Statistical theory of inhomogeneous spectral line shapes applied to financial markets

Abstract

It was found empirically that distributions of short-term price fluctuations in financial markets exhibit striking similarities to those of velocity differences in turbulent flows. Very similar profiles exist as inhomogeneous spectroscopic line shapes of impurity molecules in disordered solids. The paper demonstrates that a microscopic statistical theory of the line shapes can be applied to the other two phenomena. The financial data are interpreted in terms of information which becomes available to the traders and their reactions as a function of time. The comparison between theoretical distributions and actual market data shows that there is no characteristic time scale in financial markets. The similarities between the three phenomena are based on fundamental principles of statistics.