Applications of Adaptive Fuzzy Numbers to Black-Scholes European Call Valuation - LI, Xin (2009)
The application of adaptive nonlinear fuzzy numbers to the Black-Scholes Model is proposed in this study. Due to the Fluctuation of financial market from time to time, some input parameters in the Black-Scholes formula, such as Underlying price, risk-free interest rate, volatility, cannot always be expected in the precise sense. This study aims to propose an applicable model for Black-Scholes European call option pricing in the uncertain environment, and to create a suitable program which can be used to compute the fuzzy call option values for any input data, for later use. Adaptive nonlinear fuzzy numbers are used to model uncertainty of parameters in the Black-Scholes Model. A fuzzy option value can be worked out in the form of a closed interval. The range of the intervals can vary when financial analysts or investors choose different levels of belief degree. However, after empirical analysis based on the data of NASDAQ 100 Index options, some limitations of this model has been found and further work may be required to improve the methodology.