Nonparametric Estimation of Self- and Cross-Impact

2025-10-08

AI Summary

To address the “parameter explosion” problem arising from dimensional expansion in parametric propagation models for multi-asset markets, this paper proposes a shape-constrained nonparametric estimation framework for jointly modeling intra-asset (self-) and inter-asset (cross-) price impact functions. The method leverages meta-order flow proxies and publicly available order flow data, integrating kernel estimation with concavity projection—introducing concavity as a novel structural assumption in multi-asset impact modeling. Empirically, self-impact follows a shifted power-law decay, while cross-impact exhibits nonlinearity and liquidity-driven asymmetry. Experiments demonstrate that the approach eliminates parameter redundancy and substantially improves explanatory power; validates the generalizability of the square-root law to cross-impact; and achieves marginally superior predictive accuracy relative to classical parametric benchmarks.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Learning with Manifolds
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: The sharing economy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Estimating multi-asset market impact nonparametrically from price data
• Analyzing concave self-impact decay and cross-impact effects empirically
• Developing interpretable kernel projections outperforming parametric model accuracy

Innovation

• Nonparametric estimator for multi-asset propagator models
• Concave specifications outperform linear cross-impact models
• Shape-constrained projection ensures interpretability and accuracy