Computing option price for Levy process with fuzzy parameters

In the following paper we propose the method for option pricing based on application of stochastic analysis and theory of fuzzy numbers. The process of underlying asset trajectory belongs to a subclass of Levy processes with jumps. From practical point of view some parameters of such trajectory cannot be precisely described. Therefore, some degree of the market uncertainly has to be reflected in the description of the model itself. For example, the parameters (like interest rate, volatility) of financial market fluctuate from time to time and experts may have different opinions about such parameters. Using theory of fuzzy numbers and stochastic analysis enables us to take into account many sources of uncertainty, not only the probabilistic one. In our paper we apply the theory of Levy characteristics and present some numerical experiments based on Monte Carlo simulations. In detail, we present pricing formula for classical example of European call option.