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Option implied moments obtained through fuzzy regression

Author

Listed:
  • Silvia Muzzioli

    (University of Modena and Reggio Emilia)

  • Luca Gambarelli

    (University of Modena and Reggio Emilia)

  • Bernard Baets

    (Ghent University)

Abstract

The aim of this paper is to investigate the potential of fuzzy regression methods for computing more reliable estimates of higher-order moments of the risk-neutral distribution. We improve upon the formula of Bakshi et al. (RFS 16(1):101–143, 2003), which is used for the computation of market volatility and skewness indices (such as the VIX and the SKEW indices traded on the Chicago Board Options Exchange), through the use of fuzzy regression methods. In particular, we use the possibilistic regression method of Tanaka, Uejima and Asai, the least squares fuzzy regression method of Savic and Pedrycz and the hybrid method of Ishibuchi and Nii. We compare the fuzzy moments with those obtained by the standard methodology, based on the Bakshi et al. (2003) formula, which relies on an ex-ante choice of the option prices to be used and cubic spline interpolation. We evaluate the quality of the obtained moments by assessing their forecasting power on future realized moments. We compare the competing forecasts by using both the Model Confidence Set and Mincer–Zarnowitz regressions. We find that the forecasts for skewness and kurtosis obtained using fuzzy regression methods are closer to the subsequently realized moments than those provided by the standard methodology. In particular, the lower bound of the fuzzy moments obtained using the Savic and Pedrycz method is the best ones. The results are important for investors and policy makers who can rely on fuzzy regression methods to get a more reliable forecast for skewness and kurtosis.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:fuzodm:v:19:y:2020:i:2:d:10.1007_s10700-020-09316-x
    DOI: 10.1007/s10700-020-09316-x
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    References listed on IDEAS

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    2. Jorge De Andrés-Sánchez, 2024. "Calculating Insurance Claim Reserves with an Intuitionistic Fuzzy Chain-Ladder Method," Mathematics, MDPI, vol. 12(6), pages 1-24, March.

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