时间分数阶亚式期权定价高精度的显-隐和隐-显差分方法  

The High-precision Explicit-implicit and Implicit-explicit Difference Method for Time Fractional Asian Options Pricing

作　　者：谢万姗 孙玉东 XIE Wanshan;SUN Yudong(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China;School of Political and Economic Management,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：《湖北民族大学学报（自然科学版）》2022年第2期215-225,共11页Journal of Hubei Minzu University:Natural Science Edition

基　　金：贵州省科学技术基金项目([2015]2076).

摘　　要：针对时间分数阶的算术平均亚式期权定价问题,提出了一个时间2-α阶、空间4阶高精度的显-隐式差分方法和隐-显式差分方法,并通过该方法得出了Black-Scholes模型下亚式期权定价的数值结果.并结合傅里叶方法和数学归纳法分析了差分格式的稳定性及收敛性.通过数值模拟结果说明了差分格式求解时间分数阶Black-Scholes模型下亚式期权是可行的.Aiming at the problem of time fractional arithmetic average Asian option pricing,an explicit-implicit and implicit-explicit difference method with high accuracy in time 2-αand space 4 is proposed,Through this method,the numerical results of Asian option pricing under the Black-Scholes model are obtained.By combining Fourier method and mathematical induction method,the stability and convergence of the difference scheme are analyzed.The numerical simulation shows that the difference scheme is feasible to solve the Asian options under the time fractional Black-Scholes model.

关 键 词：时间分数阶Black-Scholes模型 亚式期权 显-隐式差分格式 隐-显式差分格式 

分 类 号：F830.91[经济管理—金融学] O241.82[理学—计算数学]