quant research // summarizing the paperLOADING
Yang Zhou, Jianwen Chen, Ruipeng Wei · 2026-07-05
The paper builds a simulated limit-order-book market with many interacting agents, calibrated to Tokyo Stock Exchange data, to test why market impact follows the 'square-root law' (that trading a metaorder of size Q moves price roughly in proportion to the square root of Q). It finds that three existing theoretical explanations don't match the measured exponent, and instead shows via 'switch-it-off' experiments that two mechanisms are jointly essential: traders splitting big orders into pieces, and market makers replenishing liquidity. Removing either one breaks the square-root relationship, while other features (momentum trading, price limits, order-size tails) barely matter.
Why it matters: For anyone executing large orders, this reinforces that the square-root impact law—widely used to estimate execution costs—emerges from how orders are split over time and how liquidity refills, not from the size distribution of orders or the visible order book alone. It suggests execution-cost models should focus on splitting dynamics and liquidity replenishment behavior rather than on snapshot book shape.
⚠ Results come entirely from a stylized agent-based simulation calibrated to one market, not from live trading, so the causal claims may not transfer directly to real execution.
Three quantitative predictions have been advanced for the square-root law (SRL) of market impact, $I/σ_D = c\,(Q/V_D)^δ$ with $δ\approx 0.5$: GGPS ($δ=β-1$), FGLW ($δ=α-1$), and LOB walking ($δ=1/(1+γ)$). Using a minimal limit-order-book model populated by heterogeneous interacting agents and calibrated against the Tokyo Stock Exchange benchmark ($\langleδ\rangle = 0.489$~\citep{satoStrictUniversalitySquareRoot2025}), we test all three on identical simulated data and find that none matches the per-stock measured $δ$: GGPS and FGLW over-predict by factors of two and four respectively, while LOB walking under-predicts. The model reproduces $\langleδ\rangle = 0.539\pm 0.048$ across 2000 independently parameterised stocks. To identify which mechanisms are causally responsible, we perform counterfactual ablation by selectively suppressing each component. Removing order splitting collapses $δ$ from $0.549$ to $0.324$; removing liquidity replenishment by market makers drops it to $0.386$; perturbations that leave both intact (momentum trading, price limits, splitting rule, background liquidity) move $δ$ by less than $10\%$. Order splitting and liquidity replenishment are thus jointly identified as the necessary mechanisms for the SRL within this model, with the simulated SRL depending on neither the metaorder size tail nor the visible book shape in isolation.
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AI summary generated from the paper’s public abstract via arXiv; it may miss nuance — read the source before relying on it. Thank you to arXiv for its open-access interoperability; StockTools is not affiliated with arXiv, and all rights remain with the authors. Educational only, not financial advice.