Limit Order Book

Optimal Quoting under Adverse Selection and Price Reading ArXiv ID: 2508.20225 “View on arXiv” Authors: Alexander Barzykin, Philippe Bergault, Olivier Guéant, Malo Lemmel Abstract Over the past decade, many dealers have implemented algorithmic models to automatically respond to RFQs and manage flows originating from their electronic platforms. In parallel, building on the foundational work of Ho and Stoll, and later Avellaneda and Stoikov, the academic literature on market making has expanded to address trade size distributions, client tiering, complex price dynamics, alpha signals, and the internalization versus externalization dilemma in markets with dealer-to-client and interdealer-broker segments. In this paper, we tackle two critical dimensions: adverse selection, arising from the presence of informed traders, and price reading, whereby the market maker’s own quotes inadvertently reveal the direction of their inventory. These risks are well known to practitioners, who routinely face informed flows and algorithms capable of extracting signals from quoting behavior. Yet they have received limited attention in the quantitative finance literature, beyond stylized toy models with limited actionability. Extending the existing literature, we propose a tractable and implementable framework that enables market makers to adjust their quotes with greater awareness of informational risk. ...

Bimodal Dynamics of the Artificial Limit Order Book Stock Exchange with Autonomous Traders ArXiv ID: 2508.17837 “View on arXiv” Authors: Matej Steinbacher, Mitja Steinbacher, Matjaz Steinbacher Abstract This paper explores the bifurcative dynamics of an artificial stock market exchange (ASME) with endogenous, myopic traders interacting through a limit order book (LOB). We showed that agent-based price dynamics possess intrinsic bistability, which is not a result of randomness but an emergent property of micro-level trading rules, where even identical initial conditions lead to qualitatively different long-run price equilibria: a deterministic zero-price state and a persistent positive-price equilibrium. The study also identifies a metastable region with elevated volatility between the basins of attraction and reveals distinct transient behaviors for trajectories converging to these equilibria. Furthermore, we observe that the system is neither entirely regular nor fully chaotic. By highlighting the emergence of divergent market outcomes from uniform beginnings, this work contributes a novel perspective on the inherent path dependence and complex dynamics of artificial stock markets. ...

Detecting Multilevel Manipulation from Limit Order Book via Cascaded Contrastive Representation Learning ArXiv ID: 2508.17086 “View on arXiv” Authors: Yushi Lin, Peng Yang Abstract Trade-based manipulation (TBM) undermines the fairness and stability of financial markets drastically. Spoofing, one of the most covert and deceptive TBM strategies, exhibits complex anomaly patterns across multilevel prices, while often being simplified as a single-level manipulation. These patterns are usually concealed within the rich, hierarchical information of the Limit Order Book (LOB), which is challenging to leverage due to high dimensionality and noise. To address this, we propose a representation learning framework combining a cascaded LOB representation architecture with supervised contrastive learning. Extensive experiments demonstrate that our framework consistently improves detection performance across diverse models, with Transformer-based architectures achieving state-of-the-art results. In addition, we conduct systematic analyses and ablation studies to investigate multilevel manipulation and the contributions of key components for detection, offering broader insights into representation learning and anomaly detection for complex time series data. ...

Prediction of high-frequency futures return directions based on the mean uncertainty classification methods: An application in China’s future market ArXiv ID: 2508.06914 “View on arXiv” Authors: Ying Peng, Yifan Zhang, Xin Wang Abstract In this paper, we mainly focus on the prediction of short-term average return directions in China’s high-frequency futures market. As minor fluctuations with limited amplitude and short duration are typically regarded as random noise, only price movements of sufficient magnitude qualify as statistically significant signals. Therefore data imbalance emerges as a key problem during predictive modeling. From the view of data distribution imbalance, we employee the mean-uncertainty logistic regression (mean-uncertainty LR) classification method under the sublinear expectation (SLE) framework, and further propose the mean-uncertainty support vector machines (mean-uncertainty SVM) method for the prediction. Corresponding investment strategies are developed based on the prediction results. For data selection, we utilize trading data and limit order book data of the top 15 liquid products among the most active contracts in China’s future market. Empirical results demonstrate that comparing with conventional LR-related and SVM-related imbalanced data classification methods, the two mean-uncertainty approaches yields significant advantages in both classification metrics and average returns per trade. ...

