AN ADAPTIVE FINITE DIFFERENCE METHOD USING FAR-FIELD BOUNDARY CONDITIONS FOR THE BLACK-SCHOLES EQUATION

被引：5

作者：

Jeong, Darae ^{[1
]}

Ha, Taeyoung ^{[2
]}

Kim, Myoungnyoun ^{[2
]}

Shin, Jaemin ^{[3
]}

Yoon, In-Han ^{[1
]}

Kim, Junseok ^{[1
]}

机构：

[1] Korea Univ, Dept Math, Seoul 136713, South Korea

[2] Natl Inst Math Sci, Div Computat Sci Math, Taejon 305811, South Korea

[3] Ewha Womans Univ, Inst Math Sci, Seoul 120750, South Korea

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2014年 / 51卷 / 04期

关键词：

Black-Scholes equation; finite difference method; far-field boundary conditions; adaptive grid; Peclet condition; OPTION VALUATION; AMERICAN;

D O I：

10.4134/BKMS.2014.51.4.1087

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present an accurate and efficient numerical method for solving the Black-Scholes equation. The method uses an adaptive grid technique which is based on a far-field boundary position and the Peclet condition. We present the algorithm for the automatic adaptive grid generation: First, we determine a priori suitable far-field boundary location using the mathematical model parameters. Second, generate the uniform fine grid around the non-smooth point of the payoff and a non-uniform grid in the remaining regions. Numerical tests are presented to demonstrate the accuracy and efficiency of the proposed method. The results show that the computational time is reduced substantially with the accuracy being maintained.

引用

页码：1087 / 1100

页数：14

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