides a framework for bounding dependence measures in extreme value copulas.

## Abstract

For extreme value copulas with a known upper tail dependence coefficient we find pointwise upper and lower bounds, which are used to establish upper and lower bounds of the Spearman and Kendall correlation coefficients. We shown that in all cases the lower bounds are attained on Marshall--Olkin copulas, and the upper ones, on copulas with piecewise linear dependence functions.