Limit Order Book (LOB)

Event-Based Limit Order Book Simulation under a Neural Hawkes Process: Application in Market-Making ArXiv ID: 2502.17417 “View on arXiv” Authors: Unknown Abstract In this paper, we propose an event-driven Limit Order Book (LOB) model that captures twelve of the most observed LOB events in exchange-based financial markets. To model these events, we propose using the state-of-the-art Neural Hawkes process, a more robust alternative to traditional Hawkes process models. More specifically, this model captures the dynamic relationships between different event types, particularly their long- and short-term interactions, using a Long Short-Term Memory neural network. Using this framework, we construct a midprice process that captures the event-driven behavior of the LOB by simulating high-frequency dynamics like how they appear in real financial markets. The empirical results show that our model captures many of the broader characteristics of the price fluctuations, particularly in terms of their overall volatility. We apply this LOB simulation model within a Deep Reinforcement Learning Market-Making framework, where the trading agent can now complete trade order fills in a manner that closely resembles real-market trade execution. Here, we also compare the results of the simulated model with those from real data, highlighting how the overall performance and the distribution of trade order fills closely align with the same analysis on real data. ...

TLOB: A Novel Transformer Model with Dual Attention for Price Trend Prediction with Limit Order Book Data ArXiv ID: 2502.15757 “View on arXiv” Authors: Unknown Abstract Price Trend Prediction (PTP) based on Limit Order Book (LOB) data is a fundamental challenge in financial markets. Despite advances in deep learning, existing models fail to generalize across different market conditions and assets. Surprisingly, by adapting a simple MLP-based architecture to LOB, we show that we surpass SoTA performance; thus, challenging the necessity of complex architectures. Unlike past work that shows robustness issues, we propose TLOB, a transformer-based model that uses a dual attention mechanism to capture spatial and temporal dependencies in LOB data. This allows it to adaptively focus on the market microstructure, making it particularly effective for longer-horizon predictions and volatile market conditions. We also introduce a new labeling method that improves on previous ones, removing the horizon bias. We evaluate TLOB’s effectiveness across four horizons, using the established FI-2010 benchmark, a NASDAQ and a Bitcoin dataset. TLOB outperforms SoTA methods in every dataset and horizon. Additionally, we empirically show how stock price predictability has declined over time, -6.68 in F1-score, highlighting the growing market efficiency. Predictability must be considered in relation to transaction costs, so we experimented with defining trends using an average spread, reflecting the primary transaction cost. The resulting performance deterioration underscores the complexity of translating trend classification into profitable trading strategies. We argue that our work provides new insights into the evolving landscape of stock price trend prediction and sets a strong foundation for future advancements in financial AI. We release the code at https://github.com/LeonardoBerti00/TLOB. ...

Limit Order Book Event Stream Prediction with Diffusion Model ArXiv ID: 2412.09631 “View on arXiv” Authors: Unknown Abstract Limit order book (LOB) is a dynamic, event-driven system that records real-time market demand and supply for a financial asset in a stream flow. Event stream prediction in LOB refers to forecasting both the timing and the type of events. The challenge lies in modeling the time-event distribution to capture the interdependence between time and event type, which has traditionally relied on stochastic point processes. However, modeling complex market dynamics using stochastic processes, e.g., Hawke stochastic process, can be simplistic and struggle to capture the evolution of market dynamics. In this study, we present LOBDIF (LOB event stream prediction with diffusion model), which offers a new paradigm for event stream prediction within the LOB system. LOBDIF learns the complex time-event distribution by leveraging a diffusion model, which decomposes the time-event distribution into sequential steps, with each step represented by a Gaussian distribution. Additionally, we propose a denoising network and a skip-step sampling strategy. The former facilitates effective learning of time-event interdependence, while the latter accelerates the sampling process during inference. By introducing a diffusion model, our approach breaks away from traditional modeling paradigms, offering novel insights and providing an effective and efficient solution for learning the time-event distribution in order streams within the LOB system. Extensive experiments using real-world data from the limit order books of three widely traded assets confirm that LOBDIF significantly outperforms current state-of-the-art methods. ...

MarketGPT: Developing a Pre-trained transformer (GPT) for Modeling Financial Time Series ArXiv ID: 2411.16585 “View on arXiv” Authors: Unknown Abstract This work presents a generative pre-trained transformer (GPT) designed for modeling financial time series. The GPT functions as an order generation engine within a discrete event simulator, enabling realistic replication of limit order book dynamics. Our model leverages recent advancements in large language models to produce long sequences of order messages in a steaming manner. Our results demonstrate that the model successfully reproduces key features of order flow data, even when the initial order flow prompt is no longer present within the model’s context window. Moreover, evaluations reveal that the model captures several statistical properties, or ‘stylized facts’, characteristic of real financial markets and broader macro-scale data distributions. Collectively, this work marks a significant step toward creating high-fidelity, interactive market simulations. ...

