Bessel Processes and a Functional of Brownian Motion

Abstract

The goal of this paper is to give a concise account of the connection between Besselprocesses and the integral of geometric Brownian motion. The latter appears in thepricing of Asian options. Bessel processes are defined and some of their propertiesare given. The known expressions for the probability density function of the integralof geometric Brownian motion are stated, and other related results are given, inparticular the Geman &Y or (1993) Laplace transform for Asian option prices.