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.

翻译：我们提出一个金融市场订单流的微观结构模型，该模型区分了作为Hawkes过程建模的{\it 核心订单}与{\it 反应流}。该模型具有自然的标度极限，能够调和一系列显著的实证特征：持续的有符号订单流、粗糙的交易量与波动率、以及幂律市场影响。在我们的框架中，所有这些量均由单一统计量$H_0$决定，该统计量衡量了核心流的持续性。具体而言，有符号订单流收敛于一个具有Hurst指数$H_0$的分式过程与一个鞅的和，而极限交易量是一个具有Hurst指数$H_0-1/2$的粗糙过程。无套利约束意味着波动率是粗糙的，其Hurst参数为$2H_0-3/2$，且交易的价量影响遵循指数为$2-2H_0$的幂律。对有符号订单流数据的分析得出估计值$H_0 \approx 3/4$。这不仅与市场影响的平方根定律一致，而且与交易量和波动率粗糙度的估计值也惊人地吻合。