Direct observation of high-frequency traders' strategies and theoretical foundation for financial Brownian motion

Brownian motion has been a pillar of statistical physics for more than a century, and recent high-frequency trading data have shed new light on microstructure of Brownian motion in financial markets. Though evidences of trend-following behaviour of traders were indirectly shown in such trading data, the microscopic model has not been established so far by direct observation of trajectories for individual traders. In this paper, we present a minimal microscopic model for financial Brownian motion through an intensive analysis of trajectory data for all individuals in a foreign exchange market. This model includes a novel empirical law quantifying traders' trend-following behaviour that can create the inertial motion in market prices over short durations. We present a systematic solution paralleling molecular kinetic theory to reveal mesoscopic and macroscopic dynamics of our model. Our model exhibits quantitative agreements with empirical results strongly supporting our analysis.