文章基本信息

标题：An adaptive moving mesh method for a time-fractional Black–Scholes equation
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作者：Jian Huang ; Zhongdi Cen ; Jialiang Zhao 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2019
卷号：2019
期号：1
页码：1-14
DOI：10.1186/s13662-019-2453-1
出版社：Hindawi Publishing Corporation
摘要：In this paper we study the numerical method for a time-fractional Black–Scholes equation, which is used for option pricing. The solution of the fractional-order differential equation may be singular near certain domain boundaries, which leads to numerical difficulty. In order to capture the singular phenomena, a numerical method based on an adaptive moving mesh is developed. A finite difference method is used to discretize the time-fractional Black–Scholes equation and error analysis for the discretization scheme is derived. Then, an adaptive moving mesh based on an a priori error analysis is established by equidistributing monitor function. Numerical experiments support these theoretical results.
关键词：Option valuation ; Black–Scholes equation ; fractional-order derivative ; finite difference method ; adaptive moving mesh ;