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Option Valuation with Normal Mixture GARCH Models

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Author Info

  • Badescu Alex

    ()
    (University of Calgary)

  • Kulperger Reg

    ()
    (University of Western Ontario)

  • Lazar Emese

    ()
    (ICMA Centre, The University of Reading)

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    Abstract

    The class of mixture GARCH models introduced by Haas, Mittnik and Paollela (2004) and Alexander and Lazar (2006) provides a better alternative for fitting financial data than various other GARCH models driven by the normal or skewed t-distribution. In this paper we propose different option pricing methodologies when the underlying stock dynamic is modeled by an asymmetric normal mixture GARCH model with K volatility components. Since under GARCH models the market is incomplete there are an infinite number of martingale measures one can use for pricing. For our mixture setting we analyze the impact of three risk-neutral candidates: a generalized local risk neutral valuation relationship, an Esscher transform and an extended Girsanov principle. We investigate the out-of-sample performance of an asymmetric GARCH model with a mixture density of two normals for Call options written on the S&P 500 Index. The performance under all three transformations is quite impressive when compared to the benchmark GARCH model with normal driving noise. The overall improvement is explained not only by the skewness and leptokurtosis exhibited by the innovation mixture distribution, but also by the richer parametrization used in modeling the dynamics of the multi-component conditional volatility.

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    Bibliographic Info

    Article provided by De Gruyter in its journal Studies in Nonlinear Dynamics & Econometrics.

    Volume (Year): 12 (2008)
    Issue (Month): 2 (May)
    Pages: 1-42

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    Handle: RePEc:bpj:sndecm:v:12:y:2008:i:2:n:5

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    Cited by:
    1. Badescu, Alex & Elliott, Robert J. & Siu, Tak Kuen, 2009. "Esscher transforms and consumption-based models," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 337-347, December.
    2. Guégan, Dominique & Ielpo, Florian & Lalaharison, Hanjarivo, 2013. "Option pricing with discrete time jump processes," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2417-2445.
    3. Jeroen V.K. Rombouts & Lars Stentoft, 2010. "Multivariate Option Pricing with Time Varying Volatility and Correlations," CREATES Research Papers 2010-19, School of Economics and Management, University of Aarhus.
    4. Anastassios A. Drakos & Georgios P. Kouretas & Leonidas P. Zarangas, 2010. "Forecasting financial volatility of the Athens stock exchange daily returns: an application of the asymmetric normal mixture GARCH model," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 15(4), pages 331-350.

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