Journal of Applied Mathematics and Decision Sciences
Volume 3 (1999), Issue 1, Pages 63-73
Some applications of occupation times of Brownian motion with
drift in mathematical finance
Center of Asset Pricing and Financial Products Development, Deutsche Genossenschaftsbank Frankfurt am Main, Am Platz der Republik, Frankfurt am Main D–60325, Germany
Copyright © 1999 Andreas Pechtl. 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.
In the last few years new types of path-dependent options called corridor options
or range options have become well-known derivative instruments in European options markets.
Since the payout profiles of those options are based on occupation times of the underlying security
the purpose of this paper is to provide closed form pricing formulae of Black & Scholes type for
some significant representatives. Alternatively we demonstrate in this paper a relatively simple
derivation of the Black & Scholes price for a single corridor option – based on a static portfolio representation – which does not make use of the distribution of occupation times (of Brownian
motion). However, knowledge of occupation times' distributions is a more powerful tool.