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A reliable treatment of residual power series method for time-fractional Black–Scholes European option pricing equations

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  • Dubey, Ved Prakash
  • Kumar, Rajnesh
  • Kumar, Devendra

Abstract

Approximate analytical solution of a fractional Black–Scholes pricing model is much relevant due to its practical importance to financial markets. In this article, a powerful approximate iterative mathematical scheme based on residual power series (RPS) algorithm is presented to achieve the numerical results of the nonlinear time fractional Black–Scholes (BS) equations based on European options. The Caputo-type fractional derivatives are considered in the present article. The residual power series method (RPSM) developed by Arqub (2013) is the novel technique for finding the analytical Taylor series solutions of systems of linear and nonlinear ODEs and PDEs. The residual power series technique supplies the approximate analytical solutions of the problem in truncated series form using residual error concept along with given initial conditions. The numerical procedures reveal that only a few iterations are sufficient for better approximations of the solutions, which clearly exhibits the reliability and effectiveness of this iterative scheme. This article shows that the adopted scheme is quite systematic as well as computationally attractive regarding solution procedure. In addition, effects of fractional order of time derivatives on the solutions for various particular cases are also depicted through graphs.

Suggested Citation

  • Dubey, Ved Prakash & Kumar, Rajnesh & Kumar, Devendra, 2019. "A reliable treatment of residual power series method for time-fractional Black–Scholes European option pricing equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    • Handle: RePEc:eee:phsmap:v:533:y:2019:i:c:s037843711931177x
    DOI: 10.1016/j.physa.2019.122040
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    Citations

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    Cited by:

    1. Chaeyoung Lee & Soobin Kwak & Youngjin Hwang & Junseok Kim, 2023. "Accurate and Efficient Finite Difference Method for the Black–Scholes Model with No Far-Field Boundary Conditions," Computational Economics, Springer;Society for Computational Economics, vol. 61(3), pages 1207-1224, March.
    2. Muhammad Imran Liaqat & Ali Akgül & Hanaa Abu-Zinadah, 2023. "Analytical Investigation of Some Time-Fractional Black–Scholes Models by the Aboodh Residual Power Series Method," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    3. Bhatter, Sanjay & Mathur, Amit & Kumar, Devendra & Nisar, Kottakkaran Sooppy & Singh, Jagdev, 2020. "Fractional modified Kawahara equation with Mittag–Leffler law," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    4. Dubey, Ved Prakash & Singh, Jagdev & Alshehri, Ahmed M. & Dubey, Sarvesh & Kumar, Devendra, 2022. "Forecasting the behavior of fractional order Bloch equations appearing in NMR flow via a hybrid computational technique," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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