A robust and accurate finite difference method for a generalized Black-Scholes equation

作者：Cen Zhongdi^*; Le Anbo

来源：Journal of Computational and Applied Mathematics, 2011, 235(13): 3728-3733.

DOI：10.1016/j.cam.2011.01.018

• Black-Scholes equation
• Option valuation
• Singularity
• Central difference scheme
• Piecewise uniform mesh

In this paper 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.

• 出版日期2011-5-1
• 单位浙江万里学院