Uncertain parameters as fuzzy numbers in option pricing models

In this paper we show that the so called fuzzy--stochastic approach in financial models is an efficient way to handle the uncertainty about parameters. We show the possible applications in the option pricing models with a constant and stochastic volatility. Fuzzy numbers, extension principle, sensitivity analysis, fuzzy stochastic approach in financial models, option pricing models

Fuzzy Uncertainty in the Heston Stochastic Volatility Model

Stochastic volatility models for option pricing are suitable to explain many empirical stylized facts in financial markets. Among the other models, Heston provides a good analytical tractability because a quasi closed formula for the price of a European call option can be derived. The estimation of the Heston model parameters is nowadays a subject of on-going research; the aim of this paper is to manage uncertainty about parameters through fuzzy logic preserving the probabilistic structure of the Heston model