Vector copulas

TL;DR

This paper develops a new framework called vector copulas for modeling dependence between multivariate vectors, based on measure transportation, and demonstrates their application in financial contagion analysis.

Contribution

It introduces vector copulas and establishes a vector version of Sklar's theorem, enabling flexible modeling of multivariate dependence structures.

Findings

Established a theoretical foundation for vector copulas.

Constructed elliptical and Kendall families of vector copulas.

Applied vector copulas to analyze financial contagion.

Abstract

This paper introduces vector copulas associated with multivariate distributions with given multivariate marginals, based on the theory of measure transportation, and establishes a vector version of Sklar's theorem. The latter provides a theoretical justification for the use of vector copulas to characterize nonlinear or rank dependence between a finite number of random vectors (robust to within vector dependence), and to construct multivariate distributions with any given non overlapping multivariate marginals. We construct Elliptical and Kendall families of vector copulas, derive their densities, and present algorithms to generate data from them. The use of vector copulas is illustrated with a stylized analysis of international financial contagion.