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

Topcu Guloksuz Ç., Kumar P.

Studies in Nonlinear Dynamics and Econometrics, vol.26, no.2, pp.273-285, 2022 (SSCI) identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.1515/snde-2019-0096
  • Journal Name: Studies in Nonlinear Dynamics and Econometrics
  • Journal Indexes: Social Sciences Citation Index (SSCI), Scopus, IBZ Online, International Bibliography of Social Sciences, ABI/INFORM, Business Source Elite, Business Source Premier, EconLit, zbMATH
  • Page Numbers: pp.273-285
  • Keywords: Archimedean copula, dependence, generator function, Monte Carlo simulation, stock prices, value at risk
  • TED University Affiliated: No

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.