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Boltzmann distribution and market temperature

Author

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  • Kleinert, H.
  • Chen, X.J.

Abstract

We show that the minute fluctuations of S&P 500 and NASDAQ 100 indices show Boltzmann statistics over a wide range of positive as well as negative returns, thus allowing us to define a market temperature for either sign. With increasing time the sharp Boltzmann peak broadens into a Gaussian whose volatility σ measured in 1/min is related to the temperature T by T=σ/2. Plots over the years 1990–2006 show that the arrival of the 2000 crash was preceded by an increase in market temperature, suggesting that this increase can be used as a warning signal for crashes.

Suggested Citation

  • Kleinert, H. & Chen, X.J., 2007. "Boltzmann distribution and market temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 513-518.
    • Handle: RePEc:eee:phsmap:v:383:y:2007:i:2:p:513-518
    DOI: 10.1016/j.physa.2007.04.101
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    References listed on IDEAS

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    1. Silva, A.Christian & Yakovenko, Victor M., 2003. "Comparison between the probability distribution of returns in the Heston model and empirical data for stock indexes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 303-310.
    2. Silva, A. Christian & Prange, Richard E. & Yakovenko, Victor M., 2004. "Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 227-235.
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    Cited by:

    1. Jan Novotny, 2010. "Were Stocks during the Financial Crisis More Jumpy: A Comparative Study," CERGE-EI Working Papers wp416, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    2. Vincenzo Crescimanna & Luca Di Persio, 2016. "Herd Behavior and Financial Crashes: An Interacting Particle System Approach," Journal of Mathematics, Hindawi, vol. 2016, pages 1-7, February.
    3. Sosa-Correa, William O. & Ramos, Antônio M.T. & Vasconcelos, Giovani L., 2018. "Investigation of non-Gaussian effects in the Brazilian option market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 525-539.
    4. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
    5. Christoph J. Borner & Ingo Hoffmann & John H. Stiebel, 2023. "On the Connection between Temperature and Volatility in Ideal Agent Systems," Papers 2303.15164, arXiv.org.
    6. Ramos, Antônio M.T. & Carvalho, J.A. & Vasconcelos, G.L., 2016. "Exponential model for option prices: Application to the Brazilian market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 161-168.

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