Lattice Boltzmann Method for the Generalized Black-Scholes Equation

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Mathematical Physics Pub Date : 2023-01-18 DOI:10.1155/2023/1812518
Fangfang Wu, Duoduo Xu, Ming-Feng Tian, Yingying Wang
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Abstract

In this paper, an efficient lattice Boltzmann model for the generalized Black-Scholes equation governing option pricing is proposed. The Black-Scholes equation is firstly equivalently transformed into an initial value problem for a partial differential equation with a source term using the variable substitution and the derivative rules, respectively. Then, applying the multiscale Chapman-Enskog expansion, the amending function is expanded to second order to recover the convective and source terms of the macroscopic equation. The D1Q3 lattice Boltzmann model with spatial second-order accuracy is constructed, and the accuracy of the established D1Q5 model is greater than second order. The numerical simulation results demonstrate the effectiveness and numerical accuracy of the proposed models and indicate that our proposed models are suitable for solving the Black-Scholes equation. The proposed lattice Boltzmann model can also be applied to a class of partial differential equations with variable coefficients and source terms.
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广义Black-Scholes方程的点阵Boltzmann方法
本文针对期权定价的广义Black-Scholes方程,提出了一个有效的格子Boltzmann模型。首先,分别使用变量代换和导数规则,将Black-Scholes方程等价地转化为具有源项的偏微分方程的初值问题。然后,应用多尺度Chapman-Enskog展开,将修正函数扩展到二阶,以恢复宏观方程的对流项和源项。建立了具有空间二阶精度的D1Q3格子Boltzmann模型,所建立的D1Q5模型的精度大于二阶。数值模拟结果证明了所提模型的有效性和数值精度,并表明所提模型适用于求解Black-Scholes方程。所提出的格子Boltzmann模型也可以应用于一类具有变系数和源项的偏微分方程。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Advances in Mathematical Physics
Advances in Mathematical Physics 数学-应用数学
CiteScore
2.40
自引率
8.30%
发文量
151
审稿时长
>12 weeks
期刊介绍: Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.
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