Two high-order compact difference schemes with temporal graded meshes for time-fractional Black-Scholes equation-Reference-Cited by-同舟云学术

Two high-order compact difference schemes with temporal graded meshes for time-fractional Black-Scholes equation

Published:2023 Issue:4 Volume:18 Page:1692-1712
ISSN:1556-1801
Container-title:Networks and Heterogeneous Media
language:
Short-container-title:NHM

Author:

Gu Jie¹,Nong Lijuan²,Yi Qian²,Chen An¹

Affiliation:

1. College of Science, Guilin University of Technology, Guilin, 541004, China

2. College of Mathematics and Statistic, Guangxi Normal University, Guilin, 541004, China

Abstract

<abstract><p>In this paper, two high-order compact difference schemes with graded meshes are proposed for solving the time-fractional Black-Scholes equation. We first eliminate the convection term in the equivalent form of the considered equation by using exponential transformation, then combine the sixth-order/eighth-order compact difference method with a temporal graded meshes-based trapezoidal formulation for the temporal integral term to obtain the fully discrete high-order compact difference schemes. The stability and convergence analysis of the two proposed schemes are studied by applying Fourier analysis. Finally, the effectiveness of the proposed schemes and the correctness of the theoretical results are verified by two numerical examples.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Computer Science Applications,General Engineering,Statistics and Probability

Reference30 articles.

1. N. Abdi, H. Aminikhah, A. R. Sheikhani, High-order compact finite difference schemes for the time-fractional Black-Scholes model governing European options, Chaos Solitons Fractals, 162 (2022), 112423. https://doi.org/10.1016/j.chaos.2022.112423

2. Z. Cen, J. Huang, A. Xu, A. Le, Numerical approximation of a time-fractional Black–Scholes equation, Comput. Math. Appl., 75 (2018), 2874–2887. https://doi.org/10.1016/j.camwa.2018.01.016

3. C. M. Chen, F. Liu, I. Turner, V. Anh, A Fourier method for the fractional diffusion equation describing sub-diffusion, J. Comput. Phys., 227 (2007), 886–897. https://doi.org/10.1016/j.jcp.2007.05.012

4. W. Chen, X. Xu, S. P. Zhu, Analytically pricing double barrier options based on a time-fractional Black–Scholes equation, Comput. Math. Appl., 69 (2015), 1407–1419. https://doi.org/10.1016/j.camwa.2015.03.025

5. H. Ding, C. Li, High‐order compact difference schemes for the modified anomalous subdiffusion equation, Numer. Methods Partial Differ. Equ., 32 (2016), 213–242. https://doi.org/10.1002/num.21992

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. An Efficient Higher-Order Numerical Scheme for Solving Fractional Black-Scholes PDE Using Analytical Weights;Iranian Journal of Science;2024-02-06