In this paper, we focus on the tempered subdiffusive Black–Scholes model. The main part of our work consists of the finite difference method as a numerical approach to option pricing in the considered model. We derive the governing fractional differential equation and the related weighted numerical scheme. The proposed method has an accuracy order \(2-\alpha \) with respect to time, where \(\alpha \in (0,1)\) is the subdiffusion parameter and 2 with respect to space. Furthermore, we provide stability and convergence analysis. Finally, we present some numerical results.

中文翻译：

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调和的次扩散 Black-Scholes 模型

在本文中，我们重点关注调和的次扩散 Black-Scholes 模型。我们工作的主要部分包括有限差分法作为所考虑模型中期权定价的数值方法。我们推导了控制分数阶微分方程和相关的加权数值格式。该方法相对于时间的精度阶为\(2-\alpha \) ，其中\(\alpha \in (0,1)\)是次扩散参数，相对于空间的精度阶为 2。此外，我们还提供稳定性和收敛性分析。最后，我们提出一些数值结果。