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

Ruyi Xing, Meng Liu, Kexin Meng and Shuli Mei
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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

Mathematics, 2021, vol. 9, issue 14, 1-15

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.

Keywords: Haar wavelet; homotopy perturbation method; variational iteration method; Black–Scholes model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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