Fuzzy Option Value with Stochastic Volatility Models

Uncertainty and vagueness play a central role in financial models and fuzzy numbers can be a profitable way to manage them. In this paper we generalize the Black and Scholes option valuation model (with constant volatility) to the framework of a volatility supposed to vary in a stochastic way. The models we take under consideration belongs to the main classes of stochastic volatility models: the endogenous and the exogenous source of risk. Fuzzy calculus for financial applications requires massive computations and when a good parametric representation for fuzzy numbers is adopted, then the arithmetic operations and fuzzy calculus can be efficiently managed. Good in this context means that the shape of the resulting fuzzy numbers can be observed and studied in order to state fundamental properties of the model.