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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-06 DOI:10.1007/s11075-024-01909-6

Saurabh Bansal, Srinivasan Natesan

引用次数: 0

Abstract

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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为欧洲和亚洲期权定价的新型高阶高效计算方法

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.