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Pricing bivariate option under GARCH processes with time-varying copula

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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," Documents de travail du Centre d'Economie de la Sorbonne b08015, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:b08015
    DOI: 10.1016/j.insmatheco.2008.02.003
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Aloui, Riadh & Hammoudeh, Shawkat & Nguyen, Duc Khuong, 2013. "A time-varying copula approach to oil and stock market dependence: The case of transition economies," Energy Economics, Elsevier, vol. 39(C), pages 208-221.
    6. 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.
    7. Emmanuel Afuecheta & Saralees Nadarajah & Stephen Chan, 2021. "A Statistical Analysis of Global Economies Using Time Varying Copulas," Computational Economics, Springer;Society for Computational Economics, vol. 58(4), pages 1167-1194, December.
    8. Thijs Markwat, 2014. "The rise of global stock market crash probabilities," Quantitative Finance, Taylor & Francis Journals, vol. 14(4), pages 557-571, April.

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    Keywords

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    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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