Copulas Approximation and New Families

24 Pages Posted: 26 Nov 2007 Last revised: 3 Apr 2009

See all articles by Valdo Durrleman

Valdo Durrleman

Ecole Polytechnique - Centre de Mathematiques Appliquees - CNRS

Ashkan Nikeghbali

affiliation not provided to SSRN

Thierry Roncalli

Amundi Asset Management; University of Evry

Date Written: August 21, 2000

Abstract

In this paper, we study the approximation procedures introduced by Li, Mikusinski, Sherwood and Taylor [1997]. We show that there exists a bijection between the set of the discretized copulas and the set of the doubly stochastic matrices. For the Bernstein and checkerboard approximations, we then provide analytical formulas for the Kendall's tau and Spearman's rho concordance measures. Moreover, we demonstrate that these approximations do not exhibit tail dependences. Finally, we consider the general case of approximations induced by partitions of unity. Moreover, we show that the set of copulas induced by partition of unity is a Markov sub - algebra with respect to the *-product of Darsow, Nguyen and Olsen [1992].

Keywords: Doubly stochastic matrices, Bernstein polynomials approximation, checkerboard copula, partitions of unity, Markov algebras, product of copulas

JEL Classification: G00

Suggested Citation

Durrleman, Valdo and Nikeghbali, Ashkan and Roncalli, Thierry, Copulas Approximation and New Families (August 21, 2000). Available at SSRN: https://ssrn.com/abstract=1032547 or http://dx.doi.org/10.2139/ssrn.1032547

Valdo Durrleman

Ecole Polytechnique - Centre de Mathematiques Appliquees - CNRS ( email )

Palaiseau, 91128
France

Ashkan Nikeghbali

affiliation not provided to SSRN ( email )

No Address Available

Thierry Roncalli (Contact Author)

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

University of Evry ( email )

Boulevard Francois Mitterrand
F-91025 Evry Cedex
France

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