时间分数阶CEV模型下算术亚式期权的加权差分格式  

Weighted format of arithmetic Asian options under time fractional CEV model

作　　者：龙敏 孙玉东 LONG Min;SUN Yu-dong(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,贵州贵阳550025 [2]贵州民族大学政治与经济管理学院,贵州贵阳550025

出　　处：《云南民族大学学报（自然科学版）》2023年第6期801-808,共8页Journal of Yunnan Minzu University: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,提出了一个加权平均的差分方法.将偏微分方程的二维空间变量降到一维,得到了CEV模型下算术亚式期权定价的偏微分方程.将显式差分格式与隐式差分格式进行加权得到加权有限差分格式,并分析该差分格式的稳定性和收敛性.通过数值模拟说明了加权有限差分方法求解时间分数阶CEV模型是可行的.Aiming at the problem of arithmetic Asian option pricing under the time fractional CEV model,a weighted average difference method is proposed.The spatial variables are reduced from two dimensions to one dimension,and the partial differential equation for arithmetic Asian option pricing under the CEV model is obtained.The explicit difference scheme and the implicit difference scheme are weighted to obtain the weighted finite difference scheme,and the stability and convergence of the difference scheme are analyzed.Finally,numerical simulation shows that the weighted finite difference method is feasible to solve the time fractional CEV model.

关 键 词：亚式期权 CEV模型 加权有限差分方法 稳定性 收敛性 

分 类 号：O241.82[理学—计算数学] F830.91[理学—数学]