| The financial options market is an extremely important part of the financial market,but there are some problems in the process of options trading.On the one hand,the short-term fluctuation of stock prices may allow operators to make huge profits from the expiration of options;on the other hand,operators may engage in behind the scenes trading,thus causing damage to corporate interests.In order to protect the interests of investors in all aspects,this paper selects the more representative Asian option pricing issues in exotic options for research.However,the settlement price of Asian options depends on the average price during the contract period,and it is difficult to understand the changes in the lognormal distribution and random variables,which will affect the calculation of the settlement price of Asian options.Based on this problem,this paper constructs two differential formats for the Asian option pricing problem.(1)A weighted difference format of order in time 2-α and order 2 in space is proposed.The right R-L discretization method is used to discretize the variables in time,the central difference method is used to discretize the variables in space,and the obtained explicit and implicit difference formats are weighted and collapsed to obtain the weighted difference format.(2)An explicit-implicit difference format of order in time 2-α and order 4 in space is proposed.The explicit difference format and the implicit difference format are cross-applied on the odd and even layers,and the explicit-implicit difference format is collated to obtain the explicit-implicit difference format.Regarding the stability and convergence of the above two differential formats,this paper uses mathematical induction and Fourier methods to analyze and demonstrate,and select appropriate model parameters to do numerical simulations by applying R software.The numerical results confirm the feasibility of the difference format for solving Asian option under the time-fractional order CEV model. |
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