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.
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Acknowledgment
This work is supported by the Fund for Less Developed Regions of the National Natural Science Foundation of China (No. 10961002); the Project Supported by State Ethnic Affairs Commission (No. 12BFZ019); Zizhu Science Foundation of Beifang University of Nationalities (No. 2011ZQY026).
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Yang, Lf., Hu, Xl. (2013). A New High-Order Compact Finite Difference Scheme for Solving Black-Scholes Equation. In: Qi, E., Shen, J., Dou, R. (eds) Proceedings of 20th International Conference on Industrial Engineering and Engineering Management. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40063-6_99
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DOI: https://doi.org/10.1007/978-3-642-40063-6_99
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