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Pricing Multivariate European Equity Option Using Gaussians Mixture Distributions and EVT‐Based Copulas

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Listed:
  • Abba Mallam Hassane
  • Barro Diakarya
  • Yaméogo WendKouni
  • Saley Bisso

Abstract

In this article, we present an approach which allows taking into account the effect of extreme values in the modeling of financial asset returns and in the valorisation of associated options. Specifically, the marginal distribution of asset returns is modelled by a mixture of two Gaussian distributions. Moreover, we model the joint dependence structure of the returns using a copula function, the extremal one, which is suitable for our financial data, particularly the extreme values copulas. Applications are made on the Atos and Dassault Systems actions of the CAC40 index. Monte Carlo method is used to compute the values of some equity options such as the call on maximum, the call on minimum, the digital option, and the spreads option with the basket (Atos, Dassault systems) as underlying.

Suggested Citation

  • Abba Mallam Hassane & Barro Diakarya & Yaméogo WendKouni & Saley Bisso, 2021. "Pricing Multivariate European Equity Option Using Gaussians Mixture Distributions and EVT‐Based Copulas," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jijmms:v:2021:y:2021:i:1:n:7648093
    DOI: 10.1155/2021/7648093
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    References listed on IDEAS

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    1. Hassane Abba Mallam & Diakarya Barro & Yameogo WendKouni & Bisso Saley, 2021. "Pricing multivariate european equity option using gaussian mixture distributions and evt-based copulas," Papers 2105.10599, arXiv.org.
    2. Joshua Rosenberg, 1999. "Semiparametric Pricing of Multivariate Contingent Claims," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-028, New York University, Leonard N. Stern School of Business-.
    3. Abba Mallam Hassane & Barro Diakarya & Yaméogo WendKouni & Saley Bisso & Sergejs Solovjovs, 2021. "Pricing Multivariate European Equity Option Using Gaussians Mixture Distributions and EVT-Based Copulas," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2021, pages 1-9, September.
    4. Stulz, ReneM., 1982. "Options on the minimum or the maximum of two risky assets : Analysis and applications," Journal of Financial Economics, Elsevier, vol. 10(2), pages 161-185, July.
    5. Johnson, Herb, 1987. "Options on the Maximum or the Minimum of Several Assets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(3), pages 277-283, September.
    6. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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