A New Algorithm to Simulate the First Exit Times of a Vector of Brownian Motions, with an Application to Finance

TL;DR

This paper introduces a novel algorithm for simulating the first exit times of multiple Brownian motions from an orthant, applicable to higher dimensions and different drift conditions, with applications in finance.

Contribution

The paper presents a new simulation method for first exit times of multidimensional Brownian motions, especially efficient when drifts are zero, extending previous techniques to higher dimensions.

Findings

Effective simulation of first exit times in higher dimensions

Simplified algorithm for zero-drift cases

Potential applications in financial modeling

Abstract

We provide a new methodology to simulate the first exit times of a vector of Brownian motions from an orthant. This new approach can be used to simulate the first exit times of dimension higher than two. When at least one Brownian motion has non-zero drift, the joint density function of the first exit times in N dimensions needs to be known, or approximated. However, when the drifts are all zero, a simpler simulation algorithm is obtained without using the joint density function.