fuzzy random variable; plain vanilla option; Monte Carlo simulation

The option pricing model performance crucially depends on the ability to estimate all necessary input parameters successfully. Within the standard models of Black-Scholes type, the most important parameter is volatility. Since it is often very difficult to obtain a single number, an alternative can be to apply interval approach or more generalized fuzzy-random approach. In this paper recent knowledge of fuzzy numbers and their approximations is utilized in order to suggest fuzzy-random simulation approach to option price modeling, ie. we use fuzzy-random variables. In particular, we suggest to replace a crisp volatility parameter in the standard market model (ie. Black-Scholes type) by a fuzzy random variable, which can be easily evaluated by Monte Carlo simulation. Application possibilities are shown on illustrative examples. In particular, we evaluate the model for various input data and option types. The results are compared to the Black-Scholes option price and market option prices.