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

Alternating Direction Implicit Finite Element Method for Multi-Dimensional Black-Scholes Models
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Year:    2019

Author:    Limei Li, Alexander Lapin, Shuhua Zhang

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2018-0144

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 535–558

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Black-Scholes models finite element method semi-implicit approximation alternating direction method.

Author Details

Limei Li

Alexander Lapin

Shuhua Zhang

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