Optimal Execution with Passive Market Impact

2026-07-30

AI Summary

This study addresses the trade-off among execution probability, adverse selection, and opportunity cost in limit order trading by proposing a mesoscale optimal passive execution strategy. Embedding two empirically observed microstructural features—namely, the exponential decay of limit order fill probability with quote distance and the short-term linear price response to order flow imbalance—into a stochastic control framework, the work derives for the first time a passively induced market impact rate exhibiting exponential decay and solves for the corresponding optimal liquidation policy. The model is validated on both NASDAQ equity and foreign exchange data and extends naturally to settings involving heterogeneous decay rates, instantaneous impact, and target execution schedules, thereby establishing a theoretical foundation and practical mechanism for tactical passive execution.

Abstract

We derive a mesoscopic model for optimal execution with limit orders that incorporates microstructural features of passive price impact. Our framework is based on two empirical observables: the approximately exponential decay of limit-order fill probabilities with distance from the midprice, and the short-term linear response of price changes to order flow imbalance. Combining these ingredients, we obtain a reduced-form passive impact rate that decays exponentially with quote distance. The model describes passive execution at a tactical level, where fills arise from a sequence of quote adjustments that balance execution probability, adverse selection, and opportunity cost. We formulate and solve an optimal liquidation problem in which the trader controls the aggressiveness of passive sell quotes. This generates a trade-off between higher fill intensity and larger accumulated impact on the one hand, and lower impact but greater non-execution risk on the other. Empirical calibration using NASDAQ equities and public FX supports the empirical foundations of the model. We also analyse extensions with heterogeneous decay rates, transient impact, and target execution schedules.

Problem

• optimal execution
• passive market impact
• limit orders
• order flow imbalance
• price impact

Innovation

• optimal execution
• passive market impact
• limit-order fill probability
• order flow imbalance
• exponential decay