In this paper, we propose an iterative splitting method to solve the partial differential equations in option pricing problems. We focus on the Heston stochastic volatility model and the derived two-dimensional partial differential equation (PDE). We take the European option as an example and conduct numerical experiments using different boundary conditions. The iterative splitting method transforms the two-dimensional equation into two quasi one-dimensional equations with the variable on the other dimension fixed, which helps to lower the computational cost. Numerical results show that the iterative splitting method together with an artificial boundary condition (ABC) based on the method by Li and Huang (2019) gives the most accurate option price and Greeks compared to the classic finite difference method with the commonly-used boundary conditions in Heston (1993).

中文翻译：

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Heston模型下欧式期权定价的迭代分裂方法☆

在本文中，我们提出了一种迭代分裂方法来求解期权定价问题中的偏微分方程。我们专注于 Heston 随机波动率模型和导出的二维偏微分方程 (PDE)。我们以欧式期权为例，利用不同的边界条件进行数值实验。迭代分裂法将二维方程转化为两个准一维方程，另一维上的变量固定，有助于降低计算成本。