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Pricing bivariate option under GARCH processes with time-varying copula

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  • Jing Zhang

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, ECNU - East China Normal University [Shangaï])

  • Dominique Guegan

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

This paper develops a method for pricing bivariate contingent claims under General Autoregressive Conditionally Heteroskedastic (GARCH) process. As the association between the underlying assets may vary over time, the dynamic copula with time-varying parameter offers a better alternative to any static model for dependence structure and even to the dynamic copula model determined by dynamic dependence measure. Therefore, the proposed method proves to play an important role in pricing bivariate options. The approach is illustrated with one type of better-of-two-markets claims: call option on the better performer of Shanghai and Shenzhen Stock Composite Indexes. Results show that the option prices obtained by the time-varying copula model differ substantially from the prices implied by the static copula model and even the dynamic copula model derived from the dynamic dependence measure. Moreover, the empirical work displays the advantages of the suggested method.

Suggested Citation

  • Jing Zhang & Dominique Guegan, 2008. "Pricing bivariate option under GARCH processes with time-varying copula," PSE-Ecole d'économie de Paris (Postprint) halshs-00286054, HAL.
    • Handle: RePEc:hal:pseptp:halshs-00286054
    DOI: 10.1016/j.insmatheco.2008.02.003
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00286054
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    References listed on IDEAS

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    Cited by:

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    3. Xing Yang & Yi-ting Ye & Jia-wen Li & Jun-long Mi, 2023. "Asymmetric time-varying dependence and variable structure dependence measurement and analysis of EUA and CER," International Journal of Low-Carbon Technologies, Oxford University Press, vol. 18, pages 609-621.

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