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用金融玻尔兹曼方程建模高频交易者

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

本文基于外汇市场高频交易者的观察数据，构建金融价格运动的微观描述。文章追踪单个交易者的轨迹，并报告发现了一种传统订单簿模型无法捕捉的集体趋势跟随模式。

随后，作者借鉴分子动理论的思想对交易者之间的互动建模。通过应用 Bogoliubov–Born–Green–Kirkwood–Yvon 层级，他们推导出类似玻尔兹曼方程和朗之万方程的市场动态描述。作者报告称，该模型在介观和全市场尺度上都与实证发现定量吻合。文档没有提供数据样本、估计选择或能否推广至观察市场以外范围的详情，这些问题仍未解决。

核心观点

  • 追踪单个HFT的轨迹，可以发现集体趋势跟随模式。
  • 该模型将分子动理论应用于金融市场动态描述。
  • 方程层级推导出类似玻尔兹曼方程和朗之万方程的描述。
  • 作者报告称，模型结果在多个尺度上与实证结果定量吻合。
  • 文档没有说明数据集或模型的适用范围。

标签

外汇高频交易市场微观结构趋势跟踪统计学
全文
# 1703.06739


# Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders









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.

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。