Hitting time for Bessel processes - walk on moving spheres algorithm (WoMS)

TL;DR

This paper develops a new efficient algorithm to compute the hitting time of boundaries for Bessel processes, with applications to financial models like Cox-Ingersoll-Ross, using adapted image methods and process connections.

Contribution

It introduces a novel walk on moving spheres algorithm for Bessel processes' hitting times, applicable in finance and control problems.

Findings

Algorithm accurately estimates hitting times for Bessel processes.

Application to Cox-Ingersoll-Ross process demonstrates practical utility.

Method improves computational efficiency over existing techniques.

Abstract

In this article we investigate the hitting time of some given boundaries for Bessel processes. The main motivation comes from mathematical finance when dealing with volatility models, but the results can also be used in optimal control problems. The aim here is to construct a new and efficient algorithm in order to approach this hitting time. As an application we will consider the hitting time of a given level for the Cox-Ingersoll-Ross process. The main tools we use are on one side, an adaptation of the method of images to this particular situation and on the other side, the connection that exists between Cox-Ingersoll-Ross processes and Bessel processes.