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Letters to Nature
Nature 381, 767 - 770 (27 June 1996); doi:10.1038/381767a0

Turbulent cascades in foreign exchange markets

S. Ghashghaie*, W. Breymann, J. Peinke, P. Talkner§ & Y. Dodge

* Fürstensteinerstrasse 4, 4053 Basel, Switzerland
Institute für Physik der Universität Basel, 4056 Basel, Switzerland
Experimentalphysik II, Universität Bayreuth, 95440 Bayreuth, Germany
§ Paul Scherrer Institut, 5232 Villigen, Switzerland
Groupe de Statistiques, Université de Neuchâtel, 2000 Neuchâtel, Switzerland

THE availability of high-frequency data for financial markets has made it possible to study market dynamics on timescales of less than a day1. For foreign exchange (FX) rates Müller 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 turbulence3–8. Specifically, the relationship between the probability density of FX price changes (δx) and the time delay (δt) (Fig. la) is much the same as the relationship between the probability density of the velocity differences (δv) of two points in a turbulent flow and their spatial separation δr (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.

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