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A comparative assessment of different fuzzy regression methods for volatility forecasting

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Abstract

The aim of this paper is to compare different fuzzy regression methods in the assessment of the information content on future realised volatility of option-based volatility forecasts. These methods offer a suitable tool to handle both imprecision of measurements and fuzziness of the relationship among variables. Therefore, they are particularly useful for volatility forecasting, since the variable of interest (realised volatility) is unobservable and a proxy for it is used. Moreover, measurement errors in both realised volatility and volatility forecasts may affect the regression results. We compare both the possibilistic regression method of Tanaka et al. (IEEE Trans Syst Man Cybern 12:903–907, 1982) and the least squares fuzzy regression method of Savic and Pedrycz (Fuzzy Sets Syst 39:51–63, 1991). In our case study, based on intra-daily data of the DAX-index options market, both methods have proved to have advantages and disadvantages. Overall, among the two methods, we prefer the Savic and Pedrycz (Fuzzy Sets Syst 39:51–63, 1991) method, since it contains as special case (the central line) the ordinary least squares regression, is robust to the analysis of the variables in logarithmic terms or in levels, and provides sharper results than the Tanaka et al. (IEEE Trans Syst Man Cybern 12:903–907, 1982) method.

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Acknowledgments

The authors gratefully acknowledge financial support from Fondazione Cassa di Risparmio di Modena for the project “Volatility modelling and forecasting with option prices: the proposal of a volatility index for the Italian market” and MIUR.

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Authors and Affiliations

  1. Department of Economics and CEFIN, University of Modena and Reggio Emilia, V.le Berengario 51, 41121 , Modena, Italy

    S. Muzzioli

  2. KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Ghent, Belgium

    B. De Baets

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  1. S. Muzzioli
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  2. B. De Baets
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Correspondence to S. Muzzioli.

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Muzzioli, S., De Baets, B. A comparative assessment of different fuzzy regression methods for volatility forecasting. Fuzzy Optim Decis Making 12, 433–450 (2013). https://doi.org/10.1007/s10700-013-9161-1

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