[1]吴哲,黄蓉,田朝薇.时间分数阶Black-Scholes方程的重心Lagrange插值配点法[J].华侨大学学报(自然科学版),2023,44(2):269-276.[doi:10.11830/ISSN.1000-5013.202211022]
　WU Zhe,HUANG Rong,TIAN Zhaowei.Barycentric Lagrange Interpolation Collocation Method for Time-Fractional Black-Scholes Equation[J].Journal of Huaqiao University(Natural Science),2023,44(2):269-276.[doi:10.11830/ISSN.1000-5013.202211022]
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时间分数阶Black-Scholes方程的重心Lagrange插值配点法()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第44卷
期数:
2023年第2期
页码:
269-276
栏目:
出版日期:
2023-03-14

文章信息/Info

Title:
Barycentric Lagrange Interpolation Collocation Method for Time-Fractional Black-Scholes Equation
文章编号:
1000-5013(2023)02-0269-08
作者:
吴哲;  黄蓉;  田朝薇
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
WU Zhe;  HUANG Rong;  TIAN Zhaowei
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
Caputo型分数阶导数;  Black-Scholes 方程;  Laplace变换;  重心Lagrange插值配点法
Keywords:
Caputo-type fractional order derivative;  Black-Scholes equation;  Laplace transformation;  barycentric Lagrange interpolation collocation method
分类号:
O241.82
DOI:
10.11830/ISSN.1000-5013.202211022
文献标志码:
A
摘要:
针对欧式期权定价的时间分数阶Black-Scholes模型,设计一种重心Lagrange插值配点法格式.首先,采用Laplace变换近似Caputo型分数阶导数,将分数阶方程转化为整数阶方程;然后,在时-空方向上均采用重心Lagrange插值配点法进行离散,构造重心Lagrange插值配点法格式.结果表明:时间分数阶Black-Scholes方程的重心Lagrange插值配点法具有高精度和有效性.
Abstract:
The barycentric Lagrange interpolation collocation method scheme is designed for European option pricing time-fractional order Black-Scholes model. Firstly, Laplace transform is used to approximate Caputo-type fractional order derivative, and the fractional equation is transformed into an integer order equation. Then, barycentric Lagrange interpolation collocation method is used to discretize in both time and space directions, and barycentric Lagrange interpolation collocation method scheme is constructed. The results show that the barycentric Lagrange interpolation collocation method for time-fractional order Black-Scholes equation has high accuracy and effectiveness.

参考文献/References:

[1] BLACK F,SCHOLES M.The pricing of options and corporate liabilities[J].Journal of Political Economy,1973,81(3):637-654.DOI:10.1086/260062.
[2] MANDELBROT B.The variation of certain speculative prices[J].Journal of Business,1963,36(4):394-419.DOI:10.1142/9789814566926_0003.
[3] MESGARANI H,BEIRANVAND A,AGHDAM Y E.The impact of the Chebyshev collocation method on solutions of the time-fractional Black-Scholes[J].Mathematical Sciences,2021,15(2):137-143.DOI:10.1007/s40096-020-00357-2.
[4] AN Xingyu,LIU Fawang,ZHENG Minling,et al.A space-time spectral method for time-fractional Black-Scholes equation[J].Applied Numerical Mathematics,2021,165:152-166.DOI:10.1016/j.apnum.2021.02.009.
[5] SHE Mianfu,LI Lili,TANG Renxuan,et al.A novel numerical scheme for a time fractional Black-Scholes equation[J].Journal of Applied Mathematics and Computing,2021,66(1/2):853-870.DOI:10.1007/s12190-020-01467-9.
[6] TIAN Zhaowei,ZHAI Shuying,WENG Zhifeng.A compact quadratic spline collocation method for the time-fractional Black-Scholes model[J].Journal of Applied Mathematics and Computation,2021,66(1/2):327-350.DOI:10.1007/s12190-020-01439-z.
[7] 张俊良,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.DOI:1003-3998(2022)05-1496-10.
[8] REN Jincheng,SUN Zhizhong,DAI Weizhong.New approximations for solving the Caputo-type fractional partial differential equations[J].Applied Mathematical Modeling,2016,40(4):2625-2636.DOI:10.1016/j,apm.2015.10.011.
[9] 汪精英,邓杨芳,翟术英.利用Lapalce变换求解分数阶 Allen-Cahn方程[J].华侨大学学报(自然科学版),2020,41(4):549-554.DOI:10.11830/ISSN.1000-5013.201910013.
[10] 虎小燕,韩惠丽.重心插值配点法求解分数阶Fredholm积分方程[J].郑州大学学报(理学版),2017,49(1):17-23.DOI:10.13705/j.issn.1671-6841.2016203.
[11] 翁智峰,姚泽丰,赖淑琴.重心插值配点法求解 Allen Cahn方程[J].华侨大学学报(自然科学版),2019,40(1):133-140.DOI:10.11830/ISSN.1000-5013.201806043.
[12] 黄蓉,翁智峰.时间分数阶Allen-Cahn方程的重心插值配点法[J].华侨大学学报(自然科学版).2022,43(4):553-560.DOI:10.11830/ISSN.1000-5013.202104060.
[13] 王兆清,徐子康.基于平面问题的位移压力混合配点法[J].计算物理,2018,35(1):77-86.DOI:10.19596/j.cnki.1001246x.7585.
[14] ZHANG H M,LIU F W,TURNER I,et al.Numerical solution of the time fractional Black-Scholes model governing European options[J].Computers and Mathematics with Applications,2016,71(9):1772-1783.DOI:10.1016/j.camwa.2016.02.007.
[15] LIAO Wenyuan.A compact high-order finite difference method for unsteady convection-diffusion equation[J].International Journal for Computational Methods in Engineering Science and Mechanics,2012,13(3):135-145.DOI:10.1080/15502287.2012.660227.
[16] YI Shichao,YAO Linquan.A steady barycentric Lagrange interpolation method for the 2D higher-order time-fractional telegraph equation with nonlocal boundary condition with error analysis[J].Numerical Methods for Partial Equations,2019,35(5):1694-1716.DOI:10.1002/num.22371.

备注/Memo

备注/Memo:
收稿日期: 2022-11-28
通信作者: 田朝薇(1977-),女,副教授,主要从事偏微分数值计算的研究.E-mail:tzhw@hqu.edu.cn.
基金项目: 福建省自然科学基金面上资助项目(2022J01308); 中央高校基本科研业务费专项基金资助项目(ZQN702)
更新日期/Last Update: 2023-03-20