Volume 11, Issue 2
Alternating Direction Implicit Finite Element Method for Multi-Dimensional Black-Scholes Models

Limei Li, Alexander Lapin & Shuhua Zhang

Adv. Appl. Math. Mech., 11 (2019), pp. 535-558.

Published online: 2019-01

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  • 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.


  • Keywords

Black-Scholes models finite element method semi-implicit approximation alternating direction method.

  • AMS Subject Headings

65M06 65M12 65M15 65M60

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COPYRIGHT: © Global Science Press

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@Article{AAMM-11-535, author = {Limei Li, Alexander Lapin and Shuhua Zhang}, title = {Alternating Direction Implicit Finite Element Method for Multi-Dimensional Black-Scholes Models}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {2}, pages = {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.


}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0144}, url = {http://global-sci.org/intro/article_detail/aamm/12976.html} }
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