Measures of Dependences

Abstract

In the previous chapter, we have shown how to describe with copulas the general dependence structure of several random variables, with the goal of modeling baskets of asset returns, or more generally, any multivariate financial risk. However, the general framework provided by copulas does not exclude more specific measures of dependences that can be useful to target particular ranges of variations of the random variables.

This chapter presents and describes in detail the most important dependence measures. Starting with the description of the basic concept of linear dependence, through linear correlation and canonical N-correlation coefficients, we then focus on concordance measures and on more interesting families of dependence measures. We then turn to measures of extreme dependence. In each case, we underline their relationship with copulas.