Diffusive and Arrestedlike Dynamics in Currency Exchange Markets

This work studies the symmetry between colloidal dynamics and the dynamics of the Euro–U.S. dollar currency exchange market (EURUSD). We consider the EURUSD price in the time range between 2001 and 2015, where we find significant qualitative symmetry between fluctuation distributions from this market and the ones belonging to colloidal particles in supercooled or arrested states. In particular, we find that models used for arrested physical systems are suitable for describing the EURUSD fluctuation distributions. Whereas the corresponding mean-squared price displacement (MSPD) to the EURUSD is diffusive for all years, when focusing in selected time frames within a day, we find a two-step MSPD when the New York Stock Exchange market closes, comparable to the dynamics in supercooled systems. This is corroborated by looking at the price correlation functions and non-Gaussian parameters and can be described by the theoretical model. We discuss the origin and implications of this analogy.

Figure 1

Time evolution of the EURUSD price (a) and Cartesian trajectories from a colloid embedded in a quasi-two-dimensional colloidal glass (b).

Figure 2

EURUSD fluctuation distributions, $\delta (\tau )$ (a), for 2010–2015 (open circles), 2001 (solid circles), and 2007 (crosses). From bottom to top, $\tau =25$, 125, and 625 min (shifted vertically for clarity). Fit to the experimental PDF (b) over the period 2010–2015 with the van Hove function of Eq. (1) (lines). From bottom to top, $\tau =5$, 25, 125, 625, and 3125 min (shifted).

Figure 3

EURUSD MSPDs as calculated from 1 min experimental data for the period 2010–2015 (open circles), to the year 2001 (solid circles), and to the year 2007 (crosses). The line is the MSPD according to the van Hove function of Eq. (1), with the same parameters as Fig. 2.

Figure 4

EURUSD MSPD as calculated from 2015 experimental data by considering time periods of 24 h (ET). In the time range 9:30 a.m.–6:00 p.m. (a), a transition from diffusive to an undercooled dynamics is observed. Commencing times are labeled. By contrast, in the time frame of 6:00 p.m.–9:30 a.m., the transition is reversed (b). The lines are the fitting of the model for the different cases. The insets show the price correlation function $S(q,\tau )$ (a) and non-Gaussian parameter ${\alpha }_2$ (b).