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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 735919, 6 pages
http://dx.doi.org/10.1155/2013/735919
Research Article

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

School of Accounting, Capital University of Economics and Business, 121 Zhangjialukou, Huaxiang Fengtai District, Beijing 100070, China

Received 31 December 2012; Revised 14 February 2013; Accepted 17 February 2013

Academic Editor: Lan Xu

Copyright © 2013 Huahong Yan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.