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A Generalized SMART Fuzzy Disjunction of Volatility Indicators Applied to Option Pricing in a Binomial Model

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Soft Methods for Data Science (SMPS 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 456))

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Abstract

In this paper we extend our previous contributions on the elicitation of the fuzzy volatility membership function in option pricing models. More specifically we generalize the SMART disjunction for a multi-model volatility behavior (Uniform, LogNormal, Gamma, ...) and within a double-source (direct vs. indirect) information set. The whole procedure is then applied to the Cox-Ross-Rubinstein framework for option pricing on the S&P500 Index where the historical volatility, computed from the Index returns’ time series, and the VIX Index observed data are respectively considered as the direct and indirect sources of knowledge. A suitable distance among the resulting fuzzy option prices and the market bid-ask spread make us appreciate the proposed procedure against the classical fuzzy mean.

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Notes

  1. 1.

    Reported results refer to trading on October 21st, 2010.

References

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Acknowledgments

This work was partially supported by INdAM-GNAMPA through the Project 2015 U2015/000418 and by DMI—Universitá degli Studi di Perugia ricerca di base project 2016 “Operatori SMART per aggregazioni fuzzy”.

Author information

Authors and Affiliations

  1. Dipartimento Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy

    Andrea Capotorti

  2. Dipartimento Economia, Università degli Studi di Perugia, Perugia, Italy

    Gianna Figà-Talamanca

Authors
  1. Andrea Capotorti
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  2. Gianna Figà-Talamanca
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Corresponding author

Correspondence to Andrea Capotorti .

Editor information

Editors and Affiliations

  1. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Maria Brigida Ferraro

  2. Department of Statistical Sciences, Sapienza University of Rome, Roma, Italy

    Paolo Giordani

  3. Dept of Basic & Applied Sciences Engg, Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

  4. Dept of Stoc Metds,Polish Academy of Sci, Systems Research Institute, Warsaw, Poland

    Marek Gagolewski

  5. Dept of Statis&OR and MD, Univ de Oviedo, Oviedo, Spain

    María Ángeles Gil

  6. Dept of Stoc Metds,Polish Aca of Science, Systems Res Inst, Warsaw, Poland

    Przemysław Grzegorzewski

  7. Sys Res Inti, Dept of Stoch Methods, Polish Acadmy Sci in Warsaw, Warsaw, Poland

    Olgierd Hryniewicz

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Capotorti, A., Figà-Talamanca, G. (2017). A Generalized SMART Fuzzy Disjunction of Volatility Indicators Applied to Option Pricing in a Binomial Model. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_12

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  • DOI: https://doi.org/10.1007/978-3-319-42972-4_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42971-7

  • Online ISBN: 978-3-319-42972-4

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