Modelling of Limit Order Books by General Compound Hawkes Processes with Implementations

Anatoliy Swishchuk ()
Additional contact information
Anatoliy Swishchuk: University of Calgary

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 1, 399-428

Abstract: Abstract In this paper, we study so-called general compound and regime-switching general compound Hawkes processes to model the price processes in the limit order books. We prove Law of Large Numbers (LLNs) and Functional Central Limit Theorems (FCLTs), the main results of the present paper, for both cases, non-regime-switching (Lemma 1 and Theorem 1) and regime-switching (Lemma 2 and Theorem 2) cases. The latter two FCLTs are applied to limit order books, where we use these asymptotic methods to study the link between price volatility and order flow in our two models by investigating the diffusion limits of these price processes. The volatilities of price changes are expressed in terms of parameters describing the arrival rates and price changes. Numerical examples are presented for LOBster and Cisco data.

Keywords: General compound Hawkes processes; Regime-switching general compound Hawkes processes; Limit order books; Diffusion limits; Law of large numbers (LLN); Functional central limit theorem (FCLT); LOBster and Cisco data; Primary: 60G55; Secondary: 60F05; 91B26; 91B70 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s11009-020-09803-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:metcap:v:23:y:2021:i:1:d:10.1007_s11009-020-09803-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-020-09803-z

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().