Diffusive Market Impact: A Consistent Microfoundation

Paper: arXiv 2610.11691

Authors: Julius F. Bonart

Abstract

Structural price diffusivity explains many empirical regularities of market impact including the square-root law'' and its crossover to a linear regime for low trading rates \citep{bonart2026diffusive}. One of its central predictions is that an information-neutral trading strategy generates a diffusive impact state. We microfound this result in an economy with a trader and many arbitrageurs who progressively eliminate predictable returns. Each arbitrageur observes realized returns and a private signal of one component of the fundamental return. As aggregate private information becomes complete and under suitable convergence to a stationary limit, the trader's impact law is of the form $j=U\cdot w$, where $w$ is the innovation in the trading schedule and $U$ is causal all-pass. Impact returns are therefore white, even though no individual arbitrageur can reconstruct the underlying trading strategy. We then investigate the economic meaning of the impact phase. We argue that the $U$ which has minimum distance from the filter $L$ generating the trade flow is an especially interesting candidate: Trade flow is then minimally distorted under impact and arbitrage, and it always guarantees positive impact costs. Under a trader flow generated by a biexponential $L$ (the simplest form allowed in our model) an interesting result emerges: Impact decline is confined to a narrow band of $50\%$--$60\%$, lower than some empirical estimates and quite consistent with others. More complicated flow models can lead to different decays. Finally, we argue that in real markets, the impact phase is probably somewhat distorted’’ in its long-term tails which allows for a full relaxation of the impact propagator. The effect is weak, long-term mean-reversion of the impact state.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a highly theoretical and mathematically intensive microfoundation for market impact, demonstrating significant novelty in its approach. However, it lacks empirical validation or backtesting, focusing purely on theoretical derivations and economic interpretations. The clarity is good for a theoretical paper, but reproducibility is limited by the absence of code or data.

Research Flowchart

  flowchart TD
    A[Research Goal: Microfound Diffusive Market Impact] --> B{Key Methodology: Arbitrageurs & Information Elimination};
    B --> C[Inputs: Trader & Many Arbitrageurs, Realized Returns, Private Signals];
    C --> D{Computational Process: Model Convergence to Stationary Limit};
    D --> E[Outcome 1: Impact Law J = U * W (White Impact Returns)];
    E --> F[Outcome 2: Minimum Distance U to L implies positive impact costs, 50-60% impact decline for biexponential L];
    F --> G[Outcome 3: Long-term mean-reversion of impact state due to "distorted" tails];

Cited References (95)

1. Time Series Analysis (2016)
2. How Markets Slowly Digest Changes in Supply and Demand (2008) — link
3. Strict Universality of the Square-Root Law in Price Impact across Stocks: A Complete Survey of the Tokyo Stock Exchange (2025) — link
4. Why do financial prices exhibit Brownian motion despite predictable order flow? (2025) — link
5. The Universal Law Behind Market Price Swings (2025) — link
6. A theory of power-law distributions in financial market fluctuations (2003) — link
7. Market Microstructure Invariance: Empirical Hypotheses (2016) — link
8. A fully consistent, minimal model for non-linear market impact (2014) — link

1 of 95 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.