On exact sampling of the first passage event of Levy process with infinite Levy measure and bounded variation

TL;DR

This paper introduces an exact sampling method for the first passage event of Levy processes with infinite Levy measure and bounded variation, using embedding techniques and novel distributional properties.

Contribution

It develops a new exact sampling approach for Levy processes with infinite Levy measure, including procedures for subordinators and bounded variation processes.

Findings

Sampling method works for a wide class of Levy measures

Provides explicit procedures for processes crossing boundaries

Applicable to processes with infinite Levy measure and bounded variation

Abstract

We present an exact sampling method for the first passage event of a Levy process. The idea is to embed the process into another one whose first passage event can be sampled exactly, and then recover the part belonging to the former from the latter. The method is based on several distributional properties that appear to be new. We obtain general procedures to sample the first passage event of a subordinator across a regular non-increasing boundary, and that of a process with infinite Levy measure, bounded variation, and suitable drift across a constant level or interval. We give examples of application to a rather wide variety of Levy measures.