Valuating for European barrier options of up-and-out type with fuzzy parameters

The major purpose of this paper is to apply the fuzzy approach to analyze the valuation of European barrier options with fuzzy parameters. We mainly discuss the call and put option of up-and-out type. For a set of given fuzzy parameters, such as fuzzy interest rate, fuzzy dividend rate, fuzzy volatility rate and fuzzy stock price, we derive the fuzzy patterns of call and put European barrier option formulae. On the basis of some certain belief degrees of financial analyst, we use the trapezoidal fuzzy numbers to model the uncertain property of parameters, and corresponding to call and put option of up-and-out type, we give the computation approach of left- and right-end points of the closed interval of option price. Furthermore, we give some numerical results for some explicit parameters and belief degrees.