Metaorders

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. ...

The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility II: An Artificial Market Generator ArXiv ID: 2509.05065 “View on arXiv” Authors: Guillaume Maitrier, Grégoire Loeper, Jean-Philippe Bouchaud Abstract This work extends and complements our previous theoretical paper on the subtle interplay between impact, order flow and volatility. In the present paper, we generate synthetic market data following the specification of that paper and show that the approximations made there are actually justified, which provides quantitative support our conclusion that price volatility can be fully explained by the superposition of correlated metaorders which all impact prices, on average, as a square-root of executed volume. One of the most striking predictions of our model is the structure of the correlation between generalized order flow and returns, which is observed empirically and reproduced using our synthetic market generator. Furthermore, we were able to construct proxy metaorders from our simulated order flow that reproduce the square-root law of market impact, lending further credence to the proposal made in Ref. [“2”] to measure the impact of real metaorders from tape data (i.e. anonymized trades), which was long thought to be impossible. ...

Generating realistic metaorders from public data ArXiv ID: 2503.18199 “View on arXiv” Authors: Unknown Abstract This paper introduces a novel algorithm for generating realistic metaorders from public trade data, addressing a longstanding challenge in price impact research that has traditionally relied on proprietary datasets. Our method effectively recovers all established stylized facts of metaorders impact, such as the Square Root Law, the concave profile during metaorder execution, and the post-execution decay. This algorithm not only overcomes the dependence on proprietary data, a major barrier to research reproducibility, but also enables the creation of larger and more robust datasets that may increase the quality of empirical studies. Our findings strongly suggest that average realized short-term price impact is not due to information revelation (as in the Kyle framework) but has a mechanical origin which could explain the universality of the Square Root Law. ...

Why is the estimation of metaorder impact with public market data so challenging? ArXiv ID: 2501.17096 “View on arXiv” Authors: Unknown Abstract Estimating market impact and transaction costs of large trades (metaorders) is a very important topic in finance. However, using models of price and trade based on public market data provide average price trajectories which are qualitatively different from what is observed during real metaorder executions: the price increases linearly, rather than in a concave way, during the execution and the amount of reversion after its end is very limited. We claim that this is a generic phenomenon due to the fact that even sophisticated statistical models are unable to correctly describe the origin of the autocorrelation of the order flow. We propose a modified Transient Impact Model which provides more realistic trajectories by assuming that only a fraction of the metaorder trading triggers market order flow. Interestingly, in our model there is a critical condition on the kernels of the price and order flow equations in which market impact becomes permanent. ...