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On the exact and e-strong simulation of (jump) diffusions

Lookup NU author(s): Dr Murray Pollock

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Abstract

© 2016 ISI/BS.This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any finite collection of time points. Within this framework we extend existing exact algorithms and introduce novel adaptive approaches. We consider an application of the methodology developed within this paper which allows the simulation of upper and lower bounding processes which almost surely constrain (jump) diffusion sample paths to any specified tolerance. We demonstrate the efficacy of our approach by showing that with finite computation it is possible to determine whether or not sample paths cross various irregular barriers, simulate to any specified tolerance the first hitting time of the irregular barrier and simulate killed diffusion sample paths.

Publication metadata

Author(s): Pollock M, Johansen AM, Roberts GO

Publication type: Article

Publication status: Published

Journal: Bernoulli

Year: 2016

Volume: 22

Issue: 2

Pages: 794-856

Print publication date: 01/05/2016

Online publication date: 09/11/2015

Acceptance date: 30/04/2014

ISSN (print): 1350-7265

Publisher: International Statistical Institute

URL: http://doi.org/10.3150/14-BEJ676

DOI: 10.3150/14-BEJ676

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