Year: 2019
Author: Limei Li, Alexander Lapin, Shuhua Zhang
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 535–558
Abstract
A new numerical method is proposed and investigated for solving two- dimensional Black-Scholes option pricing model. This model is represented by Dirichlet initial-boundary value problem in a rectangular domain for a parabolic equation with advection-diffusion operator containing mixed derivatives. It is approximated by using a finite element method in spatial variables and alternating direction implicit (ADI) method in time variable. The ADI scheme is based on the semi-implicit approximation. The stability and convergence of the constructed scheme is proved rigorously. The provided computational results demonstrate the efficiency and high accuracy of the proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0144
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 535–558
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Black-Scholes models finite element method semi-implicit approximation alternating direction method.