Efficient Variations of the Fourier Transform in Applications to Option Pricing

IF 0.8 4区经济学 Q4 BUSINESS, FINANCE

Journal of Computational Finance Pub Date : 2014-12-19 DOI:10.21314/JCF.2014.277

S. Boyarchenko, S. Levendorskii

引用次数: 39

Abstract

In this paper, we clarify the relationships among popular methods for pricing European options based on the Fourier expansion of the payoff function (iFT method) and the simlified trapezoid rule. We suggest new variations that allow us to decrease the number of terms by a factor of between five and ten (when the iFT requires several dozen terms), or even by a factor of several dozen or a hundred (when the iFT may need thousands or millions of terms). We also give efficient recommendations for an (approximately) optimal choice of parameters for each numerical scheme.

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傅立叶变换的有效变换在期权定价中的应用

本文基于支付函数的傅立叶展开法(iFT法)和简化梯形法则，阐明了欧式期权定价常用方法之间的关系。我们建议新的变化，允许我们将术语的数量减少5到10倍(当iFT需要几十个术语时)，或者甚至减少几十或100倍(当iFT可能需要数千或数百万个术语时)。我们还对每个数值格式的参数(近似)最优选择给出了有效的建议。

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

Journal of Computational Finance BUSINESS, FINANCE-

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： The Journal of Computational Finance is an international peer-reviewed journal dedicated to advancing knowledge in the area of financial mathematics. The journal is focused on the measurement, management and analysis of financial risk, and provides detailed insight into numerical and computational techniques in the pricing, hedging and risk management of financial instruments. The journal welcomes papers dealing with innovative computational techniques in the following areas: Numerical solutions of pricing equations: finite differences, finite elements, and spectral techniques in one and multiple dimensions. Simulation approaches in pricing and risk management: advances in Monte Carlo and quasi-Monte Carlo methodologies; new strategies for market factors simulation. Optimization techniques in hedging and risk management. Fundamental numerical analysis relevant to finance: effect of boundary treatments on accuracy; new discretization of time-series analysis. Developments in free-boundary problems in finance: alternative ways and numerical implications in American option pricing.