求解时间分数阶B-S模型的高阶MQ拟插值方法

数学物理学报 ›› 2022, Vol. 42 ›› Issue (5): 1496-1505.

求解时间分数阶B-S模型的高阶MQ拟插值方法

张胜良*(),黄俊贤

^{南京林业大学经济管理学院南京 210037}

收稿日期:2021-09-08 出版日期:2022-10-26 发布日期:2022-09-30
通讯作者: 张胜良 E-mail:10110180035@fudan.edu.cn
基金资助:
教育部人文社会科学基金(21YJC790162);江苏省社科基金“双碳”目标下苏北杨树产业碳汇价值实现机制及支持政策研究(22EYBo10)

A High Order MQ Quasi-Interpolation Method for Time Fractional Black-Scholes Model

Shengliang Zhang*(),Junxian Huang

^{Department of Applied Economics, College of Economics and Management, Nanjing Forestry University, Nanjing 210037}

Received:2021-09-08 Online:2022-10-26 Published:2022-09-30
Contact: Shengliang Zhang E-mail:10110180035@fudan.edu.cn
Supported by:
the(21YJC790162);the Jiangsu Provincial Social Science Foundation(22EYBo10)

摘要/Abstract

摘要：

拟插值是一种具有保形性的高精度无网格逼近方法，在工程上经常被用到.基于三阶multiquadric (MQ)拟插值，该文提出了一个求解时间分数阶Black-Scholes (B-S)模型的无网格数值方法，并讨论了该方法的稳定性和收敛性.数值结果表明，该方法具有高阶精度，对非均匀节点具有较好的实现能力.

关键词: MQ拟插值, B-S模型, 期权定价, 分数阶

Abstract:

In this paper, Quasi-interpolation is a kind of high accurate meshless approximation method with shape-preserving property, which is often used in engineering. Based on cubic multiquadric (MQ) quasi-interpolation method, this paper proposes a novel meshless numerical scheme for time fractional Black-Scholes (B-S) model. The stability and convergence of the method are given. Numerical simulation shows that the method has high-order accuracy and is easy to be implemented for the nonuniform knots.

Key words: Multiquadric quasi-interpolation, Black-Scholes model, Option pricing, Fractional order

中图分类号:

O174

张胜良,黄俊贤. 求解时间分数阶B-S模型的高阶MQ拟插值方法[J]. 数学物理学报, 2022, 42(5): 1496-1505.

Shengliang Zhang,Junxian Huang. A High Order MQ Quasi-Interpolation Method for Time Fractional Black-Scholes Model[J]. Acta mathematica scientia,Series A, 2022, 42(5): 1496-1505.

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