Pricing European options based on the fuzzy pattern of BlackScholes formula
The application of fuzzy sets theory to the BlackScholes formula is proposed in this paper. Owing to the fluctuation of financial market from time to time, some input parameters in the BlackScholes formula cannot always be expected in the precise sense. Therefore, it is natural to consider the fuzzy interest rate, fuzzy volatility and fuzzy stock price. The fuzzy pattern of BlackScholes formula and putcall parity relationship are then proposed in this paper. Under these assumptions, the European option price will turn into a fuzzy number. This makes the financial analyst who can pick any European option price with an acceptable belief degree for the later use. In order to obtain the belief degree, an optimization problem has to be solved.
blackscholes formula putcall parity fuzzy numbers optimization european call option european put option fuzzy random variables