Paths and indices of maximal tail dependence

TL;DR

This paper introduces new indices of tail dependence based on paths of maximal dependence, addressing limitations of existing measures in accurately capturing extreme co-movements in risks.

Contribution

It proposes a novel concept of paths of maximal tail dependence and develops new indices that better align with modern risk management principles.

Findings

Existing tail dependence measures can underestimate extreme co-movements.

New indices are conservative and distinguish between different risky positions.

Proposed methods work for both symmetric and asymmetric copulas.

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.