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 .
A microscopic model is established for financial Brownian motion from the 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 behavior by tracking the trajectories of all individuals, which quantifies the collective motion of HFTs but has not been captured in conventional order-book models. We next introduce the corresponding microscopic model of HFTs and present its theoretical solution paralleling molecular kinetic theory : Boltzmann-like and Langevin-like equations are derived from the microscopic dynamics via the BBGKY hierarchy . Our model is the first microscopic model that has been directly validated through data analysis of the microscopic dynamics, exhibiting quantitative agreements with mesoscopic and macroscopic empirical results .
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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
A microscopic model is established for financial Brownian motion from the
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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
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
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behaviour that can create the inertial motion in market prices over short durations. We present a systematic
behavior by tracking the trajectories of all individuals, which quantifies the collective motion of HFTs but has not been captured in conventional order-book models. We next introduce the corresponding microscopic model of HFTs and present its theoretical
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to reveal mesoscopic and macroscopic dynamics of our model
: Boltzmann-like and Langevin-like equations are derived from the microscopic dynamics via the BBGKY hierarchy
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exhibits
is the first microscopic model that has been directly validated through data analysis of the microscopic dynamics, exhibiting
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empirical results strongly supporting our analysis
mesoscopic and macroscopic empirical results