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Black–Scholes option pricing equations described by the Caputo generalized fractional derivative

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  • Fall, Aliou Niang
  • Ndiaye, Seydou Nourou
  • Sene, Ndolane

Abstract

Fractional Black–Scholes equation is a constructive financial equation. The model is used to determine the value of the option without a transaction cost. The analytical solutions of the fractional Black–Scholes equations have been addressed. The Caputo generalized fractional derivative has been used. The homotopy perturbation method has been developed for obtaining the analytical solutions of the fractional Black–Scholes equation (BSE) and the generalized fractionalBSE. The analytical solutions of the fractionalBSE and the generalized fractionalBSE have been represented graphically. The effect of the order ρ of the generalized fractional derivative in the diffusion processes has been analyzed.

Suggested Citation

  • Fall, Aliou Niang & Ndiaye, Seydou Nourou & Sene, Ndolane, 2019. "Black–Scholes option pricing equations described by the Caputo generalized fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 108-118.
    • Handle: RePEc:eee:chsofr:v:125:y:2019:i:c:p:108-118
    DOI: 10.1016/j.chaos.2019.05.024
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    References listed on IDEAS

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    Cited by:

    1. Sene, Ndolane, 2020. "Second-grade fluid model with Caputo–Liouville generalized fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    2. Jugal Mohapatra & Sudarshan Santra & Higinio Ramos, 2024. "Analytical and Numerical Solution for the Time Fractional Black-Scholes Model Under Jump-Diffusion," Computational Economics, Springer;Society for Computational Economics, vol. 63(5), pages 1853-1878, May.
    3. Sivaporn Ampun & Panumart Sawangtong, 2021. "The Approximate Analytic Solution of the Time-Fractional Black-Scholes Equation with a European Option Based on the Katugampola Fractional Derivative," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
    4. Abdi, N. & Aminikhah, H. & Sheikhani, A.H. Refahi, 2022. "High-order compact finite difference schemes for the time-fractional Black-Scholes model governing European options," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Sene, Ndolane & Abdelmalek, Karima, 2019. "Analysis of the fractional diffusion equations described by Atangana-Baleanu-Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 158-164.
    6. Akgül, Esra Karatas & Akgül, Ali & Yavuz, Mehmet, 2021. "New Illustrative Applications of Integral Transforms to Financial Models with Different Fractional Derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    7. Zhang, Lihong & Wang, Jun & Wang, Bin, 2020. "Energy market prediction with novel long short-term memory network: Case study of energy futures index volatility," Energy, Elsevier, vol. 211(C).
    8. Agus Sugandha & Endang Rusyaman & Sukono & Ema Carnia, 2023. "A New Solution to the Fractional Black–Scholes Equation Using the Daftardar-Gejji Method," Mathematics, MDPI, vol. 11(24), pages 1-25, December.

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