Market Impact

Feasibility-First Satellite Integration in Robust Portfolio Architectures ArXiv ID: 2601.08721 “View on arXiv” Authors: Roberto Garrone Abstract The integration of thematic satellite allocations into core-satellite portfolio architectures is commonly approached using factor exposures, discretionary convictions, or backtested performance, with feasibility assessed primarily through liquidity screens or market-impact considerations. While such approaches may be appropriate at institutional scale, they are ill-suited to small portfolios and robustness-oriented allocation frameworks, where dominant constraints arise not from return predictability or trading capacity, but from fixed costs, irreversibility risk, and governance complexity. This paper develops a feasibility-first, non-predictive framework for satellite integration that is explicitly scale-aware. We formalize four nested feasibility layers (physical, economic, structural, and epistemic) that jointly determine whether a satellite allocation is admissible. Physical feasibility ensures implementability under concave market-impact laws; economic feasibility suppresses noise-dominated reallocations via cost-dominance threshold constraints; structural feasibility bounds satellite size through an explicit optionality budget defined by tolerable loss under thesis failure; and epistemic feasibility limits satellite breadth and dispersion through an entropy-based complexity budget. Within this hierarchy, structural optionality is identified as the primary design principle for thematic satellites, with the remaining layers acting as robustness lenses rather than optimization criteria. The framework yields closed-form feasibility bounds on satellite size, turnover, and breadth without reliance on return forecasts, factor premia, or backtested performance, providing a disciplined basis for integrating thematic satellites into small, robustness-oriented portfolios. ...

Signature approach for pricing and hedging path-dependent options with frictions ArXiv ID: 2511.23295 “View on arXiv” Authors: Eduardo Abi Jaber, Donatien Hainaut, Edouard Motte Abstract We introduce a novel signature approach for pricing and hedging path-dependent options with instantaneous and permanent market impact under a mean-quadratic variation criterion. Leveraging the expressive power of signatures, we recast an inherently nonlinear and non-Markovian stochastic control problem into a tractable form, yielding hedging strategies in (possibly infinite) linear feedback form in the time-augmented signature of the control variables, with coefficients characterized by non-standard infinite-dimensional Riccati equations on the extended tensor algebra. Numerical experiments demonstrate the effectiveness of these signature-based strategies for pricing and hedging general path-dependent payoffs in the presence of frictions. In particular, market impact naturally smooths optimal trading strategies, making low-truncated signature approximations highly accurate and robust in frictional markets, contrary to the frictionless case. ...

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. ...

Optimal hedging of an informed broker facing many traders ArXiv ID: 2506.08992 “View on arXiv” Authors: Philippe Bergault, Pierre Cardaliaguet, Wenbin Yan Abstract This paper investigates the optimal hedging strategies of an informed broker interacting with multiple traders in a financial market. We develop a theoretical framework in which the broker, possessing exclusive information about the drift of the asset’s price, engages with traders whose trading activities impact the market price. Using a mean-field game approach, we derive the equilibrium strategies for both the broker and the traders, illustrating the intricate dynamics of their interactions. The broker’s optimal strategy involves a Stackelberg equilibrium, where the broker leads and the traders follow. Our analysis also addresses the mean field limit of finite-player models and shows the convergence to the mean-field solution as the number of traders becomes large. ...

FlowOE: Imitation Learning with Flow Policy from Ensemble RL Experts for Optimal Execution under Heston Volatility and Concave Market Impacts ArXiv ID: 2506.05755 “View on arXiv” Authors: Yang Li, Zhi Chen Abstract Optimal execution in financial markets refers to the process of strategically transacting a large volume of assets over a period to achieve the best possible outcome by balancing the trade-off between market impact costs and timing or volatility risks. Traditional optimal execution strategies, such as static Almgren-Chriss models, often prove suboptimal in dynamic financial markets. This paper propose flowOE, a novel imitation learning framework based on flow matching models, to address these limitations. FlowOE learns from a diverse set of expert traditional strategies and adaptively selects the most suitable expert behavior for prevailing market conditions. A key innovation is the incorporation of a refining loss function during the imitation process, enabling flowOE not only to mimic but also to improve upon the learned expert actions. To the best of our knowledge, this work is the first to apply flow matching models in a stochastic optimal execution problem. Empirical evaluations across various market conditions demonstrate that flowOE significantly outperforms both the specifically calibrated expert models and other traditional benchmarks, achieving higher profits with reduced risk. These results underscore the practical applicability and potential of flowOE to enhance adaptive optimal execution. ...

