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Market Application of the Fuzzy-Stochastic Approach in the Heston Option Pricing Model

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Abstract

The present study analyzes the extra insights that option pricing models may achieve when uncertainty about parameters is modeled through fuzzy numbers. Specifically, the authors consider the Heston stochastic volatility model, which assumes that stock price changes and their instantaneous variance evolve as a bivariate, possibly correlated, diffusive process. The original Heston model provides a quasi-closed formula for the pricing of several derivative products such as European options. By applying the fuzzy extension principle, the authors generalize the model to the case of fuzzy parameters; given their shape the authors are able to derive the membership of the fuzzy price of a European option. Finally, to understand the extent to which their approach might be useful in practice, they give a numerical illustration of their procedure on the S&P 500 and VIX indexes. As a by-product of their research, a simple estimation method is introduced to obtain (crisp) parameters in the Heston model under the risk-neutral measure and applied in the sequel of the paper to obtain alternative shapes for the fuzzy parameters of the model.

Suggested Citation

  • Gianna Figa-Talamanca & Maria Letizia Guerra, 2012. "Market Application of the Fuzzy-Stochastic Approach in the Heston Option Pricing Model," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 62(2), pages 162-179, May.
    • Handle: RePEc:fau:fauart:v:62:y:2012:i:2:p:162-179
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    References listed on IDEAS

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    1. Cont, Rama & Kokholm, Thomas, 2009. "A Consistent Pricing Model for Index Options and Volatility Derivatives," Finance Research Group Working Papers F-2009-05, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    2. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
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    Cited by:

    1. Maria Letizia Guerra & Laerte Sorini & Luciano Stefanini, 2015. "Option prices by differential evolution," Working Papers 1511, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2015.
    2. Maria Letizia Guerra & Laerte Sorini & Luciano Stefanini, 2013. "Value function computation in fuzzy models by differential evolution," Working Papers 1311, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2013.

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    More about this item

    Keywords

    fuzzy numbers; stochastic volatility; risk-neutral measure; option pricing;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • 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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