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

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

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 diffe...

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Main Authors: Ruyi Xing, Meng Liu, Kexin Meng, Shuli Mei
Format: Article
Language:English
Published: MDPI AG 2021-07-01
Series:Mathematics
Subjects:
Haar wavelet
homotopy perturbation method
variational iteration method
Black–Scholes model
Online Access:https://www.mdpi.com/2227-7390/9/14/1642
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spelling doaj-983e9ca85bbe4e4ba8d636663610987e2021-07-23T13:52:27ZengMDPI AGMathematics2227-73902021-07-0191642164210.3390/math9141642Coupling Technique of Haar Wavelet Transform and Variational Iteration Method for a Nonlinear Option Pricing ModelRuyi Xing0Meng Liu1Kexin Meng2Shuli Mei3Education Technology Center, Hebei University of Engineering, Handan 056038, ChinaCollege of Information and Electrical Engineering, China Agricultural University, Beijing 100083, ChinaCollege of Information and Electrical Engineering, China Agricultural University, Beijing 100083, ChinaCollege of Information and Electrical Engineering, China Agricultural University, Beijing 100083, ChinaCompared 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.https://www.mdpi.com/2227-7390/9/14/1642Haar wavelethomotopy perturbation methodvariational iteration methodBlack–Scholes model
collection DOAJ
language English
format Article
sources DOAJ
author Ruyi Xing
Meng Liu
Kexin Meng
Shuli Mei
spellingShingle Ruyi Xing
Meng Liu
Kexin Meng
Shuli Mei
Coupling Technique of Haar Wavelet Transform and Variational Iteration Method for a Nonlinear Option Pricing Model
Mathematics
Haar wavelet
homotopy perturbation method
variational iteration method
Black–Scholes model
author_facet Ruyi Xing
Meng Liu
Kexin Meng
Shuli Mei
author_sort Ruyi Xing
title Coupling Technique of Haar Wavelet Transform and Variational Iteration Method for a Nonlinear Option Pricing Model
title_short Coupling Technique of Haar Wavelet Transform and Variational Iteration Method for a Nonlinear Option Pricing Model
title_full Coupling Technique of Haar Wavelet Transform and Variational Iteration Method for a Nonlinear Option Pricing Model
title_fullStr Coupling Technique of Haar Wavelet Transform and Variational Iteration Method for a Nonlinear Option Pricing Model
title_full_unstemmed Coupling Technique of Haar Wavelet Transform and Variational Iteration Method for a Nonlinear Option Pricing Model
title_sort coupling technique of haar wavelet transform and variational iteration method for a nonlinear option pricing model
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-07-01
description 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.
topic Haar wavelet
homotopy perturbation method
variational iteration method
Black–Scholes model
url https://www.mdpi.com/2227-7390/9/14/1642
work_keys_str_mv AT ruyixing couplingtechniqueofhaarwavelettransformandvariationaliterationmethodforanonlinearoptionpricingmodel
AT mengliu couplingtechniqueofhaarwavelettransformandvariationaliterationmethodforanonlinearoptionpricingmodel
AT kexinmeng couplingtechniqueofhaarwavelettransformandvariationaliterationmethodforanonlinearoptionpricingmodel
AT shulimei couplingtechniqueofhaarwavelettransformandvariationaliterationmethodforanonlinearoptionpricingmodel
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