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平方根冲击如何保持价格扩散特征

文章 arXiv papers · 作者: Yuki Sato et al.
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总结

本文探讨一个市场微观结构难题：机构拆分大额订单可能使订单流持续，但价格仍呈现扩散特征且难以预测。文中也讨论了元订单规模与其价格冲击之间的经验平方根关系。

作者将 Lillo-Mike-Farmer 模型推广到非线性价格冲击，并将其映射为一个可求解的 Lévy 行走模型。模型解表明，即使订单流具有持续性，平方根冲击也可能使价格动态保持扩散特征，而冲击函数会限制大额订单引起的价格变动。文中描述的证据来自理论模型；摘录没有提供实证检验或实施细节。因此，结论取决于模型假设，并不能证明所有市场或时间尺度都如此。

核心观点

  • 机构拆分订单可能造成持续且可预测的订单流。
  • 本文将元订单的平方根价格冲击与价格扩散行为联系起来。
  • 推广后的订单流模型被映射为可求解的 Lévy 行走模型。
  • 所述结果属于理论研究，并不能证明所有市场都呈现这种行为。

标签

市场微观结构统计学
全文
# Why do financial prices exhibit Brownian motion despite predictable order flow?


# Why do financial prices exhibit Brownian motion despite predictable order flow?









In financial market microstructure, there are two enigmatic empirical laws: (i) the market-order flow has predictable persistence due to metaorder splitters by institutional investors, well formulated as the Lillo-Mike-Farmer model. However, this phenomenon seems paradoxical given the diffusive and unpredictable price dynamics; (ii) the price impact $I(Q)$ of a large metaorder $Q$ follows the square-root law, $I(Q)\propto \sqrt{Q}$. Here we theoretically reveal why price dynamics follows Brownian motion despite predictable order flow by unifying these enigmas. We generalize the Lillo-Mike-Farmer model to nonlinear price-impact dynamics, which is mapped to an exactly solvable Lévy-walk model. Our exact solution shows that the price dynamics remains diffusive under the square-root law, even under persistent order flow. This work illustrates the crucial role of the square-root law in mitigating large price movements by large metaorders, thereby leading to the Brownian price dynamics, consistently with the efficient market hypothesis over long timescales.

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。