Dynamic heterogeneities in stock markets

Abstract

The dynamics of the New York Stock Exchange during the past decade is studied using observables borrowed from the study of glass-forming liquids. Using the log-price as equivalent to the particle position, the density autocorrelation function is calculated, which shows a stretched exponential decay. The Kohlrausch law correctly describes the decay, and the dependencies of the stretching exponent and time-scale with the wavenumber follow the same trends as for supercooled liquids. The equivalent of the overlap correlation function is also calculated and analyzed. The dynamic heterogeneities are studied using the non-Gaussian parameter and the dynamic susceptibilities, calculated from both correlation functions. The dynamic susceptibility grows from zero at short times to describe a maximum in the same time scale as the decay of the corresponding correlation function, and decays back to zero for long times. Finally, we show that avalanches of all sizes are present in the system, mimicking critical behavior previously discussed in glasses.