INDICES FOR FINANCIAL MARKET VOLATILITY OBTAINED THROUGH FUZZY REGRESSION

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 resort to fuzzy regression methods in order to include all the available information from option prices and obtain an informative volatility index. In fact, the obtained fuzzy volatility indices do 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 in order to select a representative value within this interval. Moreover, we investigate the occurrence of truncation and discretization errors in the volatility index computation by resorting to an interpolation-extrapolation method. We also test the forecasting power of each volatility index on future realized volatility.