Dynamical model of financial markets: fluctuating `temperature' causes intermittent behavior of price changes

Abstract

We present a model of financial markets originally proposed for a turbulent flow, as a dynamic basis of its intermittent behavior. Time evolution of the price change is assumed to be described by Brownian motion in a power-law potential, where the `temperature' fluctuates slowly. The model generally yields a fat-tailed distribution of the price change. Specifically a Tsallis distribution is obtained if the inverse temperature is $\chi^{2}$-distributed, which qualitatively agrees with intraday data of foreign exchange market. The so-called `volatility', a quantity indicating the risk or activity in financial markets, corresponds to the temperature of markets and its fluctuation leads to intermittency.