Critical reflexivity in financial markets: a Hawkes process analysis

By Stephen J. Hardiman, Nicolas Bercot, Jean-Philippe Bouchaud. European Physical Journal B : Condensed Matter Physics, 2013

193 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/7495d49c4dcd25cc79db0f10c279c448642874c3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

In Molecular Biology

Citations in the corpus

Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes (2015, background): “This setting is actually much more in agreement with financial data, where one not only finds that the function φ has an L1 norm close to one, but also that it has a power law tail; see [6, 19].”
Hawkes Processes in Finance (2015, background): “Using this model free estimator, Hardiman and Bouchaud [35] have confirmed their former claims that the S&P 500 future appears to have, during the last ten years, a stable level of reflexivity, close to the criticality.”
Reactive point processes: A new approach to predicting power failures in underground electrical systems (2015, unknown): “…Weber (2011), A¨ıt-Sahalia, Cacho-Diaz and Laeven (2010), Bacry et al. (2013), Filimonov and Sornette (2012), Embrechts, Lin-iger and Lin (2011), Hardiman, Bercot and Bouchaud (2013)], computational neuroscience [Johnson (1996), Krumin, Reutsky and Shoham (2010)], genome sequencing…”
The characteristic function of rough Heston models (2016, background): “Here, the 𝜑𝑖 are measurable nonnegative deterministic functions and 𝜇𝑇 and 0 < 𝑎𝑇 < 1 are some deterministic sequences of positive real numbers; see Bacry, Delattre, Hoffmann, and Muzy (2013) and the references therein for more details about the definition of Hawkes processes.”
Market Impacts and the Life Cycle of Investors Orders (2014, background): “The latter is parametrized by a parameter C having a macroscopic interpretation: the ratio of contrarian reaction (i.e. impact decay) and of the "herding" reaction (i.e. impact amplification).”
The role of volume in order book dynamics: a multivariate Hawkes process analysis (2016, background): “…arrival in time of a number of event types (trades, quotes, etc.), see for instance Bowsher (2007), Bacry et al. (2013), Filimonov and Sornette (2015), Bormetti et al. (2015), Hardiman et al. (2013), Bauwens and Hautsch (2009), Rambaldi et al. (2015) and Bacry et al. (2015) for a recent review.”
Limit theorems for nearly unstable Hawkes processes (2013, methodology): “In [21], it is suggested to use the without ancestors version of Hawkes processes introduced by Brémaud and Massoulié in [13].”
Volatility is rough (2014, background): “• The L1 norm of φ is close to one, see [23, 24, 30, 35].”
No‐arbitrage implies power‐law market impact and rough volatility (2018, unknown): “In the Hawkes process context, the degree of endogeneity of the market is measured by the L(1) norm of φ, denoted by ‖φ‖1, see [13, 17, 22, 21].”