A novel fitted finite volume method for the Black-Scholes equation governing option pricing. (English) Zbl 1147.91332

Wang, Song

IMA J. Numer. Anal. 24, No. 4, 699-720 (2004).

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 D. N. de G. Allen and 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.

Reviewer: Anatoliy Swishchuk (Calgary)

MSC:

91G20	Derivative securities (option pricing, hedging, etc.)
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
35K65	Degenerate parabolic equations

Keywords:

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

Citations:

Zbl 0064.19802