Turbulence and financial markets : a transaction cascade in foreign exchange markets

Price dynamics of speculative markets is one of the most complex phenomena in economics. Already the statistical description turns out to be difficult. The most prominent characteristic of the distribution of logarithmic price differences (returns) Δy for a given time delay Δt is its lepto- kurtosis, i.e., the pronounced frequencies with which both small and large returns occur. Proper modelling of this effect is of practical relevance for risk management. The kurtosis of the return distribution is largest for Δt of the order of minutes and decreases monotonically with increasing Δt, accompanied by an according change in the form of the distribution [1, 2]. Simultaneously, the variance of the distribution increases: it depends on the time delay according to a power law ((Δy)2) ~ Δt ε2.