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The Convergence Analysis of the Numerical Calculation to Price the Time-Fractional Black–Scholes Model

Author

Listed:
  • H. Mesgarani

    (Shahid Rajaee Teacher Training University)

  • M. Bakhshandeh

    (Shahid Rajaee Teacher Training University)

  • Y. Esmaeelzade Aghdam

    (Shahid Rajaee Teacher Training University)

  • J. F. Gómez-Aguilar

    (CONACyT-Tecnológico Nacional de México/CENIDET)

Abstract

In this paper, the approximate solution u(x, t) of the temporal fractional Black–Scholes model involving the time derivative in the Caputo sense with initial and boundary conditions has been studied. This equation has the main part in defining the European option in the financial activities. Time discretization is performed by linear interpolation with a temporally $$\tau ^{2-\alpha }$$ τ 2 - α order accuracy, and the Chebyshev collocation is based on the orthogonal polynomials used for spatial discretization. Additionally, the convergence and stability analysis of the specified methods are considered. Finally, the numerical solutions of some examples were obtained and compared with their analytical solutions that demonstrate the high accuracy and feasibility of the proposed approach.

Suggested Citation

  • H. Mesgarani & M. Bakhshandeh & Y. Esmaeelzade Aghdam & J. F. Gómez-Aguilar, 2023. "The Convergence Analysis of the Numerical Calculation to Price the Time-Fractional Black–Scholes Model," Computational Economics, Springer;Society for Computational Economics, vol. 62(4), pages 1845-1856, December.
    • Handle: RePEc:kap:compec:v:62:y:2023:i:4:d:10.1007_s10614-022-10322-x
    DOI: 10.1007/s10614-022-10322-x
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    References listed on IDEAS

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    1. Dwivedi, Kushal Dhar & Singh, Jagdev, 2021. "Numerical solution of two-dimensional fractional-order reaction advection sub-diffusion equation with finite-difference Fibonacci collocation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 38-50.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
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