Paper: arXiv 2301.05677

Authors: Mohammed Salek, Damien Challet, Ioane Muni Toke

Abstract

Using high-quality data, we report several statistical regularities of equity auctions in the Paris stock exchange. First, the average order book density is linear around the auction price at the time of auction clearing and has a large peak at the auction price. While the peak is due to slow traders, the order density shape is the result of subtle dynamics. The impact of a new market order or cancellation at the auction time can be decomposed into three parts as a function of the size of the additional order: (1) zero impact, caused by the discrete nature of prices, sometimes up to a surprisingly large additional volume relative to the auction volume (2) linear impact for additional orders up to a large fraction of the auction volume (3) for even larger orders price impact is non-linear, frequently super-linear.

Complexity vs Empirical Score

  • Math Complexity: 5.0/10
  • Empirical Rigor: 6.0/10 (capped from 8.0: transaction costs not modelled; no out-of-sample test; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong empirical analysis of market microstructure in equity auctions, uncovering novel non-linear price impact regimes. The methodology combines detailed order book mechanics with rigorous statistical observations from Paris stock exchange data.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze Price Impact & Order Density in Equity Auctions] --> B[Data Input: High-Quality Order Book Data from Paris Stock Exchange]
    B --> C[Methodology: Track Order Density & Simulate Additional Orders/Cancellations]
    C --> D[Compute Price Impact as a Function of Additional Order Size]
    D --> E[Outcome 1: Linear Order Density with Large Peak at Clearing Price]
    D --> F[Outcome 2: Tri-phasic Price Impact]
    F --> F1[1. Zero Impact: Small-to-Large Volumes]
    F --> F2[2. Linear Impact: Medium-to-Large Volumes]
    F --> F3[3. Non-Linear/Super-Linear Impact: Very Large Volumes]