Critical reflexivity in financial markets: a Hawkes process analysis

• Published in: The European physical journal. B, Condensed matter physics Vol. 86; no. 10
• Main Authors: Hardiman, Stephen J., Bercot, Nicolas, Bouchaud, Jean-Philippe
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2013; EDP Sciences
• Subjects: Applied sciences; Complex Systems; Condensed Matter Physics; Exact sciences and technology; Fluid- and Aerodynamics; Operational research and scientific management; Operational research. Management science; Physics; Physics and Astronomy; Portfolio theory; Regular Article; Solid State Physics; Statistical and Nonlinear Physics; Automation; Financial market; Notation; Contract; Power law; Modeling; Criticality
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2013-40107-3

We model the arrival of mid-price changes in the E-mini S&P futures contract as a self-exciting Hawkes process. Using several estimation methods, we find that the Hawkes kernel is power-law with a decay exponent close to −1.15 at short times, less than ≈ 10 3 s, and crosses over to a second power-law regime with a larger decay exponent ≈–1.45 for longer times scales in the range [10 3 , 10 6 ] seconds. More importantly, we find that the Hawkes kernel integrates to unity independently of the analysed period, from 1998 to 2011. This suggests that markets are and have always been close to criticality, challenging a recent study which indicates that reflexivity (endogeneity) has increased in recent years as a result of increased automation of trading. However, we note that the scale over which market events are correlated has decreased steadily over time with the emergence of higher frequency trading.