次扩散Black-Scholes模型下欧式期权的一种紧致差分格式  

A Compact Difference Scheme for European Options Under Sub-diffusion Black-Scholes Model

作　　者：邓乙阳 孙玉东 DENG Yiyang;SUN Yudong(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China;School of Politics and Economics 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)》2025年第1期119-125,共7页Journal of Hubei Minzu University:Natural Science 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：为解决传统布莱克-斯科尔斯(Black-Scholes, B-S)模型在低流动性市场中的局限性,利用次扩散B-S模型对市场动态进行了更为准确的刻画。首先,简单介绍次扩散B-S模型的基本概念,并给出了次扩散B-S模型下欧式看涨期权的偏微分方程;其次,模型通过Caputo导数离散化时间,采用4阶紧致差分格式离散化空间,构建了时间(2-α)阶、空间4阶精度的紧致差分格式;再次,运用傅里叶分析法和数学归纳法验证了该方法的稳定性与收敛性;最后,通过R语言模拟给出的数值结果,并分析了变量参数对期权价格的影响。结果表明,次扩散B-S模型下紧致差分法的欧式期权定价合理且有效,通过数值实验证实了其可行性。该模型的建立为期权的定价问题提供了参考。To address the limitations of the traditional Black-Scholes(B-S)model in illiquid markets,the subdiffusive B-S model was used to portray the market dynamics more accurately.Initially,the basic concept of the subdiffusive B-S model was briefly introduced,and the partial differential equation for European call options within this model was provided.Subsequently,time was discretized by the model through the Caputo derivative and space was discretized using a 4-order compact difference scheme by the model,and a compact difference scheme with time(2-α)-order and spatial 4-order accuracy was constructed.Thereafter,the stability and convergence of the method were verified using Fourier analysis and mathematical induction.Finally,the numerical results were simulated using R language,and the impact of variable parameters on option prices was analyzed.The results indicated that the European option pricing under the subdiffusive B-S model using the compact difference method was reasonable and effective,and its feasibility was confirmed through numerical experiments.A reference for option pricing issue was provided by the establishment of this model.

关 键 词：稳定性 收敛性 期权定价 几何布朗运动 CAPUTO导数 

分 类 号：O241.82[理学—计算数学] F830.91[理学—数学]