Critical reflexivity in financial markets: a Hawkes process analysis

TL;DR

This paper models the timing of price changes in E-Mini S&P futures using a Hawkes process, revealing power-law decay in event self-excitation and suggesting markets are near criticality across years, despite increased high-frequency trading.

Contribution

It demonstrates that the Hawkes kernel governing market events exhibits a consistent power-law decay and that markets have remained near criticality over time, challenging recent claims about increased reflexivity.

Findings

Hawkes kernel follows a power-law decay with exponents around -1.15 and -1.45.

The kernel's integral remains close to unity from 1998 to 2011.

The correlation scale of market events has decreased with high-frequency trading emergence.

Abstract

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 approximately 10^3 seconds, and crosses over to a second power-law regime with a larger decay exponent of approximately -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.