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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. [ABSTRACT FROM AUTHOR]

This paper models the dissolved oxygen (DO) dynamics in the Orbetello lagoon as a function of the physico-chemical and ecological system variables, including the submerged vegetation, nutrients, and hydrodynamics. It should be viewed as the concluding sequel to a previous paper describing the dynamics of the lagoon ecosystem [Giusti, E., Marsili-Libelli, S., 2006. An integrated model for the Orbetello lagoon ecosystem, Ecol. Model. 196, 379–394] by introducing the missing DO dynamics. The model considers the oxygen demand originating from the decay of carbonaceous and nitrogenous compounds, as well as photosynthesis and natural reaeration by winds and currents as the oxygen producing processes. With a fixed-parameter set the model could accurately reproduce each single circadian DO cycle, but in the long run it failed to extend this fit and could not accommodate the large DO fluctuations induced by the seasonal variability. In order to enhance the model flexibility, a fuzzy pattern recognition algorithm was designed to classify the circadian DO patterns into four typical behaviours, related to the season, and estimate the corresponding parameters, with the overall model output being a fuzzy combination of these sets. The paper discusses several methods to patch the parameter sets and compares their performance in tracking long-term DO variations. A final assessment of the model validity is obtained by incorporating the whole DO dynamics (model, fuzzy pattern recognition and parameter combination) into the general lagoon model and producing a consistently correct series of DO daily distributions over a yearly cycle. Thus the paper contains both a practical and a methodological aspect. The practical one is the linking of all the lagoon dynamics to the dissolved oxygen kinetics in order to clarify to what extent macroalgae and macrophytes influence the oxygen balance. The methodological aspect consists of extending the validity of short-term models to long time-horizons through a patching technique supported by fuzzy pattern recognition. [Copyright &y& Elsevier]