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.