Research On Time Fractional Asian Option Pricing Based On High Precision Finite Difference Method

Since option trading came into being,scholars have carried out related research on option pricing.In the case of price fluctuations,Asian options are more affordable than European options and American options,and Asian options are a new type of active and representative options.It has not only practical value but also theoretical significance to study the numerical difference method of Asian options under the time-fractional Black-Scholes(B-S)model.Aiming at the problem of Asian option pricing,time 2-? order,spatial fourth order high-precision ? difference method,high-precision explicit-implicit(E-I)difference method,and high-precision implicit-explicit(I-E)difference method are proposed.They use the right Riemann-Liouville(R-L)differentiation on the time variable for discretization,and use the central difference method for discretization on the space variable.The high-precision explicit difference scheme and the highprecision implicit difference scheme of Asian options under the time fractional BlackScholes(B-S)model are obtained.First of all,through the idea of fusion calculation,the high-precision explicit difference format and the high-precision implicit difference format are weighted and averaged to obtain a high-precision ? difference method.Secondly,the high-precision explicit difference scheme is used on the odd-numbered layer and the high-precision implicit difference scheme on the even-numbered layer is used to obtain a high-precision explicit-implicit(E-I)difference method.Then,the high-precision implicit difference scheme is used on the odd-numbered layer and the high-precision explicit difference scheme on the even-numbered layer is used to obtain a high-precision implicit-explicit(I-E)difference method.Through the above methods,the difference scheme of Asian option pricing is obtained,and combined with mathematical induction and Fourier method,its stability and convergence are proved.Through numerical simulation,it is proved that it is feasible to solve Asian options.