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

2026-01-30

AI Summary

This study proposes a unified explanation for several stylized facts in financial markets—namely, the persistence of order flow, the roughness of trading volume and volatility, and power-law market impact. By constructing a microstructural model that distinguishes between core and reactive order flows, both modeled as Hawkes processes governed by a single long-memory parameter \( H_0 \), the authors derive the joint asymptotic behavior of these quantities under a no-arbitrage constraint. Leveraging fractional stochastic calculus, rough path theory, and scaling limit analysis, they show that an empirically estimated \( H_0 \approx 3/4 \) not only reproduces the square-root market impact law but also aligns precisely with the observed roughness of volume and volatility. This work thus reveals, for the first time, a common underlying mechanism linking these phenomena through a single parsimonious parameter.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Bridging structured and unstructured data

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.

Problem

• order flow
• market impact
• volatility
• roughness
• Hurst exponent

Innovation

• Hawkes process
• rough volatility
• market impact
• order flow
• fractional processes