Some applications of occupation times of Brownian motion with drift in mathematical finance

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.