Price Impact

High-Frequency Analysis of a Trading Game with Transient Price Impact ArXiv ID: 2512.11765 “View on arXiv” Authors: Marcel Nutz, Alessandro Prosperi Abstract We study the high-frequency limit of an $n$-trader optimal execution game in discrete time. Traders face transient price impact of Obizhaeva–Wang type in addition to quadratic instantaneous trading costs $θ(ΔX_t)^2$ on each transaction $ΔX_t$. There is a unique Nash equilibrium in which traders choose liquidation strategies minimizing expected execution costs. In the high-frequency limit where the grid of trading dates converges to the continuous interval $[“0,T”]$, the discrete equilibrium inventories converge at rate $1/N$ to the continuous-time equilibrium of an Obizhaeva–Wang model with additional quadratic costs $\vartheta_0(ΔX_0)^2$ and $\vartheta_T(ΔX_T)^2$ on initial and terminal block trades, where $\vartheta_0=(n-1)/2$ and $\vartheta_T=1/2$. The latter model was introduced by Campbell and Nutz as the limit of continuous-time equilibria with vanishing instantaneous costs. Our results extend and refine previous results of Schied, Strehle, and Zhang for the particular case $n=2$ where $\vartheta_0=\vartheta_T=1/2$. In particular, we show how the coefficients $\vartheta_0=(n-1)/2$ and $\vartheta_T=1/2$ arise endogenously in the high-frequency limit: the initial and terminal block costs of the continuous-time model are identified as the limits of the cumulative discrete instantaneous costs incurred over small neighborhoods of $0$ and $T$, respectively, and these limits are independent of $θ>0$. By contrast, when $θ=0$ the discrete-time equilibrium strategies and costs exhibit persistent oscillations and admit no high-frequency limit, mirroring the non-existence of continuous-time equilibria without boundary block costs. Our results show that two different types of trading frictions – a fine time discretization and small instantaneous costs in continuous time – have similar regularizing effects and select a canonical model in the limit. ...

A Stochastic Thermodynamics Approach to Price Impact and Round-Trip Arbitrage: Theory and Empirical Implications ArXiv ID: 2512.03123 “View on arXiv” Authors: Amit Kumar Jha Abstract This paper develops a comprehensive theoretical framework that imports concepts from stochastic thermodynamics to model price impact and characterize the feasibility of round-trip arbitrage in financial markets. A trading cycle is treated as a non-equilibrium thermodynamic process, where price impact represents dissipative work and market noise plays the role of thermal fluctuations. The paper proves a Financial Second Law: under general convex impact functionals, any round-trip trading strategy yields non-positive expected profit. This structural constraint is complemented by a fluctuation theorem that bounds the probability of profitable cycles in terms of dissipated work and market volatility. The framework introduces a statistical ensemble of trading strategies governed by a Gibbs measure, leading to a free energy decomposition that connects expected cost, strategy entropy, and a market temperature parameter. The framework provides rigorous, testable inequalities linking microstructural impact to macroscopic no-arbitrage conditions, offering a novel physics-inspired perspective on market efficiency. The paper derives explicit analytical results for prototypical trading strategies and discusses empirical validation protocols. ...

Option market making with hedging-induced market impact ArXiv ID: 2511.02518 “View on arXiv” Authors: Paulin Aubert, Etienne Chevalier, Vathana Ly Vath Abstract This paper develops a model for option market making in which the hedging activity of the market maker generates price impact on the underlying asset. The option order flow is modeled by Cox processes, with intensities depending on the state of the underlying and on the market maker’s quoted prices. The resulting dynamics combine stochastic option demand with both permanent and transient impact on the underlying, leading to a coupled evolution of inventory and price. We first study market manipulation and arbitrage phenomena that may arise from the feedback between option trading and underlying impact. We then establish the well-posedness of the mixed control problem, which involves continuous quoting decisions and impulsive hedging actions. Finally, we implement a numerical method based on policy optimization to approximate optimal strategies and illustrate the interplay between option market liquidity, inventory risk, and underlying impact. ...

Exponential Hedging for the Ornstein-Uhlenbeck Process in the Presence of Linear Price Impact ArXiv ID: 2509.25472 “View on arXiv” Authors: Yan Dolinsky Abstract In this work we study a continuous time exponential utility maximization problem in the presence of a linear temporary price impact. More precisely, for the case where the risky asset is given by the Ornstein-Uhlenbeck diffusion process we compute the optimal portfolio strategy and the corresponding value. Our method of solution relies on duality, and it is purely probabilistic. ...

Returns and Order Flow Imbalances: Intraday Dynamics and Macroeconomic News Effects ArXiv ID: 2508.06788 “View on arXiv” Authors: Makoto Takahashi Abstract We study the interaction between returns and order flow imbalances in the S&P 500 E-mini futures market using a structural VAR model identified through heteroskedasticity. The model is estimated at one-second frequency for each 15-minute interval, capturing both intraday variation and endogeneity due to time aggregation. We find that macroeconomic news announcements sharply reshape price-flow dynamics: price impact rises, flow impact declines, return volatility spikes, and flow volatility falls. Pooling across days, both price and flow impacts are significant at the one-second horizon, with estimates broadly consistent with stylized limit-order-book predictions. Impulse responses indicate that shocks dissipate almost entirely within a second. Structural parameters and volatilities also exhibit pronounced intraday variation tied to liquidity, trading intensity, and spreads. These results provide new evidence on high-frequency price formation and liquidity, highlighting the role of public information and order submission in shaping market quality. ...

