On the Exact Simulation of (Jump) Diffusion Bridges

TL;DR

This paper presents a method for exact simulation of (jump) diffusion bridges, enabling error-free sample path generation by leveraging recent advances in simulating finite-dimensional skeletons of these processes.

Contribution

It introduces a novel approach for exact simulation of (jump) diffusion bridges using a mathematical framework for finite-dimensional skeletons, avoiding discretisation errors.

Findings

Efficient exact simulation of (jump) diffusion bridges achieved.

Framework for simulating finite-dimensional skeletons developed.

Method reduces simulation errors compared to traditional discretisation techniques.

Abstract

In this paper we outline methodology to efficiently simulate (jump) diffusion bridge sample paths without discretisation error. We achieve this by considering the simulation of conditioned (jump) diffusion bridge sample paths in light of recent work developing a mathematical framework for simulating finite dimensional sample path skeletons (which flexibly characterise the entirety of sample paths).