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

Yadh Hafsi, Fabrizio Lillo and Gr\'egoire Szymanski

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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.

Date: 2026-10
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