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.
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)
出处
《哈尔滨商业大学学报（自然科学版）》
CAS
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).
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
Asian options
CEV model
explicit-implicit difference scheme
implicit-explicit difference scheme
stablility
convergence
