A theory of passive market impact

ArXiv ID: 2412.07461 “View on arXiv”

Authors: Unknown

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.

Keywords: Market Microstructure, Limit Order Book, Passive Market Impact, Liquidity Dynamics, Scaling Limits, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper is highly mathematical, featuring advanced stochastic calculus, Hawkes processes, scaling limits, and rigorous proofs (e.g., Theorem 2.1, Appendix proofs), which drives a high math complexity score. However, it is primarily theoretical with a focus on model derivation and approximations (e.g., closed-form formulas) rather than implementation details, backtesting, or empirical data analysis, resulting in low empirical rigor.

  flowchart TD
    A["Research Goal: Investigate passive market impact of limit orders"] --> B["Microstructure Model Development"]
    B --> C["Key Innovation: Trade info content function f<br>dependent on limit order book volume"]
    C --> D["Methodology: Scaling Limits &<br>Analysis of Passive Metaorders"]
    D --> E["Computational Process: Derive closed-form<br>impact approximations & formulas"]
    E --> F["Outcome: Market impact curve shape<br>prediction for practical application"]
    F --> G["Key Finding: Passive impact scaling<br>differs from aggressive orders"]