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Zbl 1131.65301
Angermann, Lutz; Wang, Song
Convergence of a fitted finite volume method for the penalized Black-Scholes equation governing European and American Option pricing. (English)
[J] Numer. Math. 106, No. 1, 1-40 (2007). ISSN 0029-599X; ISSN 0945-3245/e

Summary: In this paper we present an analysis of a numerical method for a degenerate partial differential equation, called the Black-Scholes equation, governing American and European option pricing. The method is based on a fitted finite volume spatial discretization and an implicit time stepping technique. The analysis is performed within the framework of the vertical method of lines, where the spatial discretization is formulated as a Petrov-Galerkin finite element method with each basis function of the trial space being determined by a set of two-point boundary value problems. We establish the stability and an error bound for the solutions of the fully discretized system. Numerical results are presented to validate the theoretical results.

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
91B28 Finance etc.

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Zentralblatt MATH Berlin [Germany]