Simulation of Brownian motion at first-passage times
Zaeern A Burq, Owen D Jones
MATHEMATICS AND COMPUTERS IN SIMULATION | ELSEVIER SCIENCE BV | Published : 2008
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 δ Z for some δ > 0. Central to our method is an algorithm for the exact simulation of τ, 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. © 2007 IMACS.