Option price sensitivities through fuzzy numbers

The main motivation in using fuzzy numbers in finance lies in the need for modelling the uncertainty and vagueness that are implicit in many situations. However, the fuzzy approach should not be considered as a substitute for the probabilistic approach but rather as a complementary way to describe the model peculiarities. Here, we consider, in particular, the Black and Scholes model for option pricing, and we show that the fuzzification of some key parameters enables a sensitivity analysis of the option price with respect to the risk-free interest rate, the final value of the underlying stock price, the volatility, and also better forecasts (see Thavaneswaran et al. (2009) [12] for details). The sensitivities with respect to the variables of the model are represented by different letters of the Greek alphabet and they play an important role in the definition of the shape of the fuzzy option price.