Proper Orthogonal Decomposition for Pricing Options

IF 0.8 4区经济学 Q4 BUSINESS, FINANCE

Journal of Computational Finance Pub Date : 2012-09-01 DOI:10.21314/JCF.2012.246

O. Pironneau

引用次数: 7

Abstract

In a paper that appeared in volume 2 (2011) of SIAM Financial Mathematics by R. Cont, N. Lantos and the author, it was shown that by writing the solution of the Black-Scholes partial dierential equation on a small set of basis functions the computing time can be dramatically reduced. In this study we show that it is in fact a P.O.D. method and in some other variable it is also a spectral method. It allows us to nd a good preconditioning matrix to minimize the ill conditioned linear system, and even have explicit solutions.

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定价期权的适当正交分解

R. Cont, N. Lantos和作者在SIAM金融数学第2卷(2011)中发表的一篇论文表明，通过在一小组基函数上写出Black-Scholes偏微分方程的解可以大大减少计算时间。在这项研究中，我们表明它实际上是一种P.O.D.方法，在某些其他变量中，它也是一种谱方法。它允许我们找到一个好的预处理矩阵来最小化病态线性系统，甚至有显式解。

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.