## Abstract and Applied Analysis

### Adaptive Wavelet Precise Integration Method for Nonlinear Black-Scholes Model Based on Variational Iteration Method

Huahong Yan

#### Abstract

An adaptive wavelet precise integration method (WPIM) based on the variational iteration method (VIM) for Black-Scholes model is proposed. Black-Scholes model is a very useful tool on pricing options. First, an adaptive wavelet interpolation operator is constructed which can transform the nonlinear partial differential equations into a matrix ordinary differential equations. Next, VIM is developed to solve the nonlinear matrix differential equation, which is a new asymptotic analytical method for the nonlinear differential equations. Third, an adaptive precise integration method (PIM) for the system of ordinary differential equations is constructed, with which the almost exact numerical solution can be obtained. At last, the famous Black-Scholes model is taken as an example to test this new method. The numerical result shows the method's higher numerical stability and precision.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 735919, 6 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393449857

Digital Object Identifier
doi:10.1155/2013/735919

Mathematical Reviews number (MathSciNet)
MR3035311

Zentralblatt MATH identifier
1275.65072

#### Citation

Yan, Huahong. Adaptive Wavelet Precise Integration Method for Nonlinear Black-Scholes Model Based on Variational Iteration Method. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 735919, 6 pages. doi:10.1155/2013/735919. https://projecteuclid.org/euclid.aaa/1393449857

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