Dynamical model of financial markets: fluctuating ‘temperature’ causes intermittent behavior of price changes

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 χ2-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.