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Finite volume methods for the valuationof American options

Published online by Cambridge University Press:  21 June 2006

Julien Berton  and
Robert Eymard
Julien Berton
Affiliation:
Université de Marne-la-Vallée, Champs-sur-Marne, 77454 Marne-la-Vallée, France. eymard@math.univ-mlv.fr
Robert Eymard
Affiliation:
Université de Marne-la-Vallée, Champs-sur-Marne, 77454 Marne-la-Vallée, France. eymard@math.univ-mlv.fr
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Abstract

We consider the use of finite volume methods for the approximation of aparabolic variational inequality arising in financial mathematics.We show, under some regularityconditions, the convergence of the upwind implicit finite volume schemeto a weak solution of the variational inequality in a bounded domain.Some results, obtained in comparison with other methodson two dimensional cases, show that finite volume schemes can be accurate and efficient.

Keywords

American optionvariational inequalityfinite volume methodconvergence of numerical scheme.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 2 , March 2006 , pp. 311 - 330
Copyright
© EDP Sciences, SMAI, 2006

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