Title: Multidimensional portfolio risk measurement: a mixed copula approach

Authors: Wen-Li Cai; Na Liu; Yu-Xuan Wu; Xiang-Dong Liu

Addresses: Department of Mathematics, China University of Mining and Technology, Ding No.11 Xueyuan Road, Haidian District, Beijing, 100083, China ' Department of Mathematics, China University of Mining and Technology, Ding No.11 Xueyuan Road, Haidian District, Beijing, 100083, China ' Department of Mathematics, China University of Mining and Technology, Ding No.11 Xueyuan Road, Haidian District, Beijing, 100083, China ' Department of Mathematics, China University of Mining and Technology, Ding No.11 Xueyuan Road, Haidian District, Beijing, 100083, China

Abstract: It is an increasingly challenging task to explore the risk measurement for multidimensional portfolios with nonlinear correlative assets. A risk measurement scheme based on the mixed copula theory is proposed in this paper, where the mixed copula is constructed by the linear combination of three single Archimedean copulas, embodying greater flexibility than single copula in connecting different types of marginal distributions. In the scenario, ARMA-EGARCH model with t innovation is employed to fit marginal distributions, and the parameter values of the mixed copulas are inferred by maximum likelihood estimation (MLE) method, and interior point algorithm is used to calculate the extreme values of the MLE, VaR and CVaR, corresponding to the optimal portfolio with the minimum risk. Finally, an empirical study on five international stock market indexes in Europe is performed to verify the feasibility and effectiveness of the scheme.

Keywords: ARMA-EGARCH; CVaR; mixed copula; risk measurement.

DOI: 10.1504/IJCSM.2020.111708

International Journal of Computing Science and Mathematics, 2020 Vol.12 No.3, pp.228 - 238

Received: 09 Jul 2018
Accepted: 26 Nov 2018
Published online: 11 Dec 2020 *

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