A Spread-Gated Hawkes-Flocking Model for Best Bid and Ask Dynamics, with an Application to Limit Order Placement

Paper: arXiv 2609.36631

Authors: Hyoeun Lee, Kiseop Lee

Abstract

We study the joint dynamics of the best bid and ask prices with a spread-gated Hawkes-flocking model. The model tracks four types of best-quote movements: spread-narrowing movements are switched off when the spread is at its one-tick minimum, and a cross-side excitation term, whose activation depends on the prevailing spread, links the two sides of the book. We show that the process is non-explosive on every finite horizon, give an $O(N)$ recursive likelihood, and validate the maximum likelihood estimator by simulation. On real intraday limit order book data for two large-tick stocks, INTC and MSFT, the restriction that removes the cross-side term is rejected, and the full model improves fit substantially by AIC and BIC; the likelihood is multimodal on a single day, so estimation uses a multi-start search. As an application, we derive the closed-form optimal size of a single-period limit order placed at the best or second-best quote, given the model’s next-event probabilities and externally supplied execution probabilities.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically sophisticated Hawkes-flocking model with a non-explosion proof and an O(N) recursive likelihood. It validates the model with real intraday LOB data and applies it to a practical trading problem, demonstrating both theoretical depth and empirical relevance.

Research Flowchart

  flowchart TD
    A[Research Goal: Model & Optimize Best Bid/Ask Dynamics] --> B{Methodology: Spread-Gated Hawkes-Flocking Model};
    B --> C[Model Features: Spread-Gating, Cross-Side Excitation, Non-Explosive Process];
    C --> D{Data/Inputs: Intraday LOB Data (INTC, MSFT)};
    D --> E[Computational Processes: O(N) Recursive Likelihood, ML Estimator (Multi-Start Search)];
    E --> F[Key Findings: Cross-Side Term Validated, Full Model Improves Fit (AIC/BIC), Optimal Limit Order Size Derived];

Cited References (114)

1. Stability of Nonlinear H awkes Processes (1996)
2. Point Processes and Queues: Martingale Dynamics (1981)
3. An Introduction to the Theory of Point Processes, Volume I: Elementary Theory and Methods (2003) — link
4. LOBSTER : Limit Order Book Reconstruction System (2011)
5. Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes (1988)
6. Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests under Nonstandard Conditions (1987)
7. Optimal placement of a small order in a diffusive limit order book (2018) — link
8. Modeling Bid and Ask Price Dynamics with an Extended H awkes Process and Its Empirical Applications for High-Frequency Stock Market Data (2023) — link

1 of 114 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.