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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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00259242, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00259242
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00259242
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    References listed on IDEAS

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    1. Brennan, M J, 1979. "The Pricing of Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 34(1), pages 53-68, March.
    2. 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.
    3. van den Goorbergh, Rob W.J. & Genest, Christian & Werker, Bas J.M., 2005. "Bivariate option pricing using dynamic copula models," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 101-114, August.
    4. U. Cherubini & E. Luciano, 2002. "Bivariate option pricing with copulas," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(2), pages 69-85.
    5. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. 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-.
    8. 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.
    9. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, vol. 7(2), pages 407-425, Autumn.
    10. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    11. 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.
    12. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    13. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
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    Cited by:

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    2. Rombouts, Jeroen V.K. & Stentoft, Lars, 2011. "Multivariate option pricing with time varying volatility and correlations," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2267-2281, September.
    3. Stavrakoudis, Athanassios & Panagiotou, Dimitrios, 2016. "Price dependence between coffee qualities: a copula model to evaluate asymmetric responses," MPRA Paper 75994, University Library of Munich, Germany.
    4. Rombouts, Jeroen & Stentoft, Lars & Violante, Franceso, 2014. "The value of multivariate model sophistication: An application to pricing Dow Jones Industrial Average options," International Journal of Forecasting, Elsevier, vol. 30(1), pages 78-98.
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    6. Thijs Markwat, 2014. "The rise of global stock market crash probabilities," Quantitative Finance, Taylor & Francis Journals, vol. 14(4), pages 557-571, April.
    7. 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.
    8. Branger, Nicole & Muck, Matthias, 2012. "Keep on smiling? The pricing of Quanto options when all covariances are stochastic," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1577-1591.

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    More about this item

    Keywords

    time-varying parameter; Call-on-max option; GARCH process; Kendall's tau; Copula; Dynamic Copula; time-varying parameter.; Processus GARCH; Copules dynamiques; Call d'une option; Tau de Kendall; paramètre temps-variable.;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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