Table of Contents
ISRN Probability and Statistics
Volume 2012 (2012), Article ID 946415, 37 pages
http://dx.doi.org/10.5402/2012/946415
Research Article

Efficient Hedging of Options with Probabilistic Haar Wavelets

1Departamento de Matemática, Universidade Estadual de Campinas, 13.081-97 Campinas, SP, Brazil
2Department of Mathematics, Ryerson University, 350 Victoria Street, Toronto, ON, Canada M5B 2K3
3Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, 7600 Mar del Plata, Argentina

Received 29 March 2012; Accepted 19 April 2012

Academic Editors: M. Galea, J. Hu, and P. E. Jorgensen

Copyright © 2012 Pedro José Catuogno et al. 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

The paper brings forward the issue of efficient representations of financial claims; in particular it addresses the problem of large transaction costs in hedging replications. Inspired by the localized properties of wavelets basis, Haar systems associated with space-time discretizations of continuous stochastic processes are proposed as a means to address the issue of efficient pathwise approximation. Theoretical developments are presented that justify the use of these approximations to construct self-financing portfolios by means of binary options. Upper bounds on the volume of transactions required to implement these portfolios are then established to illustrate the quality of the proposed approximations. The approach is applicable to general financial claims of European type, including path-dependent ones, for continuous underlying processes. Several numerical results and comparisons with delta hedging are also presented.