European option pricing under fuzzy environments

The application of fuzzy sets theory to the Black-Scholes formula is proposed in this article. Owing to the vague fluctuation of financial markets from time to Lime. the risk-free interest rate. volatility, and the price of underlying assets may occur imprecisely. In this case, it is natural to consider the fuzzy interest rate, fuzzy volatility, and fuzzy stock price. The form of "Resolution Identity" in fuzzy sets theory will be invoked to propose the fuzzy price of European options. Under these assumptions, the European option price at time t will turn into a fuzzy number. This will allow a financial analyst to choose the European price at his (her) acceptable degree of belief. To obtain the belief degree, the optimization problems have to be solved. (C) 2005 Wiley Periodicals, Inc.