Turbulent cascades in foreign exchange markets

The availability of high-frequency data for financial markets has made it possible to study market dynamics on timescales of less than a day(1). For foreign exchange (FX) rates Muller et al.(2) have shown that there is a net flow of information from long to short timescales: the behaviour of long-term traders (who watch the markets only from time to time) influences the behaviour of short-term traders (who watch the markets continuously). Motivated by this hierarchical feature, we have studied FX market dynamics in more detail, and report here an analogy between these dynamics and hydrodynamic turbulence(3-8). Specifically, the relationship between the probability density of FX price changes (Delta x) and the time delay (Delta t) (Fig. 1a) is much the same as the relationship between the probability density of the velocity differences (Delta x) of two points in a turbulent how and their spatial separation Delta r (Fig. 1b). Guided by this similarity we claim that there is an information cascade in FX market dynamics that corresponds to the energy cascade in hydrodynamic turbulence, On the basis of this analogy we can now rationalize the statistics of FX price differences at different time delays, which is important for, for example, option pricing. The analogy also provides a conceptual framework for understanding the short-term dynamics of speculative markets.