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Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market

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  • 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)

  • 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])

Abstract

This paper develops the method for pricing bivariate contingent claims under General Autoregressive Conditionally Heteroskedastic (GARCH) process. In order to provide a general framework being able to accommodate skewness, leptokurtosis, fat tails as well as the time varying volatility that are often found in financial data, generalized hyperbolic (GH) distribution is used for innovations. As the association between the underlying assets may vary over time, the dynamic copula approach is considered. Therefore, the proposed method proves to play an important role in pricing bivariate option. The approach is illustrated for Chinese market with one type of better-of-two-markets claims : call option on the better performer of Shanghai Stock Composite Index and Shenzhen Stock Composite Index. Results show that the option prices obtained by the GARCH-GH model with time-varying copula differ substantially from the prices implied by the GARCH-Gaussian dynamic copula model. Moreover, the empirical work displays the advantage of the suggested method.

Suggested Citation

  • Dominique Guegan & Jing Zhang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00368336, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00368336
    DOI: 10.1080/13518470902895344
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00368336
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    Cited by:

    1. D. Guegan & J. Zhang, 2010. "Change analysis of a dynamic copula for measuring dependence in multivariate financial data," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 421-430.
    2. Christophe Chorro & Dominique Guegan & Florian Ielpo, 2010. "Option pricing for GARCH-type models with generalized hyperbolic innovations," Post-Print halshs-00469529, HAL.
    3. Cyril Caillault, Dominique Guégan, 2009. "Forecasting VaR and Expected Shortfall Using Dynamical Systems: A Risk Management Strategy," Frontiers in Finance and Economics, SKEMA Business School, vol. 6(1), pages 26-50, April.
    4. Dominique Guegan & Jing Zhang, 2010. "Change analysis of a dynamic copula for measuring dependence in multivariate financial data," Post-Print halshs-00368334, HAL.
    5. See-Woo Kim & Yong-Ki Ma & Ciprian Necula, 2023. "Modeling Tail Dependence Using Stochastic Volatility Model," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 129-147, June.
    6. Li, Johnny Siu-Hang & Ng, Andrew C.Y. & Chan, Wai-Sum, 2015. "Managing financial risk in Chinese stock markets: Option pricing and modeling under a multivariate threshold autoregression," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 217-230.
    7. Dominique Guegan & Jing Zhang, 2010. "Change analysis of a dynamic copula for measuring dependence in multivariate financial data," PSE-Ecole d'économie de Paris (Postprint) halshs-00368334, HAL.
    8. Cyril Caillault & Dominique Guegan, 2009. "Forecasting VaR and Expected Shortfall using Dynamical Systems: A Risk Management Strategy," PSE-Ecole d'économie de Paris (Postprint) halshs-00375765, HAL.
    9. Christophe Chorro & Dominique Guegan & Florian Ielpo, 2012. "Option Pricing for GARCH-type Models with Generalized Hyperbolic Innovations," PSE-Ecole d'économie de Paris (Postprint) hal-00511965, HAL.
    10. Christophe Chorro & Dominique Guegan & Florian Ielpo, 2012. "Option Pricing for GARCH-type Models with Generalized Hyperbolic Innovations," Post-Print hal-00511965, HAL.

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    More about this item

    Keywords

    Call-on-max option; GARCH process; generalized hyperbolic (GH) distribution; normal inverse Gaussian (NIG) distribution; copula; dynamic copula;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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