On the exact and $\epsilon$-strong simulation of (jump) diffusions

Abstract

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.

Published at http://dx.doi.org/10.3150/14-BEJ676 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (2)

• Exact simulation of diffusions
• Simple simulation of diffusion bridges with application to likelihood inference for diffusions

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• Numerical aspects of shot noise representation of infinitely divisible laws and related processes
• Consistency of Bayesian nonparametric inference for discretely observed jump diffusions
• Unbiased simulation of rare events in continuous time
• A recursive representation for decoupling time-state dependent jumps from jump-diffusion processes