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GARCH Option Pricing Under Skew

Author

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  • Sofiane ABOURA

    (ESSEC Busienss School)

Abstract

This article is an empirical study dedicated to the GARCH Option pricing model of Duan (1995) applied to the FTSE 100 European style options for various maturities. The beauty of this model is to have used the standard GARCH theory in an option perspective and also it is its flexibility to adapt to different rich GARCH specifications. We analyze the valididy of the model given its ability to price one-day ahead out- of-sample call options and also its ability to capture the empirical dynamic of the volatility skew. We get severe mispricing for deep out- of-the-money and short term call options, which tend to decrease the global performance of the model that is relatively correct. We note that long term skews tend to be more stable across time and strikes, which explains why we had a decreasing pricing bias for longer maturity contracts. We also get that skews tend to deform into smiles as we go toward the expiry date. This model reveals a good ability to capture the change of regime in the implied volatility surface judging from the transformation observed from smiles to skews.

Suggested Citation

  • Sofiane ABOURA, 2004. "GARCH Option Pricing Under Skew," Finance 0405032, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0405032
    Note: Type of Document - pdf; pages: 14
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    References listed on IDEAS

    as
    1. 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.
    2. Blair, Bevan J. & Poon, Ser-Huang & Taylor, Stephen J., 2001. "Forecasting S&P 100 volatility: the incremental information content of implied volatilities and high-frequency index returns," Journal of Econometrics, Elsevier, vol. 105(1), pages 5-26, November.
    3. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    4. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
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    Keywords

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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