In this work, the Fourier-cosine series (COS) method has been combined with the Boundary Element Method (BEM) for a fast evaluation of barrier option prices. After a description of its use in the Black and Scholes (BS) model, the focus of the paper is on the application of the proposed methodology to the barrier option evaluation in the Heston model, where its contribution is fundamental to improve computational efficiency and to make BEM appealing among finance practitioners as a valid alternative to Monte Carlo (MC) or other more traditional approaches. An error analysis is provided on the number of terms used in the Fourier-cosine series expansion, where the error bound estimation is based on the characteristic function of the log-asset price process. A Matlab code implementing this technique is attached at the end of the paper.

中文翻译：

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Heston 模型中 COS BEM 方法的快速障碍期权定价（使用 Matlab 代码）

在这项工作中，傅里叶余弦级数 (COS) 方法已与边界元法 (BEM) 相结合，用于快速评估障碍期权价格。在描述了它在 Black and Scholes (BS) 模型中的使用之后，本文的重点是将所提出的方法应用于 Heston 模型中的障碍选项评估，其贡献对于提高计算效率和使 BEM 作为蒙特卡罗 (MC) 或其他更传统方法的有效替代方案在金融从业者中具有吸引力。对傅立叶余弦级数展开中使用的项数进行了误差分析，其中误差界限估计基于对数资产价格过程的特征函数。论文末尾附有实现该技术的 Matlab 代码。