In this paper, we focus on the tempered subdiffusive Black-Scholes (tsB-S) model. The main part of our work consists of the finite difference (FD) method as a numerical approach to the option pricing in the considered model. We derive the governing fractional differential equation and the related weighted numerical scheme. The proposed method has $2-\alpha$ order of accuracy with respect to time where $\alpha\in(0,1)$ is the subdiffusion parameter, and $2$ with respect to space. Furthermore, we provide the stability and convergence analysis. Finally, we present some numerical results.
翻译:在本文中,我们侧重于温和的亚硬硬度黑雪球模型(tsB-S),我们工作的主要部分是有限的差异法(FD),作为在考虑的模型中选择定价的一种数字方法,我们从中得出调节的分差方程式和相关加权数字法,拟议方法的准确度为2美元到阿尔法元(0,1美元)是分射参数,在空间方面为2美元。此外,我们提供了稳定性和趋同性分析。最后,我们提出了一些数字结果。