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];