Tensor Approximation of Generalized Correlated Diffusions for Decomposing Copulas: Part A

34 Pages Posted: 22 Jul 2016 Last revised: 5 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: June 19, 2016

Abstract

We develop a new class of techniques that takes a copula function and quantifies the dependence properties through a localized coefficient of dependence in the state space. Effectively we develop a numerical procedure to map any copula function to a generalized Gaussian copula function. This allows us to visualize and interpret the copula functions characteristics. This is particularly useful in understanding the relationships between copula model parameters and the strength of induced concordance structures captured by particular copula types. The copula mapping is entirely based on tensor algebra and is part of a new modelling framework we also propose consisting of the tensor approximation of the infinitesimal generator associated to multidimensional correlated diffusion. This new result provides the representation in a tensor space of both correlated diffusive transition densities and generalized copula densities. We demonstrate the simplicity and intuition behind the copula mapping through illustrative examples and all the copula functions mapping results are exact up to the tensor space local discretization error.

Keywords: 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, Tensor Approximation of Generalized Correlated Diffusions for Decomposing Copulas: Part A (June 19, 2016). Available at SSRN: https://ssrn.com/abstract=2813135 or http://dx.doi.org/10.2139/ssrn.2813135

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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