A New High-Order Compact Finite Difference Scheme for Solving Black-Scholes Equation

Lu-feng Yang () and Xu-lin Hu
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Lu-feng Yang: Beifang University of Nationalities
Xu-lin Hu: Beifang University of Nationalities

A chapter in Proceedings of 20th International Conference on Industrial Engineering and Engineering Management, 2013, pp 1007-1019 from Springer

Abstract: Abstract Richardson extrapolation is a commonly used technique in financial applications for accelerating the convergence of numerical methods. In this paper an unconditionally stable high-order compact finite difference scheme is proposed for solving the Black-Scholes equation, and the convergence rate is second-order in time and fourth-order in space. Then a Richardson extrapolation algorithm develops to make the final computed solution sixth-order accurate both in time and space when the time step equals the spatial mesh size. Numerical experiments show the effectiveness of the method.

Keywords: Black-Scholes equation; High-order compact scheme; Richardson extrapolation; Unconditional stability (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-40063-6_99

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DOI: 10.1007/978-3-642-40063-6_99

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