Extreme dependence for multivariate data

TL;DR

This paper introduces a new framework for measuring and manipulating extreme dependence between multivariate data vectors, with applications in financial stress testing and risk management.

Contribution

It generalizes the concept of extreme dependence using cross-covariance matrices and proposes methods to quantify and enhance dependence while maintaining marginals.

Findings

Defines a generalized extremality measure based on cross-covariance matrices

Provides a method to quantify dependence strength between multivariate series

Enables stress-testing of dependence in financial variables

Abstract

This article proposes a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the cross-covariance matrices, we also generalize the notion of positive upper dependence. We then proposes a means to quantify the strength of the dependence between two given multivariate series and to increase this strength while preserving the marginal distributions. This allows for the design of stress-tests of the dependence between two sets of financial variables, that can be useful in portfolio management or derivatives pricing.