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Zbl 1214.91130
Cen, Zhongdi; Le, Anbo
A robust and accurate finite difference method for a generalized Black-Scholes equation. (English)
[J] J. Comput. Appl. Math. 235, No. 13, 3728-3733 (2011). ISSN 0377-0427

Summary: We present a numerical method for a generalized Black-Scholes equation, which is used for option pricing. The method is based on a central difference spatial discretization on a piecewise uniform mesh and an implicit time stepping technique. Our scheme is stable for arbitrary volatility and arbitrary interest rate, and is second-order convergent with respect to the spatial variable. Furthermore, the present paper efficiently treats the singularities of the non-smooth payoff function. Numerical results support the theoretical results.

MSC 2000:: *91G60
65M06 Finite difference methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)
65M50 Mesh generation and refinement (IVP of PDE)

Keywords: Black-Scholes equation; option valuation; singularity; central difference scheme; piecewise uniform mesh

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Zentralblatt MATH Berlin [Germany]