为欧洲和亚洲期权定价的新型高阶高效计算方法

IF 1.7 3区 数学 Q2 MATHEMATICS, APPLIED Numerical Algorithms Pub Date : 2024-08-06 DOI:10.1007/s11075-024-01909-6
Saurabh Bansal, Srinivasan Natesan
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引用次数: 0

摘要

本文提出了一种四阶精确数值方法,用于求解描述欧洲和亚洲期权的广义 Black-Scholes PDE。首先,我们采用 Crank-Nicolson 方案对时间导数进行离散化,然后在均匀网格上采用中心差分方案对所得到的半离散问题进行离散化。为了提高所提方案的收敛阶次,我们采用了 Richardson 外推法,通过使用两个不同的网格来求解完全离散问题。对稳定性和收敛性进行了研究。为了验证所提出的技术,我们进行了几次数值实验。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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A novel higher-order efficient computational method for pricing European and Asian options

In this article, we present a fourth-order accurate numerical method for solving generalized Black-Scholes PDE describing European and Asian options. Initially, we discretize the time derivative by the Crank-Nicolson scheme, and then the resultant semi-discrete problem by the central difference scheme on uniform meshes. In order to enhance the order of convergence of the proposed scheme, we employ the Richardson extrapolation method, by using two different meshes to solve the fully discrete problem. The stability and convergence are studied. To validate the proposed technique, several numerical experiments are carried out.

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来源期刊
Numerical Algorithms
Numerical Algorithms 数学-应用数学
CiteScore
4.00
自引率
9.50%
发文量
201
审稿时长
9 months
期刊介绍: The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.
期刊最新文献
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