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高频限价订单簿动态的扩散近似

文章 arXiv papers · 作者: Rama Cont et al.
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总结

本文对流动性充足市场中高频到达的买卖盘队列建模，推导其联合动态的函数型中心极限定理，并表明随着订单到达频率提高，订单簿可用正象限中的马尔可夫跳扩散过程近似。过程特征以底层订单流的统计属性表示，使该框架能够适应不同的分布和时间依赖性。

这些近似使研究者可以在给定当前订单簿状态的条件下，分析价格上涨概率、下一次价格变动所需时间等量。所述框架适用于广泛的随机订单流模型，包括泊松点过程、自激过程和 ACD-GARCH 模型。本文介绍理论结果及其潜在分析用途，并未报告具体的实证交易检验。该近似依赖较高的订单到达频率，简要描述也未说明其在不同市场或参数设置下的准确度如何变化。

核心观点

  • 函数型中心极限定理描述买卖盘队列的联合动态。
  • 在订单到达频率较高时，限价订单簿可近似为马尔可夫跳扩散过程。
  • 该近似支持对价格方向和下一次价格变动时间进行条件分析。
  • 该框架涵盖泊松、自激和 ACD-GARCH 等订单流过程。

标签

市场微观结构统计学高频交易交易执行
全文
# Order book dynamics in liquid markets: limit theorems and diffusion approximations


# Order book dynamics in liquid markets: limit theorems and diffusion approximations









We propose a model for the dynamics of a limit order book in a liquid market where buy and sell orders are submitted at high frequency. We derive a functional central limit theorem for the joint dynamics of the bid and ask queues and show that, when the frequency of order arrivals is large, the intraday dynamics of the limit order book may be approximated by a Markovian jump-diffusion process in the positive orthant, whose characteristics are explicitly described in terms of the statistical properties of the underlying order flow. This result allows to obtain tractable analytical approximations for various quantities of interest, such as the probability of a price increase or the distribution of the duration until the next price move, conditional on the state of the order book. Our results allow for a wide range of distributional assumptions and temporal dependence in the order flow and apply to a wide class of stochastic models proposed for order book dynamics, including models based on Poisson point processes, self-exciting point processes and models of the ACD-GARCH family.

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。