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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

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

szhang@tjufe.edu.cn (Shuhua Zhang)

  • BibTex
  • RIS
  • TXT
@Article{AAMM-11-535, author = {Li , LimeiLapin , Alexander and Zhang , Shuhua}, 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} }
TY - JOUR T1 - Alternating Direction Implicit Finite Element Method for Multi-Dimensional Black-Scholes Models AU - Li , Limei AU - Lapin , Alexander AU - Zhang , Shuhua JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 535 EP - 558 PY - 2019 DA - 2019/01 SN - 11 DO - http://doi.org/10.4208/aamm.OA-2018-0144 UR - https://global-sci.org/intro/article_detail/aamm/12976.html KW - Black-Scholes models, finite element method, semi-implicit approximation, alternating direction method. AB -

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.

Limei Li, Alexander Lapin & Shuhua Zhang. (2020). Alternating Direction Implicit Finite Element Method for Multi-Dimensional Black-Scholes Models. Advances in Applied Mathematics and Mechanics. 11 (2). 535-558. doi:10.4208/aamm.OA-2018-0144
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