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Zbl 1147.91332
Wang, Song
A novel fitted finite volume method for the Black-Scholes equation governing option pricing.
(English)
[J] IMA J. Numer. Anal. 24, No. 4, 699-720 (2004). ISSN 0272-4979; ISSN 1464-3642/e

The author proposes and analyses a novel fitted volume numerical method for a degenerate partial differential equation, Black-Scholes-type equation, governing option pricing. The fitting technique is based on the idea proposed by {\it D. N. de G. Allen} and {\it R. V. Southwell} [Q. J. Mech. Appl. Math. 8, 129--145 (1955; Zbl 0064.19802)]. The author shows that the system matrix of the discretization scheme is an $M$-matrix, so that the discretization is monotonic. Then it is formulated as a Petrov-Galerkin finite element method to establish the stability of the method with respect to a discrete energy norm. Author shows that the error of the numerical solution in the energy norm is bounded by $O(h)$, where h denotes the mesh parameter. Numerical experiments are performed to demonstrate the effectiveness of the method.
[Anatoliy Swishchuk (Calgary)]
MSC 2000:
*91B28 Finance etc.
65M60 Finite numerical methods (IVP of PDE)
65M15 Error bounds (IVP of PDE)
35K65 Parabolic equations of degenerate type

Keywords: Black-Scholes equation; option pricing; fitted finite volume method; Petrov-Galerkin method; degenerate partial differential equation

Citations: Zbl 0064.19802

Cited in: Zbl 1235.91172 Zbl 1235.65114

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