Table of Contents
ISRN Applied Mathematics
Volume 2011 (2011), Article ID 120253, 22 pages
http://dx.doi.org/10.5402/2011/120253
Research Article

Some Sequential Boundary Crossing Results for Geometric Brownian Motion and Their Applications in Financial Engineering

Laboratoire Thema, Université de Cergy-Pontoise, 33 boulevard du port, 95011 Cergy-Pontoise Cedex, France

Received 21 March 2011; Accepted 12 April 2011

Academic Editors: L. Ju and M. Skliar

Copyright © 2011 Tristan Guillaume. 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

This paper provides new explicit results for some boundary crossing distributions in a multidimensional geometric Brownian motion framework when the boundary is a piecewise constant function of time. Among their various possible applications, they enable accurate and efficient analytical valuation of a large number of option contracts traded in the financial markets belonging to the classes of barrier and look-back options.