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Critical reflexivity in financial markets: a Hawkes process analysis

Author

Listed:
  • Stephen J. Hardiman
  • Nicolas Bercot
  • Jean-Philippe Bouchaud

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.

Suggested Citation

  • Stephen J. Hardiman & Nicolas Bercot & Jean-Philippe Bouchaud, 2013. "Critical reflexivity in financial markets: a Hawkes process analysis," Papers 1302.1405, arXiv.org, revised Jun 2013.
  • Handle: RePEc:arx:papers:1302.1405
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    References listed on IDEAS

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    1. Carmen M. Reinhart & Kenneth S. Rogoff, 2009. "Varieties of Crises and Their Dates," Introductory Chapters,in: This Time Is Different: Eight Centuries of Financial Folly Princeton University Press.
    2. Reinhart, Karmen & Rogoff, Kenneth, 2009. ""This time is different": panorama of eight centuries of financial crises," Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 1, pages 77-114, March.
    3. Oecd, 2002. "Access for Business," OECD Digital Economy Papers 67, OECD Publishing.
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    Citations

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    Cited by:

    1. Omar El Euch & Mathieu Rosenbaum, 2016. "The characteristic function of rough Heston models," Papers 1609.02108, arXiv.org.
    2. El Euch Omar & Fukasawa Masaaki & Rosenbaum Mathieu, 2016. "The microstructural foundations of leverage effect and rough volatility," Papers 1609.05177, arXiv.org.
    3. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    4. Thibault Jaisson & Mathieu Rosenbaum, 2015. "Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes," Papers 1504.03100, arXiv.org.
    5. Fernanda Fuentes & Rodrigo Herrera & Adam Clements, 2016. "Modelling Extreme Risks in Commodities and Commodity Currencies," NCER Working Paper Series 115, National Centre for Econometric Research.
    6. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    7. Gresnigt, Francine & Kole, Erik & Franses, Philip Hans, 2015. "Interpreting financial market crashes as earthquakes: A new Early Warning System for medium term crashes," Journal of Banking & Finance, Elsevier, vol. 56(C), pages 123-139.
    8. Lucio Maria Calcagnile & Giacomo Bormetti & Michele Treccani & Stefano Marmi & Fabrizio Lillo, 2015. "Collective synchronization and high frequency systemic instabilities in financial markets," Papers 1505.00704, arXiv.org.
    9. Aur'elien Alfonsi & Pierre Blanc, 2014. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Papers 1404.0648, arXiv.org, revised Jun 2015.
    10. Wheatley, Spencer & Filimonov, Vladimir & Sornette, Didier, 2016. "The Hawkes process with renewal immigration & its estimation with an EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 120-135.
    11. Pierre Blanc & Jonathan Donier & Jean-Philippe Bouchaud, 2015. "Quadratic Hawkes processes for financial prices," Papers 1509.07710, arXiv.org.
    12. Jean-Philippe Bouchaud & Damien Challet, 2016. "Why have asset price properties changed so little in 200 years," Papers 1605.00634, arXiv.org.
    13. Frédéric Abergel & Aymen Jedidi, 2015. "Long Time Behaviour Of A Hawkes Process-Based Limit Order Book," Post-Print hal-01121711, HAL.
    14. Emmanuel Bacry & Thibault Jaisson & Jean-Francois Muzy, 2014. "Estimation of slowly decreasing Hawkes kernels: Application to high frequency order book modelling," Papers 1412.7096, arXiv.org.
    15. Marcello Rambaldi & Emmanuel Bacry & Fabrizio Lillo, 2016. "The role of volume in order book dynamics: a multivariate Hawkes process analysis," Papers 1602.07663, arXiv.org.
    16. repec:hal:wpaper:hal-01121711 is not listed on IDEAS
    17. Massil Achab & Emmanuel Bacry & Jean-Franc{c}ois Muzy & Marcello Rambaldi, 2017. "Analysis of order book flows using a nonparametric estimation of the branching ratio matrix," Papers 1706.03411, arXiv.org.
    18. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    19. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2017. "Hybrid marked point processes: characterisation, existence and uniqueness," Papers 1707.06970, arXiv.org, revised Dec 2017.
    20. Marcello Rambaldi & Vladimir Filimonov & Fabrizio Lillo, 2016. "Detection of intensity bursts using Hawkes processes: an application to high frequency financial data," Papers 1610.05383, arXiv.org.
    21. Blanc, Pierre & Chicheportiche, Rémy & Bouchaud, Jean-Philippe, 2014. "The fine structure of volatility feedback II: Overnight and intra-day effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 58-75.
    22. Aur'elien Alfonsi & Pierre Blanc, 2015. "Extension and calibration of a Hawkes-based optimal execution model," Papers 1506.08740, arXiv.org.

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