A theory of passive market impact

TL;DR

This paper develops a microstructure model to analyze the impact of passive limit orders on market prices, introducing a volume-dependent impact function and deriving practical formulas for impact curves.

Contribution

It introduces a novel volume-dependent impact model for passive orders and provides closed-form formulas for market impact analysis.

Findings

Derived impact curves with practical approximation formulas

Analyzed scaling limits of passive market impact

Connected liquidity dynamics with price movements

Abstract

While the market impact of aggressive orders has been extensively studied, the impact of passive orders, those executed through limit orders, remains less understood. The goal of this paper is to investigate passive market impact by developing a microstructure model connecting liquidity dynamics and price moves. A key innovation of our approach is to replace the traditional assumption of constant information content for each trade by a function that depends on the available volume in the limit order book. Within this framework, we explore scaling limits and analyze the market impact of passive metaorders. Additionally, we derive useful approximations for the shape of market impact curves, leading to closed-form formulas that can be easily applied in practice.