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Evidence On Delta Hedging And Implied Volatilities For The Black‐Scholes, Gamma, And Weibull Option Pricing Models

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  • Robert Savickas

Abstract

Modifying the distributional assumptions of the Black‐Scholes model is one way to accommodate the skewness of underlying asset returns. Simple models based on the compensated gamma and Weibull distributions of asset prices are shown to produce some improvements in option pricing. To evaluate these assertions, I construct and compare delta hedges of all S&P 500 options traded on the Chicago Board Options Exchange between September 2001 and October 2003 for the Weibull, Black‐Scholes, and gamma models. I also compare implied volatilities and their smiles (i.e., nonlinearities) among the three models. None of the three models improves over the others as far as delta hedging is concerned. Volatilities implied by all three models exhibit statistically significant smiles.

Suggested Citation

  • Robert Savickas, 2005. "Evidence On Delta Hedging And Implied Volatilities For The Black‐Scholes, Gamma, And Weibull Option Pricing Models," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 28(2), pages 299-317, June.
    • Handle: RePEc:bla:jfnres:v:28:y:2005:i:2:p:299-317
    DOI: 10.1111/j.1475-6803.2005.00126.x
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    Cited by:

    1. Pascal François & Lars Stentoft, 2021. "Smile‐implied hedging with volatility risk," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(8), pages 1220-1240, August.
    2. Molina Barreto, Andrés Mauricio & Jiménez Moscoso, José Alfredo, 2014. "Valoración de derivados europeos con mixtura de distribuciones Weibull [Valuation for European derivatives with mixture-Weibull distributions]," MPRA Paper 118572, University Library of Munich, Germany, revised 08 Aug 2014.
    3. Ben Boukai, 2021. "On the RND under Heston's stochastic volatility model," Papers 2101.03626, arXiv.org.
    4. Talbot, Edward & Artiach, Tracy & Faff, Robert, 2013. "What drives the commodity price beta of oil industry stocks?," Energy Economics, Elsevier, vol. 37(C), pages 1-15.
    5. Ben Boukai, 2021. "The Generalized Gamma distribution as a useful RND under Heston's stochastic volatility model," Papers 2108.07937, arXiv.org, revised Aug 2021.

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