广义CEV模型下欧式未定权益的一种紧致差分格式  

A Compact Difference Scheme for European Contingent Claim in Generalized CEV Models

作　　者：胡青 孙玉东 HU Qing;SUN Yudong(Guizhou Minzu University,1.School of Data Science and Information Engineering;School of Political and Economic Management,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：《湖南工程学院学报（自然科学版）》2024年第2期43-52,共10页Journal of Hunan Institute of Engineering(Natural Science Edition)

摘　　要：针对广义CEV模型下欧式未定权益定价的问题,提出一种紧致差分格式求解方法.首先,采用Crank-Nicolson格式对时间进行半离散.其次,在时间离散的基础上,采用紧致差分格式对空间进行离散,构造一个时间2阶空间4阶精度的紧致差分格式,并且证明该格式是无条件稳定的.最后,通过数值实验验证该方法的可行性.A compact difference scheme is proposed to solve the problem of European contingent claim pricing under generalized CEV model.Firstly,the time is semi-discretized using the Crank-Nicolson scheme.Secondly,on the basis of time discretization,the space is discretized using compact differential scheme,and a compact differential scheme with time order 2 and space order 4 precision is constructed.The scheme is proved to be unconditionally stable.Finally,the feasibility of the proposed method is verified by numerical experiments.

关 键 词：广义CVE模型 欧式未定权益 CRANK-NICOLSON格式 紧致差分格式 

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