Nonparametric Estimation of Self- and Cross-Impact

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.