A unified theory of order flow, market impact, and volatility

TL;DR

This paper introduces a microstructural model for order flow in financial markets that explains persistent order signs, rough trading volume and volatility, and power-law market impact through a single parameter, H_0, capturing flow persistence.

Contribution

It presents a unified theoretical framework linking order flow, market impact, and volatility using Hawkes processes and a key persistence parameter, H_0, providing new insights into market microstructure.

Findings

H_0 estimated at approximately 3/4 from data

Model explains the square-root law of market impact

Reconciles empirical properties of order flow and volatility

Abstract

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.