The variance-Hawkes process and its application to energy markets

Jessica McGillivray and Anatoliy Swishchuk

Journal of Energy Markets

Abstract: We define a new model using a Hawkes process as a subordinator in a standard Brownian motion. We demonstrate that this Hawkes-subordinated Brownian motion, or, more succinctly, variance-Hawkes process, can be fitted to 2018 and 2019 New York Mercantile Exchange natural gas and West Texas Intermediate crude oil front-month futures log returns. This variance-Hawkes process allows clustering effects to be easily encoded into financial models’ behavior in a simple and tractable way. We also compare the simulations of a square-of-variance Hawkes process with its Itô formula. We simulate both processes and compare their distributions, trajectories and percentage errors across multiple runs. We derive the generator relating to this Hawkes-subordinated Brownian motion, calculate several moments and estimate its distribution. We also provide explicit solutions to the second moments of the Hawkes process and its intensity, as well as the cross-moment between the Hawkes process and its intensity in the case of an exponential kernel.

References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.risk.net/node/7963819 (text/html)

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:rsk:journ2:7963819

Access Statistics for this article

More articles in Journal of Energy Markets from Journal of Energy Markets
Bibliographic data for series maintained by Thomas Paine ().