Part B: Evaluating Concordance Measures via a Tensor Approximation of Generalized Correlated Diffusions

Abstract

There is now an increasingly large number of proposed concordance measures available to capture, measure and quantify different notions of dependence in stochastic processes. These can include concepts such as multivariate upper negative (positive) dependence, lower negative (positive) dependence, negative (positive) dependence; multivariate negative (positive) quadrant dependence; multivariate association, co-monotinicity, stochastic ordering; regression dependence negative (positive) and extreme dependence, asymptotic tail dependence and intermediate tail dependence; as well as other concepts such as directional dependence. However, evaluation of concordance measures to quantify such types of dependence for different copula models can be challenging. Therefore, we propose a class of new methods that is highly accurate and computationally efficient procedure to evaluate concordance measures for a given copula. In addition, this then allows us to reconstruct maps of concordance measures locally in all regions of the state space for any range of copula parameters. We believe this technique will be a valuable tool for practitioners to understand better the behaviour of copula models.