Calibration of Passive Market Impact with a Queue-Sensitive Propagator Model

Paper: arXiv 2610.38442

Authors: Yadh Hafsi, Fabrizio Lillo, Grégoire Szymanski

Abstract

We develop a framework for calibrating passive market impact, defined as the price response to liquidity-providing limit orders, in contrast to the impact of liquidity-consuming market orders. We build on the model of Ouazzani Chahdi, Rosenbaum, and Szymanski (arxiv:2412.07461), which combines Hawkes-driven market-order flow with queue-reactive limit-order and cancellation dynamics. Within this model, we show that the price decomposes into a universal propagator term driven by signed order-flow imbalance and a state-dependent correction that captures the dependence of price sensitivity on volume at the best quotes. This decomposition links limit-order-book microstructure to standard propagator models and yields a regression on two observable signals: the propagator signal and the queue-weighted order-flow imbalance. We calibrate the model on high-frequency order-book data and find that the passive-impact term explains substantial variation in prices beyond the classical propagator, improving both model fit and the accuracy of predicted impact curves.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly sophisticated mathematical framework for passive market impact, building on advanced Hawkes processes and queue-reactive dynamics. It demonstrates strong empirical rigor through calibration on high-frequency order-book data and improved model fit, offering a novel decomposition of price impact.

Research Flowchart

  flowchart TD
    A[Research Goal: Calibrate Passive Market Impact] --> B{Key Methodology: Extend OCS Model (Hawkes Flow + Queue Dynamics)};
    B --> C[Model Development: Decompose Price into Propagator + Queue-Sensitive Correction];
    C --> D[Data/Inputs: High-Frequency Limit Order Book Data (Equities)];
    D --> E[Computational Process: Regression on Propagator Signal & Queue-Weighted Order-Flow Imbalance];
    E --> F[Key Finding 1: Passive Impact Explains Substantial Price Variation Beyond Classical Propagator];
    E --> G[Key Finding 2: Improved Model Fit and Accuracy of Predicted Impact Curves];