The “double” square-root law: Evidence for the mechanical origin of market impact using Tokyo Stock Exchange data ArXiv ID: 2502.16246 “View on arXiv” Authors: Unknown Abstract Understanding the impact of trades on prices is a crucial question for both academic research and industry practice. It is well established that impact follows a square-root impact as a function of traded volume. However, the microscopic origin of such a law remains elusive: empirical studies are particularly challenging due to the anonymity of orders in public data. Indeed, there is ongoing debate about whether price impact has a mechanical origin or whether it is primarily driven by information, as suggested by many economic theories. In this paper, we revisit this question using a very detailed dataset provided by the Japanese stock exchange, containing the trader IDs for all orders sent to the exchange between 2012 and 2018. Our central result is that such a law has in fact microscopic roots and applies already at the level of single child orders, provided one waits long enough for the market to “digest” them. The mesoscopic impact of metaorders arises from a “double” square-root effect: square-root in volume of individual impact, followed by an inverse square-root decay as a function of time. Since market orders are anonymous, we expect and indeed find that these results apply to any market orders, and the impact of synthetic metaorders, reconstructed by scrambling the identity of the issuers, is described by the very same square-root impact law. We conclude that price impact is essentially mechanical, at odds with theories that emphasize the information content of such trades to explain the square-root impact law. ...

TRADES: Generating Realistic Market Simulations with Diffusion Models ArXiv ID: 2502.07071 “View on arXiv” Authors: Unknown Abstract Financial markets are complex systems characterized by high statistical noise, nonlinearity, volatility, and constant evolution. Thus, modeling them is extremely hard. Here, we address the task of generating realistic and responsive Limit Order Book (LOB) market simulations, which are fundamental for calibrating and testing trading strategies, performing market impact experiments, and generating synthetic market data. We propose a novel TRAnsformer-based Denoising Diffusion Probabilistic Engine for LOB Simulations (TRADES). TRADES generates realistic order flows as time series conditioned on the state of the market, leveraging a transformer-based architecture that captures the temporal and spatial characteristics of high-frequency market data. There is a notable absence of quantitative metrics for evaluating generative market simulation models in the literature. To tackle this problem, we adapt the predictive score, a metric measured as an MAE, to market data by training a stock price predictive model on synthetic data and testing it on real data. We compare TRADES with previous works on two stocks, reporting a 3.27 and 3.48 improvement over SoTA according to the predictive score, demonstrating that we generate useful synthetic market data for financial downstream tasks. Furthermore, we assess TRADES’s market simulation realism and responsiveness, showing that it effectively learns the conditional data distribution and successfully reacts to an experimental agent, giving sprout to possible calibrations and evaluations of trading strategies and market impact experiments. To perform the experiments, we developed DeepMarket, the first open-source Python framework for LOB market simulation with deep learning. In our repository, we include a synthetic LOB dataset composed of TRADES’s generated simulations. ...

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. ...

Deep Learning Meets Queue-Reactive: A Framework for Realistic Limit Order Book Simulation ArXiv ID: 2501.08822 “View on arXiv” Authors: Unknown Abstract The Queue-Reactive model introduced by Huang et al. (2015) has become a standard tool for limit order book modeling, widely adopted by both researchers and practitioners for its simplicity and effectiveness. We present the Multidimensional Deep Queue-Reactive (MDQR) model, which extends this framework in three ways: it relaxes the assumption of queue independence, enriches the state space with market features, and models the distribution of order sizes. Through a neural network architecture, the model learns complex dependencies between different price levels and adapts to varying market conditions, while preserving the interpretable point-process foundation of the original framework. Using data from the Bund futures market, we show that MDQR captures key market properties including the square-root law of market impact, cross-queue correlations, and realistic order size patterns. The model demonstrates particular strength in reproducing both conditional and stationary distributions of order sizes, as well as various stylized facts of market microstructure. The model achieves this while maintaining the computational efficiency needed for practical applications such as strategy development through reinforcement learning or realistic backtesting. ...