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Collective behaviours in the stock market -- A maximum entropy approach

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  • Thomas Bury

Abstract

Scale invariance, collective behaviours and structural reorganization are crucial for portfolio management (portfolio composition, hedging, alternative definition of risk, etc.). This lack of any characteristic scale and such elaborated behaviours find their origin in the theory of complex systems. There are several mechanisms which generate scale invariance but maximum entropy models are able to explain both scale invariance and collective behaviours. The study of the structure and collective modes of financial markets attracts more and more attention. It has been shown that some agent based models are able to reproduce some stylized facts. Despite their partial success, there is still the problem of rules design. In this work, we used a statistical inverse approach to model the structure and co-movements in financial markets. Inverse models restrict the number of assumptions. We found that a pairwise maximum entropy model is consistent with the data and is able to describe the complex structure of financial systems. We considered the existence of a critical state which is linked to how the market processes information, how it responds to exogenous inputs and how its structure changes. The considered data sets did not reveal a persistent critical state but rather oscillations between order and disorder. In this framework, we also showed that the collective modes are mostly dominated by pairwise co-movements and that univariate models are not good candidates to model crashes. The analysis also suggests a genuine adaptive process since both the maximum variance of the log-likelihood and the accuracy of the predictive scheme vary through time. This approach may provide some clue to crash precursors and may provide highlights on how a shock spreads in a financial network and if it will lead to a crash. The natural continuation of the present work could be the study of such a mechanism.

Suggested Citation

  • Thomas Bury, 2014. "Collective behaviours in the stock market -- A maximum entropy approach," Papers 1403.5179, arXiv.org, revised Mar 2014.
  • Handle: RePEc:arx:papers:1403.5179
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    File URL: http://arxiv.org/pdf/1403.5179
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    References listed on IDEAS

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    1. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
    2. G. Livan & S. Alfarano & E. Scalas, 2011. "The fine structure of spectral properties for random correlation matrices: an application to financial markets," Papers 1102.4076, arXiv.org.
    3. Axelrod, Robert & Bennett, D. Scott, 1993. "A Landscape Theory of Aggregation," British Journal of Political Science, Cambridge University Press, vol. 23(2), pages 211-233, April.
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