Abstract
A jump-diffusion model for the pricing of options leads to a partial integro-differential equation (PIDE). Discretizing the PIDE by certain method, we get a sequence of systems of linear equations, where the coefficient matrices are Toeplitz matrices. In this paper, we decompose the coefficient matrix as the sum of a tridiagonal matrix and a near low-rank matrix, and approximate the near low-rank matrix by low-rank matrices. Then we introduce a stationary iterative method for the approximate systems of linear equations. Comparison of the performance of our algorithm to that proposed in Pang et al. (Linear Algebra Appl. 434:2325–2342, 2011) is presented.
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Acknowledgments
The research was supported by the Guangdong Provincial National Science Foundation under contract No. 10151503101000023 and Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University No. 201106003. We thank the anonymous referee for providing valuable suggestions which improve the presentation of the paper and the completeness of the contents.
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Lin, FR., Yang, HX. A fast stationary iterative method for a partial integro-differential equation in pricing options. Calcolo 50, 313–327 (2013). https://doi.org/10.1007/s10092-012-0070-4
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DOI: https://doi.org/10.1007/s10092-012-0070-4
Keywords
- Partial integro-differential equation
- Polynomial interpolation
- Fast matrix–vector multiplication
- Fast approximate inversion
- Fast stationary iterative method