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Coupling Technique of Haar Wavelet Transform and Variational Iteration Method for a Nonlinear Option Pricing Model

Author

Listed:
  • Ruyi Xing

    (Education Technology Center, Hebei University of Engineering, Handan 056038, China)

  • Meng Liu

    (College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, China)

  • Kexin Meng

    (College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, China)

  • Shuli Mei

    (College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, China)

Abstract

Compared with the linear Black–Scholes model, nonlinear models are constructed through taking account of more practical factors, such as transaction cost, and so it is difficult to find an exact analytical solution. Combining the Haar wavelet integration method, which can transform the partial differential equation into the system of algebraic equations, the homotopy perturbation method, which can linearize the nonlinear problems, and the variational iteration method, which can solve the large system of algebraic equations efficiently, a novel numerical method for the nonlinear Black–Scholes model is proposed in this paper. Compared with the traditional methods, it has higher efficiency and calculation precision.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1642-:d:593175
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    References listed on IDEAS

    as
    1. 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.
    2. Jian Huang & Zhongdi Cen, 2014. "Cubic Spline Method for a Generalized Black-Scholes Equation," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-7, March.
    3. Shu-Li Mei & De-Hai Zhu, 2013. "Interval Shannon Wavelet Collocation Method for Fractional Fokker-Planck Equation," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-12, December.
    4. Hassan A. Zedan & Eman Alaidarous, 2014. "Haar Wavelet Method for the System of Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, July.
    5. Umer Saeed & Mujeeb ur Rehman, 2014. "Haar Wavelet Operational Matrix Method for Fractional Oscillation Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-8, July.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    7. Li-wei Liu, 2013. "Interval Wavelet Numerical Method on Fokker-Planck Equations for Nonlinear Random System," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-7, October.
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