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

Author

Listed:
  • Topcu Guloksuz Cigdem
  • Kumar Pranesh

    (Department of Mathematics and Statistics, University of Northern British Columbia, 3333 University Way, Prince George, BC V2N 4Z9, Canada)

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.

Suggested Citation

  • Topcu Guloksuz Cigdem & Kumar Pranesh, 2022. "A new bivariate Archimedean copula with application to the evaluation of VaR," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 26(2), pages 273-285, April.
    • Handle: RePEc:bpj:sndecm:v:26:y:2022:i:2:p:273-285:n:2
    DOI: 10.1515/snde-2019-0096
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    More about this item

    Keywords

    Archimedean copula; dependence; generator function; Monte Carlo simulation; stock prices; value at risk;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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