Fuzzy Pricing of European Options Based on Constant Elasticity of Variance Process

Abstract

Based on the assumption that the stock price follows the CEV process, this article uses fuzzy mathematics theory to discuss the price of European options. As the financial market is constantly fluctuating, the parameter of the stock price following the CEV process should not be a constant. Therefore, considering fuzzy interest rates, fuzzy stock prices, and fuzzy initial volatility, under the assumption of fuzzy parameters, the price of the obtained option is a fuzzy number. This article first derives the pricing formula for European options with stock prices following the CEV process. Then, using the theory of fuzzy mathematics, the fuzzy pricing formula for European options with stock prices following the CEV process is derived. In order to consider the membership degree of investors to a certain option price on a fuzzy number, the classic binary method is used to solve the membership degree. It indicates the value of options that investors or stock traders most hope to obtain, and finally uses fuzzy simulation algorithms in a fuzzy environment to calculate the expected value of options under different elasticity factors and iteration steps, and compares the membership degree of option value and make a simple analysis.