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 - <p style="text-align: justify;">A new numerical method is proposed and investigated for solving two- dimensional Black-Scholes option pricing model. This model is represented&nbsp; 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.</p>