A New Homotopy Transformation Method for Solving the Fuzzy Fractional Black–Scholes European Option Pricing Equations under the Concept of Granular Differentiability

The Black–Scholes option pricing model is one of the most significant achievements in modern investment science. However, many factors are constantly fluctuating actual financial market pricing, such as risk-free interest rate, stock price, underlying and security price volatility may be inaccurate real world. Therefore, it great practical significance to study fractional fuzzy model. In this paper, we proposed a reliable approximation method, Elzaki transform homotopy perturbation method (ETHPM) based on granular differentiability, solve time-fractional European equations. Firstly, function converted number horizontal membership (HMF). Secondly, specific steps ETHPM given Finally, some examples demonstrate that new approach simple, efficient, accurate. addition, solutions have been visualized at end paper.