General Compound Hawkes Processes in Limit Order Books

Anatoliy Swishchuk and Aiden Huffman
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Anatoliy Swishchuk: Department of Mathematics and Statistics, Faculty of Science, Calgary, AL T2N1N4, Canada
Aiden Huffman: Department of Mathematics and Statistics, Faculty of Science, Calgary, AL T2N1N4, Canada

Risks, 2020, vol. 8, issue 1, 1-25

Abstract: In this paper, we study various new Hawkes processes. Specifically, we construct general compound Hawkes processes and investigate their properties in limit order books. With regard to these general compound Hawkes processes, we prove a Law of Large Numbers (LLN) and a Functional Central Limit Theorems (FCLT) for several specific variations. We apply several of these FCLTs to limit order books to study the link between price volatility and order flow, where the volatility in mid-price changes is expressed in terms of parameters describing the arrival rates and mid-price process.

Keywords: Hawkes processes; general compound Hawkes processes; limit order books; functional central limit theorems; LOBSTER data (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

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