Parametrized Fuzzy Numbers for Option Pricing

The growing interest, during the last years, in the managing of risk in financial markets has involved primarily the pricing models for derivatives. However some of these models seemed to be soon unsatisfactory due to the incapability to capture the relevant stylized facts of real markets. Many attempts of fuzzy models have been recently proposed in the literature, but they either have the disadvantage of requiring a large amount of computations (e.g. constrained optimization problems) or they suffer a relative rigidity in representing and capturing the shapes of the fuzzy quantities (data and/or results). The parametrized fuzzy numbers (LU-fuzzy representation) that we have introduced recently (in L. Stefanini, L.Sorini, M.L.Guerra, Fuzzy Sets and Systems, 2006) reveal their great flexibility and simplicity to model fuzzy financial quantities and information in option pricing (and other financial applications) and to perform quickly the required fuzzy calculus. An additional important advantage is that the overestimation effect, inherent to the use of the interval fuzzy arithmetic, is completely eliminated.