A robust and accurate finite difference method for a generalized Black-Scholes equation |
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Authors: | Zhongdi Cen Anbo Le |
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Institution: | Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, Zhejiang, PR China |
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Abstract: | 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. |
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Keywords: | 65M06 65M12 65M50 |
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