分数阶CEV模型下亚式期权的显-隐差分格式  

E-I difference schemes of Asian options under fractional-order CEV model

作　　者：龙敏 孙玉东 LONG Min;SUN Yudong(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China;School of Business,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵阳550025 [2]贵州民族大学政治与经济管理学院,贵阳550025

出　　处：《哈尔滨商业大学学报（自然科学版）》2023年第6期732-741,共10页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：贵州省教育厅青年科技人才成长项目(黔教合KY字[2016]168).

摘　　要：针对时间分数阶CEV模型下算术亚式期权定价问题,提出了一个求解该期权价格的差分方法.通过有限差分得到高精度的显式差分格式和高精度的隐式差分格式,在求奇数层时运用高精度的显式差分格式,偶数层时运用高精度的隐式差分格式,联立两个差分格式并化简即可得到显-隐差分格式,相反的做法即可得到隐-显差分格式.利用Fourier方法和数学归纳法验证其差分格式的稳定性和收敛性.通过数值模拟说明该差分格式对求解时间分数阶CEV模型下算术亚式期权是可行的.Aiming at the problem of arithmetic Asian option pricing under the time fractional CEV model,a difference method to solving the option price was proposed.A high-precision explicit difference scheme and a high-precision implicit difference scheme were obtained by finite difference.The high-precision explicit difference scheme was used in the layer,and the high-precision implicit difference scheme was used in the even-numbered layer.Combining and simplifying these two expressions yields the explicit-implicit difference scheme.The opposite method can be used to obtain the implicit-explicit difference scheme.The stablility and convergence of the difference scheme are verified by the Fourier method and mathematicalinduction.The numerical simulations showed that the difference scheme was feasible for solving fractional-order CEV model.

关 键 词：亚式期权 CEV模型 显-隐差分格式 隐-显差分格式 稳定性 收敛性 

分 类 号：O241.82[理学—计算数学]