market impact estimation

In public-market data, empirical metaorder market impact exhibits linear price drift and weak reversal, contradicting conventional transient impact models that predict concave trajectories and strong reversal. This discrepancy arises because standard statistical models ignore the endogenous generation mechanism of order flow autocorrelation. Method: We propose a corrected transient impact model incorporating the assumption that only a fraction of the metaorder generates observable order flow, and we derive a critical condition on the price–order-flow kernel that induces permanent impact. Using order-flow autocorrelation analysis, kernel dynamics modeling, and empirical financial econometrics, we calibrate the model to real execution data. Contribution/Results: Our framework successfully replicates the empirically observed linear impact path and weak reversal. It identifies a general mechanism for impact estimation distortion under publicly available data, resolving a long-standing inconsistency in market microstructure theory. The results provide a new theoretical benchmark for transaction cost modeling and refine the interpretation of impact decay in limit-order-book markets.

This study addresses the optimal execution problem in statistical arbitrage under path-dependent trading signals, incorporating temporary market impact, inventory risk, terminal liquidation, and an approximate dollar-neutrality constraint. The work innovatively models both the alpha signal and trading speed as linear functionals of time-augmented, path-truncated signatures, thereby unifying signal generation and execution within a single framework. A quadratic reduction theorem is introduced, transforming the original infinite-dimensional path-dependent optimization into a finite-dimensional concave quadratic program, which enables efficient computation of optimal strategy coefficients. Backtesting on historical stock pairs using a mean-reverting log-spread model demonstrates that the proposed strategy significantly outperforms the conventional z-score threshold benchmark in terms of turnover-adjusted returns.

This paper addresses the long-standing debate on the microfoundations of price impact: whether it arises mechanically from order flow or informationally from informed trading. Using high-frequency, trader-identified order-level data from the Tokyo Stock Exchange (2012–2018), we provide the first empirical evidence of the square-root impact law at the individual order level and discover that its temporal decay follows an inverse square-root pattern—collectively termed the “double square-root law”: impact ∝ √volume × 1/√time. Through meta-order reconstruction, anonymized control experiments, and nonparametric impact curve estimation, we demonstrate the robustness of this law and show that synthetically reconstructed meta-orders replicate observed impact dynamics. Our findings strongly support a purely mechanical origin of price impact, offering the first high-resolution empirical validation for market microstructure theory and challenging the dominant informational paradigm.

In resource exchange markets, reconciling efficiency and fairness is challenging due to endowment heterogeneity and coarse-grained priority schemes. Method: This paper proposes a novel parametric linear-equation-based trading mechanism design paradigm. Unlike conventional graph-theoretic cycle-detection clearing methods, our framework explicitly models global trading relationships and encodes fairness axioms—such as envy-freeness and proportionality—as tunable parameter constraints, ensuring mechanism transparency, interpretability, and flexible calibration. Contribution/Results: We prove that the mechanism strictly guarantees Pareto optimality and derive computationally efficient, polynomial-time algorithms for multiple classical market models. Experiments demonstrate low computational complexity, straightforward deployment, and cross-model generalizability. Our approach provides a unified, practical, and theoretically grounded modeling framework for designing fair and efficient resource exchange markets.

This study addresses the common oversight in existing reinforcement learning trading environments, which often neglect or oversimplify transaction costs, leading to strategies that fail in real-world deployment. Building upon the Almgren-Chriss framework and the square-root market impact law, this work proposes three open-source, Gymnasium-compatible trading environments that, for the first time, systematically incorporate empirically validated nonlinear market impact models. These environments support modular cost structures, exponentially decaying permanent impact, and fine-grained logging. Integrated with FinRL-Meta extensions and Optuna-based hyperparameter optimization, five state-of-the-art deep reinforcement learning algorithms are evaluated on NASDAQ-100 data. Results demonstrate that adopting the proposed model reduces average daily trading costs from $200,000 to $8,000 and turnover from 19% to 1%; hyperparameter optimization further cuts costs by up to 82%, with algorithm performance shown to be highly sensitive to the fidelity of cost modeling.

This study addresses the trade-off among execution probability, adverse selection, and opportunity cost in limit order trading by proposing a mesoscale optimal passive execution strategy. Embedding two empirically observed microstructural features—namely, the exponential decay of limit order fill probability with quote distance and the short-term linear price response to order flow imbalance—into a stochastic control framework, the work derives for the first time a passively induced market impact rate exhibiting exponential decay and solves for the corresponding optimal liquidation policy. The model is validated on both NASDAQ equity and foreign exchange data and extends naturally to settings involving heterogeneous decay rates, instantaneous impact, and target execution schedules, thereby establishing a theoretical foundation and practical mechanism for tactical passive execution.

Estimating market impact requires reconstructing counterfactual price paths for unexecuted trades under shared sources of randomness, yet these paths are inherently unobservable. This work proposes the first exact conditional simulation method for history-dependent marked point processes, leveraging a sparse representation of Poisson random measures to enable event-driven reconstruction of counterfactual trajectories under perturbed intensities. The approach yields unbiased and consistent path-level estimates of market impact for aggressive, passive, and hybrid trading strategies alike, establishing a rigorous theoretical foundation and an efficient computational framework for evaluating trading impact in high-frequency settings.

This study addresses the reproducibility challenges of the multi-market fragmentation and delayed arbitrage agent-based model proposed by Wah and Wellman (2016), which stemmed from insufficient implementation details and limited quantitative reporting. Leveraging the authors’ subsequently released code, we formalize the modeling process using the ODD protocol and enhance statistical robustness by increasing simulation runs and applying bootstrapping to construct confidence intervals. Our replication achieves relational equivalence across most metrics but rejects quantitative alignment under non-zero delay conditions. Notably, we uncover that conclusions regarding fragmentation effects are highly sensitive to the specific implementation of greedy strategies; under alternative strategies, market fragmentation actually reduces execution time and improves trader welfare. This work thus provides the first complete and transparent replication framework for the original model.

This study addresses the challenge of identifying whether algorithmic trading strategies act as net consumers or providers of liquidity using only observable transaction and price history, and quantifies their impact on market liquidity and welfare. By integrating multi-period regret decomposition, an AR(1) transaction cost model, and Roll’s implied spread estimator, the authors develop an O(Tnd)-efficient algorithm that, without access to internal signals or objective functions, uniquely recovers the informed trader–market maker dichotomy central to Kyle’s model. The work introduces a liquidity balance condition, uncovers quadratic (N²-scale) fire-sale externalities, and successfully calibrates the framework on CRSP U.S. equity data from 2016 to 2025, effectively capturing liquidity dynamics during the COVID-19 pandemic and the 2022 interest rate shocks.