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

Yan Qu, Angelos Dassios and Hongbiao Zhao

Journal of the Operational Research Society, 2021, vol. 72, issue 2, 471-484

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.

Date: 2021
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://hdl.handle.net/10.1080/01605682.2019.1657368 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:tjorxx:v:72:y:2021:i:2:p:471-484

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/tjor20

DOI: 10.1080/01605682.2019.1657368

Access Statistics for this article

Journal of the Operational Research Society is currently edited by Tom Archibald

More articles in Journal of the Operational Research Society from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().