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MULTIVARIATE COMPOSITE COPULAS

Published online by Cambridge University Press:  03 November 2021

Jiehua Xie ,
Jun Fang ,
Jingping Yang  and
Lan Bu
Jiehua Xie*
Affiliation:
School of Business Administration Nanchang Institute of TechnologyJiangxi 330099, P. R. China. E-Mail: jhxie@pku.edu.cn
Jun Fang
Affiliation:
Department of Financial Mathematics Peking UniversityBeijing 100871, P. R. China. E-Mail: fang_jun@pku.edu.cn
Jingping Yang*
Affiliation:
LMEQF, Department of Financial Mathematics Peking UniversityBeijing 100871, P. R. China. E-Mail: yangjp@math.pku.edu.cn
Lan Bu
Affiliation:
Department of Financial Mathematics Peking UniversityBeijing 100871, P. R. China. E-Mail: bulan@pku.edu.cn
*
E-Mail: jhxie@pku.edu.cn
E-Mail: yangjp@math.pku.edu.cn
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Abstract

In this paper, we present a method for generating a copula by composing two arbitrary n-dimensional copulas via a vector of bivariate functions, where the resulting copula is named as the multivariate composite copula. A necessary and sufficient condition on the vector guaranteeing the composite function to be a copula is given, and a general approach to construct the vector satisfying this necessary and sufficient condition via bivariate copulas is provided. The multivariate composite copula proposes a new framework for the construction of flexible multivariate copula from existing ones, and it also includes some known classes of copulas. It is shown that the multivariate composite copula has a clear probability structure, and it satisfies the characteristic of uniform convergence as well as the reproduction property for its component copulas. Some properties of multivariate composite copulas are discussed. Finally, numerical illustrations and an empirical example on financial data are provided to show the advantages of the multivariate composite copula, especially in capturing the tail dependence.

Keywords

Copula constructionmultivariate composite copulauniform convergencereproduction propertyC02
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 52 , Issue 1 , January 2022 , pp. 145 - 184
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The International Actuarial Association

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