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Diffusive Market Impact: A Consistent Microfoundation

Julius Bonart · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.11691 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

长期的结构性影响是最小影响的分散性解释了市场影响的许多经验性规律,包括“平方根法”和它的跨界到一个线性模式的较低的交易利率。 其核心预测之一是,信息流量中性交易策略产生了扩散性影响状态,我们在经济中发现了这种结果,交易者影响的法则与一个交易者和许多裁判员谁逐步消除可预测的回报。 每个裁判员观察到实现的回报和一个基本回报的一个组成部分的私人信号。 由于汇总的私人交易信息成为一个适当的汇总到静止的限度,交易者影响的法则是形式 $j=\dot w$,其中 $w$是分散的市场创新计划和 $U$是定义的所有流量放缓解

Machine translation (Meta M2M100); the English original follows.

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.

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Topics: Economics, Econometrics, Flow (mathematics), Arbitrage, Filter (signal processing), Aggregate (composite)

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