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Projection and Contraction Method for the Valuation of American Options

Published online by Cambridge University Press:  06 March 2015

Haiming Song  and
Ran Zhang
Haiming Song
Affiliation:
Department of Mathematics, Jilin University, Changchun, 130012, P. R. China
Ran Zhang*
Affiliation:
Department of Mathematics, Jilin University, Changchun, 130012, P. R. China
*
*Corresponding author. Email addresses: songhm11@mails.jlu.edu.cn (H. Song), zhangran@jlu.edu.cn (R. Zhang)
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Abstract

An efficient numerical method is proposed for the valuation of American options via the Black-Scholes variational inequality. A far field boundary condition is employed to truncate the unbounded domain problem to produce the bounded domain problem with the associated variational inequality, to which our finite element method is applied. We prove that the matrix involved in the finite element method is symmetric and positive definite, and solve the discretized variational inequality by the projection and contraction method. Numerical experiments are conducted that demonstrate the superior performance of our method, in comparison with earlier methods.

Keywords

35A3590A0965K1065M1265M60American optionBlack-Scholes variational inequalityfinite element methodprojectioncontraction method
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 5 , Issue 1 , February 2015 , pp. 48 - 60
Copyright
Copyright © Global-Science Press 2015 

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