A Hawkes Process Model Linking Order Flow, Impact, and Rough Volatility

Summary

The paper proposes a market microstructure model that separates core orders from reaction flow and represents both with Hawkes processes. In its scaling limit, one persistence statistic for core order flow links several observed market patterns: persistent signed flow, rough trading volume and volatility, and power-law price impact. No-arbitrage conditions constrain how these quantities relate.

The authors estimate the persistence parameter from signed order-flow data at about three quarters. Under the model, this value is consistent with the square-root market impact relationship and with observed roughness estimates for volume and volatility. The excerpt summarizes theoretical relationships and an empirical calibration, but does not describe the dataset, estimation procedure, or robustness checks. The reported links are conditional on the model’s assumptions and do not by themselves establish that the same scaling applies across all markets or regimes.

Key ideas

• The model represents core orders and reaction flow as Hawkes processes.
• A single persistence statistic links signed order flow, volume, volatility, and market impact.
• No-arbitrage constraints imply rough volatility and a power-law impact relationship.
• An estimate near three quarters aligns with the square-root impact law and reported roughness patterns.
• The excerpt does not specify the data or robustness of the empirical estimates.

Tags

# 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.

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