Nonparametric Estimation of Self- and Cross-Impact

ArXiv ID: 2510.06879 “View on arXiv”

Authors: Natascha Hey, Eyal Neuman, Sturmius Tuschmann

Abstract

We introduce an offline nonparametric estimator for concave multi-asset propagator models based on a dataset of correlated price trajectories and metaorders. Compared to parametric models, our framework avoids parameter explosion in the multi-asset case and yields confidence bounds for the estimator. We implement the estimator using both proprietary metaorder data from Capital Fund Management (CFM) and publicly available S&P order flow data, where we augment the former dataset using a metaorder proxy. In particular, we provide unbiased evidence that self-impact is concave and exhibits a shifted power-law decay, and show that the metaorder proxy stabilizes the calibration. Moreover, we find that introducing cross-impact provides a significant gain in explanatory power, with concave specifications outperforming linear ones, suggesting that the square-root law extends to cross-impact. We also measure asymmetric cross-impact between assets driven by relative liquidity differences. Finally, we demonstrate that a shape-constrained projection of the nonparametric kernel not only ensures interpretability but also slightly outperforms established parametric models in terms of predictive accuracy.

Keywords: Market Impact, Propagator Models, Metaorders, Cross-impact, Nonparametric Estimation, Equities

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 8.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced nonparametric estimation, concave propagator models, and rigorous theoretical analysis of price manipulation, indicating high math complexity. It demonstrates high empirical rigor through implementation on both proprietary and public datasets, with statistical validation, confidence bounds, and backtest-ready predictive comparisons against parametric benchmarks.

  flowchart TD
    A["Research Goal:<br/>Estimate multi-asset<br/>market impact nonparametrically"] --> B["Methodology:<br/>Offline nonparametric estimator<br/>for concave propagator models"]
    B --> C["Data & Inputs"]
    C --> D["Proprietary CFM Metaorders<br/>& Public S&P Order Flow<br/>+ Metaorder Proxy"]
    D --> E["Computational Process:<br/>Shape-constrained projection<br/>of nonparametric kernel"]
    E --> F["Key Outcomes"]
    F --> G["1. Self-impact is concave<br/>& decays via shifted power-law"]
    F --> H["2. Cross-impact adds<br/>explanatory power; concave > linear"]
    F --> I["3. Asymmetric cross-impact<br/>driven by liquidity differences"]
    F --> J["4. Nonparametric model<br/>outperforms parametric benchmarks"]