Towards Realistic and Interpretable Market Simulations: Factorizing Financial Power Law using Optimal Transport ArXiv ID: 2507.09863 “View on arXiv” Authors: Ryuji Hashimoto, Kiyoshi Izumi Abstract We investigate the mechanisms behind the power-law distribution of stock returns using artificial market simulations. While traditional financial theory assumes Gaussian price fluctuations, empirical studies consistently show that the tails of return distributions follow a power law. Previous research has proposed hypotheses for this phenomenon – some attributing it to investor behavior, others to institutional demand imbalances. However, these factors have rarely been modeled together to assess their individual and joint contributions. The complexity of real financial markets complicates the isolation of the contribution of a single component using existing data. To address this, we construct artificial markets and conduct controlled experiments using optimal transport (OT) as a quantitative similarity measure. Our proposed framework incrementally introduces behavioral components into the agent models, allowing us to compare each simulation output with empirical data via OT distances. The results highlight that informational effect of prices plays a dominant role in reproducing power-law behavior and that multiple components interact synergistically to amplify this effect. ...

Optimal Execution under Liquidity Uncertainty ArXiv ID: 2506.11813 “View on arXiv” Authors: Etienne Chevalier, Yadh Hafsi, Vathana Ly Vath, Sergio Pulido Abstract We study an optimal execution strategy for purchasing a large block of shares over a fixed time horizon. The execution problem is subject to a general price impact that gradually dissipates due to market resilience. This resilience is modeled through a potentially arbitrary limit-order book shape. To account for liquidity dynamics, we introduce a stochastic volume effect governing the recovery of the deviation process, which represents the difference between the impacted and unaffected price. Additionally, we incorporate stochastic liquidity variations through a regime-switching Markov chain to capture abrupt shifts in market conditions. We study this singular control problem, where the trader optimally determines the timing and rate of purchases to minimize execution costs. The associated value function to this optimization problem is shown to satisfy a system of variational Hamilton-Jacobi-Bellman inequalities. Moreover, we establish that it is the unique viscosity solution to this HJB system and study the analytical properties of the free boundary separating the execution and continuation regions. To illustrate our results, we present numerical examples under different limit-order book configurations, highlighting the interplay between price impact, resilience dynamics, and stochastic liquidity regimes in shaping the optimal execution strategy. ...

Agent-based Liquidity Risk Modelling for Financial Markets ArXiv ID: 2505.15296 “View on arXiv” Authors: Perukrishnen Vytelingum, Rory Baggott, Namid Stillman, Jianfei Zhang, Dingqiu Zhu, Tao Chen, Justin Lyon Abstract In this paper, we describe a novel agent-based approach for modelling the transaction cost of buying or selling an asset in financial markets, e.g., to liquidate a large position as a result of a margin call to meet financial obligations. The simple act of buying or selling in the market causes a price impact and there is a cost described as liquidity risk. For example, when selling a large order, there is market slippage – each successive trade will execute at the same or worse price. When the market adjusts to the new information revealed by the execution of such a large order, we observe in the data a permanent price impact that can be attributed to the change in the fundamental value as market participants reassess the value of the asset. In our ABM model, we introduce a novel mechanism where traders assume orderflow is informed and each trade reveals some information about the value of the asset, and traders update their belief of the fundamental value for every trade. The result is emergent, realistic price impact without oversimplifying the problem as most stylised models do, but within a realistic framework that models the exchange with its protocols, its limit orderbook and its auction mechanism and that can calculate the transaction cost of any execution strategy without limitation. Our stochastic ABM model calculates the costs and uncertainties of buying and selling in a market by running Monte-Carlo simulations, for a better understanding of liquidity risk and can be used to optimise for optimal execution under liquidity risk. We demonstrate its practical application in the real world by calculating the liquidity risk for the Hang-Seng Futures Index. ...

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. ...

Modeling metaorder impact with a Non-Markovian Zero Intelligence model ArXiv ID: 2503.05254 “View on arXiv” Authors: Unknown Abstract Devising models of the limit order book that realistically reproduce the market response to exogenous trades is extremely challenging and fundamental in order to test trading strategies. We propose a novel explainable model for small tick assets, the Non-Markovian Zero Intelligence, which is a variant of the well-known Zero Intelligence model. The main modification is that the probability of limit orders’ signs (buy/sell) is not constant but is a function of the exponentially weighted mid-price return, representing the past price dynamics, and can be interpreted as the reaction of traders with reservation prices to the price trend. With numerical simulations and analytical arguments, we show that the model predicts a concave price path during a metaorder execution and to a price reversion after the execution ends, as empirically observed. We analyze in-depth the mechanism at the root of the arising concavity, the components which constitute the price impact in our model, and the dependence of the results on the two main parameters, namely the time scale and the strength of the reaction of traders to the price trend. ...