Boltzmann distribution and market temperature |
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Authors: | H Kleinert XJ Chen |
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Institution: | a Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany b Nomura House, 1 St Martin's-le-Grand, London EC1A 4NP, UK |
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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 is related to the temperature T by . 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. |
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