Event definition and the branching ratio: Hawkes estimates of price-change clustering in the consolidated quote feed

Paper: arXiv 2610.36317

Authors: Hyoeun Lee

Abstract

Hawkes models of price changes in the consolidated US quote feed find a sub-millisecond kernel component and a branching ratio near criticality. We show that in large-tick stocks the first is the feed’s construction: half of NBBO changes are locks or depleted quotes, resolved within a millisecond, which the model reads as excitation. Defining the event as a mid-price level persisting for one millisecond removes the component. Raw fits put three times the clean kernel mass within one second, which a simulation reproduces. Since the total branching ratio trades off against the baseline, we report kernel mass on a fixed window.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper demonstrates strong empirical rigor through its detailed data analysis, simulation studies, and robust statistical methodology, particularly in defining and testing event definitions. Its novelty lies in uncovering and quantifying the impact of consolidated feed construction on Hawkes model estimates, a previously unexamined aspect. The mathematical complexity is appropriate for the Hawkes process modeling and estimation techniques employed.

Research Flowchart

  flowchart TD
    A[Research Goal: Understand Price-Change Clustering in US Quote Feed] --> B{Methodology: Hawkes Models};
    B --> C[Data: Consolidated US Quote Feed Price Changes];
    C --> D{Computational Process: Fit Hawkes Model Parameters};
    D --> E{Analysis: Sub-millisecond Kernel & Branching Ratio Calculation};
    E --> F[Key Findings: Sub-millisecond kernel due to feed construction (locks/depleted quotes), branching ratio near criticality. Mid-price persistence event definition removes artifact. Raw fits overestimate kernel mass within 1 sec.];