时间分数阶Black-Scholes方程的重心Lagrange插值配点法  

Barycentric Lagrange Interpolation Collocation Method for Time-Fractional Black-Scholes Equation

作　　者：吴哲 黄蓉 田朝薇[1] WU Zhe;HUANG Rong;TIAN Zhaowei(School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China)

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2023年第2期269-276,共8页Journal of Huaqiao University(Natural Science)

基　　金：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)。

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.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.

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 

分 类 号：O241.82[理学—计算数学]