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Indices for Financial Market Volatility Obtained Through Fuzzy Regression

Author

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  • Silvia Muzzioli

    (Department of Economics and CEFIN, University of Modena and Reggio Emilia, Viale Berengario 51, Modena 41121, Italy)

  • Luca Gambarelli

    (Department of Economics, University of Modena and Reggio Emilia, Viale Berengario 51, Modena 41121, Italy)

  • Bernard De Baets

    (KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Coupure Link 653, Ghent B-9000, Belgium)

Abstract

The measurement of volatility is of fundamental importance in finance. Standard market practice adopted for volatility estimation from option prices leads to a considerable loss of information and the introduction of an element of arbitrariness in the volatility index computation. We propose to adopt fuzzy regression methods in order to include all the available information from option prices, and to obtain an informative volatility index. In fact, the obtained fuzzy volatility indices not only offer a most possible value, but also a lower and an upper bound for the interval of possible values, providing investors with an additional source of information. We also propose a defuzzification procedure to select a representative value within this interval. Moreover, we investigate the occurrence of truncation and discretization errors in volatility index computation by adopting an interpolation-extrapolation method. We also test the forecasting power of each volatility index on future realized volatility.

Suggested Citation

  • Silvia Muzzioli & Luca Gambarelli & Bernard De Baets, 2018. "Indices for Financial Market Volatility Obtained Through Fuzzy Regression," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(06), pages 1659-1691, November.
    • Handle: RePEc:wsi:ijitdm:v:17:y:2018:i:06:n:s0219622018500335
    DOI: 10.1142/S0219622018500335
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    References listed on IDEAS

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    Cited by:

    1. Campisi, Giovanni & Muzzioli, Silvia & De Baets, Bernard, 2024. "A comparison of machine learning methods for predicting the direction of the US stock market on the basis of volatility indices," International Journal of Forecasting, Elsevier, vol. 40(3), pages 869-880.
    2. Jorge de Andrés-Sánchez, 2023. "Fuzzy Random Option Pricing in Continuous Time: A Systematic Review and an Extension of Vasicek’s Equilibrium Model of the Term Structure," Mathematics, MDPI, vol. 11(11), pages 1-21, May.
    3. Silvia Muzzioli & Luca Gambarelli & Bernard Baets, 2020. "Option implied moments obtained through fuzzy regression," Fuzzy Optimization and Decision Making, Springer, vol. 19(2), pages 211-238, June.

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