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Multivariate Option Pricing Using Dynamic Copula Models

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  • van den Goorbergh, R.W.J.

    (Tilburg University, Center For Economic Research)

  • Genest, C.
  • Werker, B.J.M.

    (Tilburg University, Center For Economic Research)

Abstract

This paper examines the behavior of multivariate option prices in the presence of association between the underlying assets.Parametric families of copulas offering various alternatives to the normal dependence structure are used to model this association, which is explicitly assumed to vary over time as a function of the volatilities of the assets.These dynamic copula models are applied to better-of-two-markets and worse-of-two-markets options on the S&P500 and Nasdaq indexes.Results show that option prices implied by dynamic copula models differ substantially from prices implied by models that fix the dependence between the underlyings, particularly in times of high volatilities. Furthermore, the normal copula produces option prices that differ significantly from non-normal copula prices, irrespective of initial volatility levels.Within the class of non-normal copula families considered, option prices are robust with respect to the copula choice.

Suggested Citation

  • van den Goorbergh, R.W.J. & Genest, C. & Werker, B.J.M., 2003. "Multivariate Option Pricing Using Dynamic Copula Models," Discussion Paper 2003-122, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:86ec50af-0fb6-4782-b2dd-d24c1f28ae25
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    References listed on IDEAS

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    6. Rosenberg, Joshua V., 1998. "Pricing multivariate contingent claims using estimated risk-neutral density functions," Journal of International Money and Finance, Elsevier, vol. 17(2), pages 229-247, April.
    7. Umberto Cherubini & Elisa Luciano, 2002. "Multivariate Option Pricing with Copulas," ICER Working Papers - Applied Mathematics Series 05-2002, ICER - International Centre for Economic Research.
    8. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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    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:

    1. Beatriz Vaz de Melo Mendes, 2005. "Computing Conditional VaR using Time-varying CopulasComputing Conditional VaR using Time-varying Copulas," Brazilian Review of Finance, Brazilian Society of Finance, vol. 3(2), pages 251-265.
    2. Paul Doukhan & Jean-David Fermanian & Gabriel Lang, 2009. "An empirical central limit theorem with applications to copulas under weak dependence," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 65-87, February.
    3. Dominique Guegan, 2007. "La persistance dans les marchés financiers," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00179269, HAL.
    4. Manner Hans, 2010. "Testing for Asymmetric Dependence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(2), pages 1-32, March.
    5. Jean-David Fermanian, 2003. "Goodness of Fit Tests for Copulas," Working Papers 2003-34, Center for Research in Economics and Statistics.
    6. Paul Doukhan & Jean-David Fermanian & Gabriel Lang, 2005. "Copulas of a Vector-Valued Stationary Weakly Dependent Process," Working Papers 2005-48, Center for Research in Economics and Statistics.
    7. Denitsa Stefanova, 2012. "Stock Market Asymmetries: A Copula Diffusion," Tinbergen Institute Discussion Papers 12-125/IV/DSF45, Tinbergen Institute.

    More about this item

    Keywords

    option pricing; dynamic models; options;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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