Research On Fractional Fuzzy European Option Pricing Model

The Black-Scholes option pricing model is one of the most important achievements in the financial field.However,there are many uncertainties in the real market,such as risk-free interest rate,stock price,option base price and security price volatility.Fuzzy mathematics is one of the tools to describe these uncertainties.Therefore,it is of great practical importance to study fractional fuzzy option pricing models.This paper focuses on two types of fractional fuzzy European option pricing models.Two new simple and effective algorithms are proposed for solving these two types of models,and the convergence of the algorithm and the uniqueness of the solution are proved.The problem of enterprise value assessment based on fractional fuzzy European option pricing model is studied with artificial intelligence enterprises as an example study.The main contents are as follows:(1)The Elzaki transform homotopy perturbation method fot the Type-Ⅰ fuzzy fractional Black-Scholes option pricing model is studied.Firstly,Elzaki transform and homotopy perturbation method are fused to solve the Type-Ⅰ fuzzy fractional Black-Scholes option pricing equations.Secondly,numerical results are compared and analyzed with other methods through several arithmetic examples.This method does not require the calculation of fractional order differentiation or integration and is less computationally intensive.(2)The q-homotopy analysis transform method for the interval Type-Ⅱ fuzzy fractional Black-Scholes option pricing model is studied.Firstly,consider the double fuzziness of option pricing in the actual financial market.Therefore,it is more practical to use the interval Type-Ⅱ fuzzy fractional Black-Scholes equations to model the option pricing problem.Secondly,the qhomotopy analysis transform method is designed to solve the interval Type-Ⅱ fuzzy fractional Black-Scholes equations.The convergence of the q-homotopy analysis transform method and the uniqueness of the solution are proved.The outstanding advantages of the q-homotopy analysis transform method are that it does not need linearization,perturbation and discretization,and does not depend on physical parameters.It can greatly reduce the computation time.Finally,the numerical results of the q-homotopy analysis transform method and other methods are compared and analyzed by two arithmetic examples to verify the feasibility and simplicity of the q-homotopy analysis transform method.(3)Taking artificial intelligence enterprises as a case study,the enterprise value evaluation problem integrating the income approach and the fractional fuzzy Black-Scholes real option method is investigated.Firstly,Hikvision is selected as a representative of AI enterprises and its main business,development strategy and financial situation are analyzed.Secondly,the earnings method and fractional fuzzy Black-Scholes real option method are applied to evaluate the explicit value,implicit value and overall value of Hikvision respectively.Finally,the evaluation effect is verified and the results show that the fused earnings method and fractional fuzzy Black-Scholes real option method of AI enterprise value assessment model is effective.