Financial price dynamics and pedestrian counterflows: A comparison of statistical stylized facts

We propose and document the evidence for an analogy between the dynamics of granular counterflows in the presence of bottlenecks or restrictions and financial price formation processes. Using extensive simulations, we find that the counterflows of simulated pedestrians through a door display eight stylized facts observed in financial markets when the density around the door is compared with the logarithm of the price. Finding so many stylized facts is very rare indeed among all agent-based models of financial markets. The stylized properties are present when the agents in the pedestrian model are assumed to display a zero-intelligent behavior. If agents are given decision-making capacity and adapt to partially follow the majority, periods of herding behavior may additionally occur. This generates the very slow decay of the autocorrelation of absolute return due to an intermittent dynamics. Our findings suggest that the stylized facts in the fluctuations of the financial prices result from a competition of two groups with opposite interests in the presence of a constraint funneling the flow of transactions to a narrow band of prices with limited liquidity.

Figure 1

Setup of our simulation of pedestrian counterflows. The two kinds of particle filling indicate the state of the pedestrians. The arrows display their current velocities.

Figure 2

Probability density functions (PDF) of the standardized absolute returns of the time series $\rho$ for simulated automata pedestrians (a) and of the time series $\ln \left(S\right)$ for the EURUSD-1hour currency exchange data (b). The dashed lines indicate the closest Gaussian distribution as a guide to the eye to reveal the fat tails of both PDF.

Figure 3

Probability density function of the standardized absolute return of $\rho$ with $k=1$ (a) and $k=100$ (b). The dashed line indicates the closest Gaussian distribution.

Figure 4

Autocorrelation functions of the return and absolute return of the density time series for automata pedestrian system.

Figure 5

Maxima of the distributions of returns $R_{\rho }^k$ versus the number $k$ of time steps.

Figure 6

Ratio $\langle |R_{\left(\rho \right)}^k{|}^q\rangle /\langle |R_{\left(\rho \right)}^k{|\rangle }^q$ versus number $k$ of steps over which the return is calculated for $q=1.5$ (blue square), 2 (green star), 2.5 (red diamond), and 3 (black circle).

Figure 7

Comparison of the fraction $\frac{N_a}{N_p}$ for three realizations for different values of the individualistic parameter: (a) $T=0.071$ (saturated regime), (b) $T=0.078$ (transition regime), and (c) $T=0.150$ (nonsaturated regime).

Figure 8

Fraction of the population $\frac{N_a}{N_p}$ for $T=0.078$ (top) and related pedestrian density time series (bottom).

Figure 9

Autocorrelation functions of the return and absolute return for pedestrians with $T=0.078$ (a) and for EURUSD-1hour financial data (b).