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Convergence of the mimetic finite difference and fitted mimetic finite difference method for options pricing

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  • Attipoe, David Sena
  • Tambue, Antoine

Abstract

We present in this paper two novel numerical spatial discretization techniques based on the mimetic finite difference method for a degenerated partial differential equation (PDE) in one dimension. This PDE is well known as the Black-Scholes PDE which govern option pricing. To handle the degeneracy of the PDE, a novel fitted mimetic finite difference scheme is proposed together with the standard mimetic finite difference method. The temporal discretization is performing using standard implicit scheme. Furthermore rigorous convergence proofs in appropriate normed spaces are proposed. We validate the theoretical results by presenting numerical results and simulations. Those numerical experiments show that our two novel schemes outperform the standard finite difference method and the standard fitted finite volume method in terms of accuracy.

Suggested Citation

  • Attipoe, David Sena & Tambue, Antoine, 2021. "Convergence of the mimetic finite difference and fitted mimetic finite difference method for options pricing," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    • Handle: RePEc:eee:apmaco:v:401:y:2021:i:c:s0096300321001089
    DOI: 10.1016/j.amc.2021.126060
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    References listed on IDEAS

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    1. S. Wang & X. Q. Yang & K. L. Teo, 2006. "Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation," Journal of Optimization Theory and Applications, Springer, vol. 129(2), pages 227-254, May.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Cho, Junhyun & Kim, Yejin & Lee, Sungchul, 2022. "An accurate and stable numerical method for option hedge parameters," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    2. Yury Poveshchenko & Viktoriia Podryga & Parvin Rahimly, 2022. "On Convergence of Support Operator Method Schemes for Differential Rotational Operations on Tetrahedral Meshes Applied to Magnetohydrodynamic Problems," Mathematics, MDPI, vol. 10(20), pages 1-18, October.

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