Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders
Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders
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DOI：
10.1103/physrevlett.120.138301
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发表时间：
2018-03-27
影响因子：
8.6
通讯作者：
Takayasu, Misako
中科院分区：
文献类型：
--
作者：
Kanazawa, Kiyoshi;Sueshige, Takumi;Takayasu, Misako
通过直接观察外汇市场高频交易者的动态行为，建立了金融布朗运动的微观模型。此外，一个平行于分子动力学理论的理论框架，发展了系统的描述金融市场的微观动力学的高频交易。我们首先报告了一个微观的经验法则的交易者的趋势跟踪行为，通过跟踪所有个人的轨迹，量化的集体运动的高频交易，但没有被捕获在传统的订单簿模型。接下来，我们介绍了相应的微观模型的HFTS和平行的分子动力学理论的理论解：玻尔兹曼和Langevin类方程推导出的微观动力学通过Bogoliubov-Born-Green-Kirkwood-Yvon系列。我们的模型是第一个微观模型，已被直接验证，通过数据分析的微观动力学，表现出定量协议与介观和宏观的实证结果。
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 Bogoliubov-Born-Green-Kirkwood-Yvon 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.