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平方根价格冲击与可预测订单流下的扩散价格

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

本文探讨为何即使市价单订单流因长程相关性而具有可预测性，价格在长时间尺度上仍可能呈扩散特征。这种可预测性与订单通常具有正向价格冲击相结合，似乎与布朗运动式的价格动态不一致。

作者通过纳入非线性平方根价格冲击定律扩展了 Lillo–Mike–Farmer 模型。他们将所得时间序列模型映射为 Lévy 行走，这是一类具有精确解的非马尔可夫随机过程，并证明在所述假设下，价格长期仍呈扩散特征。该结果为可预测订单流如何与扩散型价格并存提供了理论解释；文档没有描述实证验证，也未说明所假设的冲击定律适用范围有多广。

核心观点

  • 长程相关性使市价单订单流具有可预测性。
  • 订单流可预测且具有正向价格冲击，这与扩散型价格之间形成表面上的矛盾。
  • 该模型扩展 Lillo–Mike–Farmer 框架，并采用平方根价格冲击。
  • 将模型映射为 Lévy 行走，有助于对其进行精确分析。
  • 作者证明，在模型假设下，价格长期呈扩散特征。

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市场微观结构统计学交易执行
全文
# Exactly solvable model for the diffusive price-dynamics paradox under long-range correlated market-order flow


# Exactly solvable model for the diffusive price-dynamics paradox under long-range correlated market-order flow









We develop an exactly solvable nonlinear time-series model by incorporating the square-root price-impact law into the Lillo--Mike--Farmer (LMF) model to resolve the diffusive price-dynamics paradox under predictable market-order flow. In financial market microstructure, it is well established that the price dynamics are approximately described by Brownian motion at long times. However, it is also well-known that market-order flow is clearly predictable due to long-range correlations, as mathematically formulated by the LMF model. Since market orders have a positive price impact in general, predictable market-order flow seems to contradict Brownian price dynamics. In this work, we resolve this diffusive price-dynamics paradox by developing nonlinear time-series models that generalize the LMF model based on the square-root price-impact law. Our time-series models can be mathematically mapped onto the Lévy-walk framework---an exactly solvable class of non-Markovian stochastic processes developed in statistical physics. We prove that the price dynamics are diffusive at long times under the square-root law even under predictable market-order flow. Our work highlights the crucial practical importance of the square-root law in understanding the microstructural foundation of the Efficient Market Hypothesis.

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。