Simulation of Brownian motion at first-passage times
We show how to simulate Brownian motion not on a regular time grid, but on a regular spatial grid. That is, when it first hits points in delta Z for some delta > 0. Central to our method is an algorithm for the exact simulation of tau, the first time Brownian motion hits +/- 1. This work is motivated by boundary hitting problems for time-changed Brownian motion, such as appear in mathematical finance when pricing barrier-options. (c) 2007 IMACS. Published by Elsevier B.V. All rights reserved.
simulation brownian motion first-passage time boundary crossing barrier-option