Comparing Some Simulation Strategies for First Passage Times of Time-Changed Brownian Motion

Abstract

The first passage time of a time-changed Brownian motion through a given boundary is investigated by means of three simulation methods. The time-changed process is constructed by composing the Brownian motion with the inverse of an α-stable subordinator process. We implement a path simulation algorithm and two variants of the hazard rate simulation algorithm. The two variants are based on different expressions for the hazard rate of the time-changed process. Results obtained by applying the different strategies are graphically compared and discussed