Faber-Schauder Wavelet Sparse Grid Approach for Option Pricing with Transactions CostReport as inadecuate




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Abstract and Applied Analysis - Volume 2014 2014, Article ID 168630, 9 pages -

Research ArticleCollege of Information and Electrical Engineering, China Agricultural University, P.O. Box 53, East Campus, 17 Qinghua Donglu Road, Haidian District, Beijing 100083, China

Received 10 February 2014; Accepted 5 April 2014; Published 28 April 2014

Academic Editor: Mohammad T. Darvishi

Copyright © 2014 Shu-Li Mei. 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

Transforming the nonlinear Black-Scholes equation into the diffusion PDE by introducing the log transform of S and can provide the most stable platform within which option prices can be evaluated. The space jump that appeared in the transformation model is suitable to be solved by the sparse grid approach. An adaptive sparse approximation solution of the nonlinear second-order PDEs was constructed using Faber-Schauder wavelet function and the corresponding multiscale analysis theory. First, we construct the multiscale wavelet interpolation operator based on the definition of interpolation wavelet theory. The operator can be used to discretize the weak solution function of the nonlinear second-order PDEs. Second, using the couple technique of the variational iteration method VIM and the precision integration method, the sparse approximation solution of the nonlinear partial differential equations can be obtained. The method is tested on three classical nonlinear option pricing models such as Leland model, Barles-Soner model, and risk adjusted pricing methodology. The solutions are compared with the finite difference method. The present results indicate that the method is competitive.





Author: Shu-Li Mei

Source: https://www.hindawi.com/



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