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

Limei Li, Alexander Lapin & Shuhua Zhang

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

Published online: 2019-01

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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.

  • Keywords

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

  • AMS Subject Headings

65M06 65M12 65M15 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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