The two square root laws of market impact and the role of sophisticated market participants

ArXiv ID: 2311.18283 “View on arXiv”

Authors: Unknown

Abstract

The goal of this paper is to disentangle the roles of volume and of participation rate in the price response of the market to a sequence of transactions. To do so, we are inspired the methodology introduced in arXiv:1402.1288, arXiv:1805.07134 where price dynamics are derived from order flow dynamics using no arbitrage assumptions. We extend this approach by taking into account a sophisticated market participant having superior abilities to analyse market dynamics. Our results lead to the recovery of two square root laws: (i) For a given participation rate, during the execution of a metaorder, the market impact evolves in a square root manner with respect to the cumulated traded volume. (ii) For a given executed volume $Q$, the market impact is proportional to $\sqrtγ$, where $γ$ denotes the participation rate, for $γ$ large enough. Smaller participation rates induce a more linear dependence of the market impact in the participation rate.

Keywords: Market Impact, Order Flow Dynamics, Square Root Law, Execution Strategies, No-Arbitrage Pricing, Equities

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats
  • Why: The paper is highly mathematically dense, featuring advanced stochastic calculus, Hawkes processes, PDEs, and scaling limits, warranting a high math complexity score. However, while it mentions data-driven assumptions (e.g., power-law decay kernels) and potential Monte Carlo applications, the excerpt is purely theoretical with no reported backtests, statistical metrics, or implementation details, resulting in low empirical rigor.
  flowchart TD
    A["Research Goal: Disentangle volume vs participation rate<br>in market price response"] --> B["Methodology: Extend no-arbitrage pricing<br>with sophisticated market participant"]
    B --> C["Model Input: Order flow dynamics<br>from past arXiv studies 1402.1288, 1805.07134"]
    C --> D["Computational Process: Derive price dynamics<br>accounting for superior analysis abilities"]
    D --> E["Outcome 1: Square Root Law I<br>Impact ∝ sqrt(volume) for fixed participation"]
    D --> F["Outcome 2: Square Root Law II<br>Impact ∝ sqrtγ for large γ, linear for small γ"]
    E --> G["Key Finding: Participation rate modulates<br>impact magnitude beyond just volume"]
    F --> G