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

Authors
Jeong, DaraeHa, TaeyoungKim, MyoungnyounShin, JaeminYoon, In-HanKim, Junseok
Issue Date
7월-2014
Publisher
KOREAN MATHEMATICAL SOC
Keywords
Black-Scholes equation; finite difference method; far-field boundary conditions; adaptive grid; Peclet condition
Citation
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, v.51, no.4, pp.1087 - 1100
Indexed
SCIE
SCOPUS
KCI
Journal Title
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
Volume
51
Number
4
Start Page
1087
End Page
1100
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/98022
DOI
10.4134/BKMS.2014.51.4.1087
ISSN
1015-8634
Abstract
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.
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