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Homotopy Perturbation Method for Fractional Black-Scholes European Option Pricing Equations Using Sumudu Transform

Author

Listed:
  • Asma Ali Elbeleze
  • Adem Kılıçman
  • Bachok M. Taib

Abstract

The homotopy perturbation method, Sumudu transform, and He’s polynomials are combined to obtain the solution of fractional Black-Scholes equation. The fractional derivative is considered in Caputo sense. Further, the same equation is solved by homotopy Laplace transform perturbation method. The results obtained by the two methods are in agreement. The approximate analytical solution of Black-Scholes is calculated in the form of a convergence power series with easily computable components. Some illustrative examples are presented to explain the efficiency and simplicity of the proposed method.

Suggested Citation

  • Asma Ali Elbeleze & Adem Kılıçman & Bachok M. Taib, 2013. "Homotopy Perturbation Method for Fractional Black-Scholes European Option Pricing Equations Using Sumudu Transform," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, May.
    • Handle: RePEc:hin:jnlmpe:524852
    DOI: 10.1155/2013/524852
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    Cited by:

    1. Ruyi Xing & Meng Liu & Kexin Meng & Shuli Mei, 2021. "Coupling Technique of Haar Wavelet Transform and Variational Iteration Method for a Nonlinear Option Pricing Model," Mathematics, MDPI, vol. 9(14), pages 1-15, July.
    2. 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.
    3. Fadugba, Sunday Emmanuel, 2020. "Homotopy analysis method and its applications in the valuation of European call options with time-fractional Black-Scholes equation," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    4. Agus Sugandha & Endang Rusyaman & Sukono & Ema Carnia, 2024. "Using a Mix of Finite Difference Methods and Fractional Differential Transformations to Solve Modified Black–Scholes Fractional Equations," Mathematics, MDPI, vol. 12(7), pages 1-15, April.

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