Exact sampling of first passage event of certain symmetric Levy processes with unbounded variation

TL;DR

This paper presents a method for exact sampling of the first passage event in certain symmetric Levy processes with unbounded variation by embedding them into subordinated Brownian motions and sampling related exit and passage events.

Contribution

It introduces a novel exact sampling technique for first passage events of Levy processes with unbounded variation using Brownian motion embedding.

Findings

Exact sampling method for Levy processes with unbounded variation.

Sampling of Brownian exit times and locations is feasible and useful.

Method applicable to processes embedded in subordinated Brownian motions.

Abstract

We show that exact sampling of the first passage event can be done for a Levy process with unbounded variation, if the process can be embedded in a subordinated standard Brownian motion. By sampling a series of first exit events of the Brownian motion and first passage events of the subordinator, the first passage event of interest can be obtained. The sampling of the first exit time and pre-exit location of the Brownian motion may be of independent interest.