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. ...

Functionally Generated Portfolios Under Stochastic Transaction Costs: Theory and Empirical Evidence ArXiv ID: 2507.09196 “View on arXiv” Authors: Nader Karimi, Erfan Salavati Abstract Assuming frictionless trading, classical stochastic portfolio theory (SPT) provides relative arbitrage strategies. However, the costs associated with real-world execution are state-dependent, volatile, and under increasing stress during liquidity shocks. Using an Ito diffusion that may be connected with asset prices, we extend SPT to a continuous-time equity market with proportional, stochastic transaction costs. We derive closed-form lower bounds on cost-adjusted relative wealth for a large class of functionally generated portfolios; these bounds provide sufficient conditions for relative arbitrage to survive random costs. A limit-order-book cost proxy in conjunction with a Milstein scheme validates the theoretical order-of-magnitude estimates. Finally, we use intraday bid-ask spreads as a stand-in for cost volatility in a back-test of CRSP small-cap data (1994–2024). Despite experiencing larger declines during the 2008 and 2020 liquidity crises, diversity- and entropy-weighted portfolios continue to beat the value-weighted benchmark by 3.6 and 2.9 percentage points annually, respectively, after cost deduction. ...

Reinforcement Learning for Trade Execution with Market Impact ArXiv ID: 2507.06345 “View on arXiv” Authors: Patrick Cheridito, Moritz Weiss Abstract In this paper, we introduce a novel reinforcement learning framework for optimal trade execution in a limit order book. We formulate the trade execution problem as a dynamic allocation task whose objective is the optimal placement of market and limit orders to maximize expected revenue. By employing multivariate logistic-normal distributions to model random allocations, the framework enables efficient training of the reinforcement learning algorithm. Numerical experiments show that the proposed method outperforms traditional benchmark strategies in simulated limit order book environments featuring noise traders submitting random orders, tactical traders responding to order book imbalances, and a strategic trader seeking to acquire or liquidate an asset position. ...

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. ...

Learning the Spoofability of Limit Order Books With Interpretable Probabilistic Neural Networks ArXiv ID: 2504.15908 “View on arXiv” Authors: Unknown Abstract This paper investigates real-time detection of spoofing activity in limit order books, focusing on cryptocurrency centralized exchanges. We first introduce novel order flow variables based on multi-scale Hawkes processes that account both for the size and placement distance from current best prices of new limit orders. Using a Level-3 data set, we train a neural network model to predict the conditional probability distribution of mid price movements based on these features. Our empirical analysis highlights the critical role of the posting distance of limit orders in the price formation process, showing that spoofing detection models that do not take the posting distance into account are inadequate to describe the data. Next, we propose a spoofing detection framework based on the probabilistic market manipulation gain of a spoofing agent and use the previously trained neural network to compute the expected gain. Running this algorithm on all submitted limit orders in the period 2024-12-04 to 2024-12-07, we find that 31% of large orders could spoof the market. Because of its simple neuronal architecture, our model can be run in real time. This work contributes to enhancing market integrity by providing a robust tool for monitoring and mitigating spoofing in both cryptocurrency exchanges and traditional financial markets. ...

Deep Learning Models Meet Financial Data Modalities ArXiv ID: 2504.13521 “View on arXiv” Authors: Unknown Abstract Algorithmic trading relies on extracting meaningful signals from diverse financial data sources, including candlestick charts, order statistics on put and canceled orders, traded volume data, limit order books, and news flow. While deep learning has demonstrated remarkable success in processing unstructured data and has significantly advanced natural language processing, its application to structured financial data remains an ongoing challenge. This study investigates the integration of deep learning models with financial data modalities, aiming to enhance predictive performance in trading strategies and portfolio optimization. We present a novel approach to incorporating limit order book analysis into algorithmic trading by developing embedding techniques and treating sequential limit order book snapshots as distinct input channels in an image-based representation. Our methodology for processing limit order book data achieves state-of-the-art performance in high-frequency trading algorithms, underscoring the effectiveness of deep learning in financial applications. ...