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We consider the use of finite volume methods for the approximation of a parabolic variational inequality arising in financial mathematics. We show, under some regularity conditions, the convergence of the upwind implicit finite volume scheme to a weak solution of the variational inequality in a bounded domain. Some results, obtained in comparison with other methods on two dimensional cases, show that finite volume schemes can be accurate and efficient. Mathematics Subject Classification. 65M12.doi:10.1051/m2an:2006011 fatcat:ivhtb7ajrzdgbimbimk2yyvypq