连接订单流、市场冲击与粗糙波动率的 Hawkes 过程模型
文章 arXiv papers · 作者: Johannes Muhle-Karbe et al.
总结
论文提出一种市场微观结构模型，将核心订单与反应流分开，并用 Hawkes 过程表示两者。在其尺度极限下，核心订单流的一个持续性统计量将若干观察到的市场模式联系起来：带符号订单流的持续性、粗糙的交易量和波动率，以及幂律价格冲击。无套利条件限制了这些量之间的关系。
作者根据带符号订单流数据估计出持续性参数约为四分之三。在模型下，该数值与平方根市场冲击关系，以及交易量和波动率的观测粗糙度估计相符。摘录概述了理论关系和一项实证校准，但没有说明数据集、估计流程或稳健性检验。报告的关联取决于模型假设，本身并不能证明相同的尺度关系适用于所有市场或市场状态。
核心观点
- 模型将核心订单和反应流表示为 Hawkes 过程。
- 一个持续性统计量将带符号订单流、交易量、波动率和市场冲击联系起来。
- 无套利约束意味着粗糙波动率和幂律冲击关系。
- 接近四分之三的估计值与平方根冲击定律及报告的粗糙度模式相符。
- 摘录未说明实证估计所用数据或其稳健性。
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# A unified theory of order flow, market impact, and volatility
# A unified theory of order flow, market impact, and volatility
We propose a microstructural model for the order flow in financial markets that distinguishes between {\it core orders} and {\it reaction flow}, both modeled as Hawkes processes. This model has a natural scaling limit that reconciles a number of salient empirical properties: persistent signed order flow, rough trading volume and volatility, and power-law market impact. In our framework, all these quantities are pinned down by a single statistic $H_0$, which measures the persistence of the core flow. Specifically, the signed flow converges to the sum of a fractional process with Hurst index $H_0$ and a martingale, while the limiting traded volume is a rough process with Hurst index $H_0-1/2$. No-arbitrage constraints imply that volatility is rough, with Hurst parameter $2H_0-3/2$, and that the price impact of trades follows a power law with exponent $2-2H_0$. The analysis of signed order flow data yields an estimate $H_0 \approx 3/4$. This is not only consistent with the square-root law of market impact, but also turns out to match estimates for the roughness of traded volumes and volatilities remarkably well.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。