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Numerical solution of time-fractional Black–Scholes equation

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Abstract

In this paper we present a numerical method for a time-fractional Black–Scholes equation, which is used for modeling the fractional structure of the financial market. The method is based on—first, discretization in time and then the weighted finite difference spatial approximation. Some properties of the spatial discretization are studied. The main difficulty (that originates from the non-local structure of the differential operator) of the algorithm is the impossibility to advance layer by layer in time. Numerical experiments are discussed.

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Acknowledgments

The authors are grateful to the anonymous referees for their fruitful comments that improved the content of this manuscript. This research was supported by the European Union under Grant Agreement number 304617 (FP7 Marie Curie Action Project Multi-ITN STRIKE—Novel Methods in Computational Finance) and Bulgarian National Fund of Science under Project I02/20-2014.

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Authors and Affiliations

  1. Department of Mathematics, Ruse University, 8 Studentska St., 7017, Ruse, Bulgaria

    Miglena N. Koleva

  2. Department of Numerical Methods and Statistics, Ruse University, 8 Studentska St., 7017, Ruse, Bulgaria

    Lubin G. Vulkov

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  1. Miglena N. Koleva
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  2. Lubin G. Vulkov
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Correspondence to Miglena N. Koleva.

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Communicated by Jorge Zubelli.

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Koleva, M.N., Vulkov, L.G. Numerical solution of time-fractional Black–Scholes equation. Comp. Appl. Math. 36, 1699–1715 (2017). https://doi.org/10.1007/s40314-016-0330-z

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  • DOI: https://doi.org/10.1007/s40314-016-0330-z

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