A. Aimi, C. Guardasoni, L. Ortiz-Gracia, S. Sanfelici
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引用次数: 2
Abstract
Abstract 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.
摘要在这项工作中,傅立叶余弦级数(COS)方法与边界元方法(BEM)相结合,用于快速评估障碍期权价格。在描述了其在Black and Scholes(BS)模型中的应用后,本文的重点是将所提出的方法应用于Heston模型中的障碍选择评估,其贡献对于提高计算效率和使BEM作为蒙特卡洛(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是至关重要的。对傅立叶余弦级数展开中使用的项的数量进行了误差分析,其中误差界估计基于对数资产价格过程的特征函数。文末附有实现该技术的Matlab代码。
期刊介绍:
The highly selective international mathematical journal Computational Methods in Applied Mathematics (CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs.
CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics.
The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.