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动力学理论推导 HFT 与价格动态的布朗模型

文章 arXiv papers · 作者: Kiyoshi Kanazawa et al.
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总结

这项研究为趋势跟踪型高频交易者的微观模型建立了动力学理论基础。研究从模型精确的相空间演化方程出发，该方程类似于力学中的刘维尔方程，并通过金融布朗运动方程的层级体系逐步简化描述。

在假设分子混沌的条件下，作者推导出类似玻尔兹曼方程的订单簿动态，以及类似朗之万方程的价格动态。他们通过解析方法研究交易者数量较大时的行为，并报告了蒙特卡洛模拟的数值验证。本文认为金融布朗运动与物理布朗运动具有平行的数学结构。其结果依赖模型和分子混沌假设；摘录没有提供底层市场数据分析细节，也没有证明这些方程适用于这一设定之外的市场。

核心观点

  • 本文使用微观框架对趋势跟踪型高频交易者进行建模。
  • 精确的相空间演化方程是动力学简化的起点。
  • 研究推导了金融布朗运动的层级方程体系。
  • 分子混沌假设导出类似玻尔兹曼方程的订单簿方程和类似朗之万方程的价格方程。
  • 研究分析了交易者数量较大时的行为，并通过蒙特卡洛模拟进行检验。

标签

高频交易趋势跟踪市场微观结构统计学
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# Kinetic Theory for Finance Brownian Motion from Microscopic Dynamics


# Kinetic Theory for Finance Brownian Motion from Microscopic Dynamics









Recent technological development has enabled researchers to study social phenomena scientifically in detail and financial markets has particularly attracted physicists since the Brownian motion has played the key role as in physics. In our previous report (arXiv:1703.06739; to appear in Phys. Rev. Lett.), we have presented a microscopic model of trend-following high-frequency traders (HFTs) and its theoretical relation to the dynamics of financial Brownian motion, directly supported by a data analysis of tracking trajectories of individual HFTs in a financial market. Here we show the mathematical foundation for the HFT model paralleling to the traditional kinetic theory in statistical physics. We first derive the time-evolution equation for the phase-space distribution for the HFT model exactly, which corresponds to the Liouville equation in conventional analytical mechanics. By a systematic reduction of the Liouville equation for the HFT model, the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchal equations are derived for financial Brownian motion. We then derive the Boltzmann-like and Langevin-like equations for the order-book and the price dynamics by making the assumption of molecular chaos. The qualitative behavior of the model is asymptotically studied by solving the Boltzmann-like and Langevin-like equations for the large number of HFTs, which is numerically validated through the Monte-Carlo simulation. Our kinetic description highlights the parallel mathematical structure between the financial Brownian motion and the physical Brownian motion.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。