Pricing path-dependent options in a Black-Scholes market from the distribution of homogeneous Brownian functionals

Abstract

We give some explicit formulae for the prices of two path-dependent options which combine Brownian averages and penalizations. Because these options are based on both the maximum and local time of Brownian motion, obtaining their prices necessitates some involved study of homogeneous Brownian functionals, which may be of interest in their own right.