Order Splitting and Liquidity Replenishment Are Jointly Necessary for the Square-Root Law of Market Impact: A Counterfactual Dissection

Battle Count: 72

The paper directly addresses the square-root law of market impact, which is fundamental to algorithmic execution, optimal trading, and transaction cost analysis. The identification of order splitting and liquidity replenishment as jointly necessary mechanisms provides actionable insight for execution algorithm design: the timing and spacing of child orders (splitting) and the availability of replenished liquidity are the key drivers of impact, not the metaorder size distribution or visible book shape alone. This has direct implications for VWAP/TWAP execution strategies, participation rate calibration, and market impact cost estimation. The rejection of GGPS, FGLW, and LOB walking as standalone explanations challenges commonly used impact models in practice.

The ABM itself is relatively straightforward to implement: four agent types with fixed rules, a continuous double-auction LOB, Pareto-distributed order sizes, Poisson child-order arrivals, and Dirichlet splitting. The simulation is embarrassingly parallel across 2000 stocks. However, the full analysis pipeline (metaorder reconstruction, per-day normalization, logarithmic binning, relative least-squares fitting, Hill estimation of tail exponents, LOB shape fitting for gamma, and eight counterfactual scenarios) requires careful implementation. The 10^6-step simulation per stock and 2000-stock ensemble demand significant compute (~3 hours on 40 cores). Reproducing the stylized-fact checks and the three-theory stress test adds further complexity.

The simulation code and analysis scripts are stated to be available from the corresponding author on reasonable request. All model parameters are explicitly specified (agent counts, Pareto shapes, Poisson rates, tick sizes, simulation lengths). The 2000-stock baseline required ~3 hours on a 40-core Xeon server. However, no public repository is linked, and the code is only available 'on reasonable request,' which limits immediate reproducibility. Random seeds are mentioned as independent per stock but not published. The model is minimal-intelligence with fixed behavioral rules, reducing ambiguity in implementation.