Boltzmann Distribution and Temperature of Stock Markets

Details Boltzmann Distribution and Temperature of Stock Markets Boltzmann Distribution and Temperature of Stock Markets

2006-09-23

arxiv.org/abs/physics/0609209v2

Physica. A 383, 583 (2007)

Physics

Physics and Society

Published version

Scientific paper

The minute fluctuations of of S&P 500 and NASDAQ 100 indices display Boltzmann statistics over a wide range of positive as well as negative returns, thus allowing us to define a {\em market temperature} for either sign. With increasing time the sharp Boltzmann peak broadens into a Gaussian whose volatility $ \sigma $ measured in $1/ \sqrt{{\rm min}}$ is related to the temperature $T$ by $T= \sigma / \sqrt{2}$. 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. A plot of the Dow Jones temperature over 78 years reveals a remarkable stability through many historical turmoils, interrupted only by short heat bursts near the crashes.

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