Exact simulation of gamma-driven Ornstein–Uhlenbeck processes with finite and infinite activity jumps

Qu, Yan, Dassios, Angelos ORCID: 0000-0002-3968-2366 and Zhao, Hongbiao (2019) Exact simulation of gamma-driven Ornstein–Uhlenbeck processes with finite and infinite activity jumps. Journal of the Operational Research Society. ISSN 0160-5682

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Abstract

We develop a distributional decomposition approach for exactly simulating two types of Gamma-driven Ornstein–Uhlenbeck (OU) processes with time-varying marginal distributions: the Gamma-OU process and the OU-Gamma process. The former has finite-activity jumps, and its marginal distribution is asymptotically Gamma; the latter has infinite-activity jumps that are driven by a Gamma process. We prove that the transition distributions of the two processes at any given time can be exactly decomposed into simple elements: at any given time, the former is equal in distribution to the sum of one deterministic trend and one compound Poisson random variable (r.v.); the latter is equal in distribution to the sum of one deterministic trend, one compound Poisson r.v., and one Gamma r.v.. The results immediately lead to very efficient algorithms for their exact simulations without numerical inversion. Extensive numerical experiments are reported to demonstrate the accuracy and efficiency of our algorithms.

Item Type:	Article
Official URL:	https://www.tandfonline.com/toc/tjor20/current
Additional Information:	© 2019 Operational Research Society
Divisions:	Statistics Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	12 Aug 2019 09:48
Last Modified:	08 Nov 2024 08:27
URI:	http://eprints.lse.ac.uk/id/eprint/101340

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