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A new bivariate Archimedean copula with application to the evaluation of VaR

  • Cigdem Topcu Guloksuz ORCID logo and Pranesh Kumar
Published/Copyright: December 21, 2020

Abstract

In this paper, a new generator function is proposed and based on this function a new Archimedean copula is introduced. The new Archimedean copula along with three representatives of Archimedean copula family which are Clayton, Gumbel and Frank copulas are considered as models for the dependence structure between the returns of two stocks. These copula models are used to simulate daily log-returns based on Monte Carlo (MC) method for calculating value at risk (VaR) of the financial portfolio which consists of two market indices, Ford and General Motor Company. The results are compared with the traditional MC simulation method with the bivariate normal assumption as a model of the returns. Based on the backtesting results, describing the dependence structure between the returns by the proposed Archimedean copula provides more reliable results over the considered models in calculating VaR of the studied portfolio.

JEL Classification: C02; C15; C18; C40; C46

Corresponding author: Cigdem Topcu Guloksuz, Department of Mathematics and Statistics, University of Northern British Columbia, Prince George, Canada, E-mail:

Funding source: Scientific and Technological Research Council of Turkey (TUBITAK)

Award Identifier / Grant number: 2219

Acknowledgment

Authors wish to place on record their appreciaiton to the Editor and the reviewers for all valuable comments and suggestions which helped us improve the quality of the article. First author also gratefully acknowledges the hospitality extended by the University of Northern British Columbia.

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: The research was supported by the award of Scientific and Technological Research Council of Turkey (TUBITAK) Grant No. 2219 to the first author.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/snde-2019-0096).


Received: 2019-08-27
Accepted: 2020-12-05
Published Online: 2020-12-21

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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