Before revision:  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.
After revision:  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 the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from microscopic dynamics of HFTs. We report first on a microscopic empirical law of traders' trend-following behaviour that can create the inertial motion in market prices over short durations.