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Critical reflexivity in financial markets: a Hawkes process analysis

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  • 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.

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  • 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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    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," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 1, pages 77-114, March.
    3. Vasilev, Aleksandar & Maksumov, Rashid, 2010. "Critical analysis of Chapter 23 of Keynes’s Notes on Mercantilism in The General Theory of Employment, Interest and Money (1936)," EconStor Research Reports 155318, ZBW - Leibniz Information Centre for Economics.
    4. Oecd, 2002. "Access for Business," OECD Digital Economy Papers 67, OECD Publishing.
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