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 core orders and 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&nbsp;<span>H₀</span>, which measures the persistence of the core flow. Specifically, the signed flow converges to the sum of a fractional process with Hurst index&nbsp;<span>H₀</span>&nbsp;and a martingale, while the limiting traded volume is a rough process with Hurst index&nbsp;<span>H₀ - 1/2</span>. No-arbitrage constraints imply that volatility is rough, with Hurst parameter 2<span>H₀ - 3/2</span>, and that the price impact of trades follows a power law with exponent 2 - 2<span>H₀</span>. The analysis of signed order flow data yields an estimate&nbsp;<span>H₀ around 3/4</span>. 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.