Alternating Direction Implicit Finite Element Method for Multi-Dimensional Black-Scholes Models

@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 – doi.org/10.4208/aamm.OA-2018-0144
UR – 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.