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.
Fuzzy regression methods Linear programming Least squares Volatility forecasting
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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.
Britten-Jones, M., & Neuberger, A. (2000). Option prices, implied price processes, and stochastic volatility. Journal of Finance, 55(2), 839–866.CrossRefGoogle Scholar
Muzzioli, S. (2010). Option-based forecasts of volatility: an empirical study in the DAX-index options market. European Journal of Finance, 16(6), 561–586.CrossRefGoogle Scholar
Nasrabadi, M. M., Nasrabadi, E., & Nasrabadi, A. R. (2005). Fuzzy linear regression analysis: A multi objective programming approach. Applied Mathematics and Computation, 163, 245–251.MathSciNetCrossRefMATHGoogle Scholar
Omrani, H., Aabdollahzadeh, S., & Alinaghian, M. (2011). A simple and efficient goal programming model for computing of fuzzy linear regression parameters with considering outliers. Journal of Uncertain Systems, 5(1), 62–71.Google Scholar
Poon, S., & Granger, C. W. (2003). Forecasting volatility in financial markets: A review. Journal of Economic Literature, 41, 478–539.CrossRefGoogle Scholar
Sánchez, J. A., & Gómez, A. T. (2003). Estimating a term structure of interest rates for fuzzy financial pricing using fuzzy regression methods. Fuzzy Sets and Systems, 139, 313–331.MathSciNetCrossRefMATHGoogle Scholar
Sánchez, J. A., & Gómez, A. T. (2004). Estimating a fuzzy term structure of interest rates using fuzzy regression techniques. European Journal of Operational Research, 154, 804–818.CrossRefMATHGoogle Scholar