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Selection of shape parameter in radial basis functions for solution of time-fractional Black–Scholes models

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  • Haq, Sirajul
  • Hussain, Manzoor

Abstract

The current work aims to exploit two techniques namely: Residual Power Series method (RPSM) and collocation based meshfree method, for the solution of time-fractional Black–Scholes models with constant and variable coefficients. Firstly, using RPSM, we obtain exact solutions of the considered models and then numerical solution by meshfree method. Computer simulations are performed for three test problems of European options pricing. The simulations features excellent agreement with exact solutions. Accuracy and efficiency of the proposed numerical method is assessed via E2, E∞ and Erms error norms. Convergence of the proposed methods is also analyzed.

Suggested Citation

  • Haq, Sirajul & Hussain, Manzoor, 2018. "Selection of shape parameter in radial basis functions for solution of time-fractional Black–Scholes models," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 248-263.
    • Handle: RePEc:eee:apmaco:v:335:y:2018:i:c:p:248-263
    DOI: 10.1016/j.amc.2018.04.045
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    Cited by:

    1. S. Banihashemi & A. Ghasemifard & A. Babaei, 2024. "On the Numerical Option Pricing Methods: Fractional Black-Scholes Equations with CEV Assets," Computational Economics, Springer;Society for Computational Economics, vol. 64(3), pages 1463-1488, September.
    2. Changhong Guo & Shaomei Fang & Yong He, 2023. "Derivation and Application of Some Fractional Black–Scholes Equations Driven by Fractional G-Brownian Motion," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1681-1705, April.
    3. Hussain, Manzoor & Haq, Sirajul & Ghafoor, Abdul, 2019. "Meshless spectral method for solution of time-fractional coupled KdV equations," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 321-334.

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