Boltzmann distribution and market temperature

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 σσ 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.