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

Limei Li ,  Alexander Lapin and Shuhua Zhang

10.4208/aamm.OA-2018-0144

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

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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.


  • History

Published online: 2019-01

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