Critical reflexivity in financial markets: a Hawkes process analysis
Capital Fund Management, 23 rue de l’Université, 75007 Paris, France
Received: 7 February 2013
Received in final form: 5 June 2013
Published online: 28 October 2013
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 ≈ 103 s, and crosses over to a second power-law regime with a larger decay exponent ≈–1.45 for longer times scales in the range [ 103,106 ] 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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2013