Efficient and Accurate Evaluation Methods for Concordance Measures via Functional Tensor Characterizations of Copulas

Dalessandro, A., Peters, G.W. Efficient and Accurate Evaluation Methods for Concordance Measures via Functional Tensor Characterizations of Copulas. Methodol Comput Appl Probab (2019). https://doi.org/10.1007/s11009-019-09752-2

Posted: 3 Oct 2016 Last revised: 16 Jul 2020

See all articles by Antonio Dalessandro

Antonio Dalessandro

University College London

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Date Written: September 1, 2019

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. However, evaluation of concordance measures to quantify such types of dependence for different copula models can be challenging. In this work, we propose a class of new methods that involves a highly accurate and computationally efficient procedure to evaluate concordance measures for a given copula, applicable even when sampling from the copula is not easily achieved. 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 and associated concordance measures expressed in terms of these copula models.

Keywords: Concordance Measures, Copula Functions, Copula Infinitesimal Generators, Martingale Problem, Multidimensional Semimartingales Decomposition Approximations, Semimartingales Decomposition, Tensor Algebra

JEL Classification: C00, C14, C60, C63

Suggested Citation

Dalessandro, Antonio and Peters, Gareth, Efficient and Accurate Evaluation Methods for Concordance Measures via Functional Tensor Characterizations of Copulas (September 1, 2019). Dalessandro, A., Peters, G.W. Efficient and Accurate Evaluation Methods for Concordance Measures via Functional Tensor Characterizations of Copulas. Methodol Comput Appl Probab (2019). https://doi.org/10.1007/s11009-019-09752-2, Available at SSRN: https://ssrn.com/abstract=2846670 or http://dx.doi.org/10.2139/ssrn.2846670

Antonio Dalessandro (Contact Author)

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

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