On Stability and Convergence of a Finite Difference Approximation to a Parabolic Variational Inequality Arising From American Option Valuation

Authors: Guanghui Wang ^a; Song Wang ^b

Affiliations:	^a Chinese Academy of Meteorological Sciences, Beijing, China
	^b School of Mathematics and Statistics, The University of Western Australia, Crawley, Australia

DOI: 10.1080/07362990600958952

Publication Frequency: 6 issues per year

Published in: journal

Stochastic Analysis and Applications, Volume 24, Issue 6 December 2006 , pages 1185 - 1204

Subjects: Statistics & Probability; Stochastic Models & Processes;

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Abstract

In this article we study the numerical solution of a degenerate variational inequality of parabolic type arising from the valuation of American options by a finite difference method. Stability and convergence of the finite difference method are established. Numerical results are also presented to show the effectiveness and usefulness of the discretization scheme.

Keywords: American option pricing; Complementarity problem; Degenerate parabolic PDE; Finite difference method

Mathematics Subject Classification: 6M06; 91B28; 90C33

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On Stability and Convergence of a Finite Difference Approximation to a Parabolic Variational Inequality Arising From American Option Valuation

Abstract