Copula-based Local Dependence Framework

Abstract

This paper proposes a novel copula-based local Kendall’s tau framework to uncover richer nonlinear local dependence between two financial return series. This framework nests the concepts of global dependence, tail dependence and local dependence. Closed form solutions of local Kendall’s tau in terms of copula link local dependence with their global dependence structure together, providing a generalized framework for investigating dependence between two return series. We further extend the copula-based local dependence framework to Spearman’s rho. Using this framework, we draw the local Kendall’s tau surfaces in different quadrants for some common used bivariate Archimedean copulas. Finally, we demonstrate the advantages of copula-based local Kendall’s tau relative to global Kendall’s tau with stock market data.