Paper: arXiv 2311.18283

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: 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.

Research Flowchart

  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

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