Optimal Execution with Reinforcement Learning ArXiv ID: 2411.06389 “View on arXiv” Authors: Unknown Abstract This study investigates the development of an optimal execution strategy through reinforcement learning, aiming to determine the most effective approach for traders to buy and sell inventory within a finite time horizon. Our proposed model leverages input features derived from the current state of the limit order book and operates at a high frequency to maximize control. To simulate this environment and overcome the limitations associated with relying on historical data, we utilize the multi-agent market simulator ABIDES, which provides a diverse range of depth levels within the limit order book. We present a custom MDP formulation followed by the results of our methodology and benchmark the performance against standard execution strategies. Results show that the reinforcement learning agent outperforms standard strategies and offers a practical foundation for real-world trading applications. ...

Optimal Execution under Incomplete Information ArXiv ID: 2411.04616 “View on arXiv” Authors: Unknown Abstract We study optimal liquidation strategies under partial information for a single asset within a finite time horizon. We propose a model tailored for high-frequency trading, capturing price formation driven solely by order flow through mutually stimulating marked Hawkes processes. The model assumes a limit order book framework, accounting for both permanent price impact and transient market impact. Importantly, we incorporate liquidity as a hidden Markov process, influencing the intensities of the point processes governing bid and ask prices. Within this setting, we formulate the optimal liquidation problem as an impulse control problem. We elucidate the dynamics of the hidden Markov chain’s filter and determine the related normalized filtering equations. We then express the value function as the limit of a sequence of auxiliary continuous functions, defined recursively. This characterization enables the use of a dynamic programming principle for optimal stopping problems and the determination of an optimal strategy. It also facilitates the development of an implementable algorithm to approximate the original liquidation problem. We enrich our analysis with numerical results and visualizations of candidate optimal strategies. ...

Attention-Based Reading, Highlighting, and Forecasting of the Limit Order Book ArXiv ID: 2409.02277 “View on arXiv” Authors: Unknown Abstract Managing high-frequency data in a limit order book (LOB) is a complex task that often exceeds the capabilities of conventional time-series forecasting models. Accurately predicting the entire multi-level LOB, beyond just the mid-price, is essential for understanding high-frequency market dynamics. However, this task is challenging due to the complex interdependencies among compound attributes within each dimension, such as order types, features, and levels. In this study, we explore advanced multidimensional sequence-to-sequence models to forecast the entire multi-level LOB, including order prices and volumes. Our main contribution is the development of a compound multivariate embedding method designed to capture the complex relationships between spatiotemporal features. Empirical results show that our method outperforms other multivariate forecasting methods, achieving the lowest forecasting error while preserving the ordinal structure of the LOB. ...

An Algebraic Framework for the Modeling of Limit Order Books ArXiv ID: 2406.04969 “View on arXiv” Authors: Unknown Abstract Introducing an algebraic framework for modeling limit order books (LOBs) with tools from physics and stochastic processes, our proposed framework captures the creation and annihilation of orders, order matching, and the time evolution of the LOB state. It also enables compositional settings, accommodating the interaction of heterogeneous traders and different market structures. We employ Dirac notation and generalized generating functions to describe the state space and dynamics of LOBs. The utility of this framework is shown through simulations of simplified market scenarios, illustrating how variations in trader behavior impact key market observables such as spread, return volatility, and liquidity. The algebraic representation allows for exact simulations using the Gillespie algorithm, providing a robust tool for exploring the implications of market design and policy changes on LOB dynamics. Future research can expand this framework to incorporate more complex order types, adaptive event rates, and multi-asset trading environments, offering deeper insights into market microstructure and trader behavior and estimation of key drivers for market microstructure dynamics. ...

Adaptive Optimal Market Making Strategies with Inventory Liquidation Cos ArXiv ID: 2405.11444 “View on arXiv” Authors: Unknown Abstract A novel high-frequency market-making approach in discrete time is proposed that admits closed-form solutions. By taking advantage of demand functions that are linear in the quoted bid and ask spreads with random coefficients, we model the variability of the partial filling of limit orders posted in a limit order book (LOB). As a result, we uncover new patterns as to how the demand’s randomness affects the optimal placement strategy. We also allow the price process to follow general dynamics without any Brownian or martingale assumption as is commonly adopted in the literature. The most important feature of our optimal placement strategy is that it can react or adapt to the behavior of market orders online. Using LOB data, we train our model and reproduce the anticipated final profit and loss of the optimal strategy on a given testing date using the actual flow of orders in the LOB. Our adaptive optimal strategies outperform the non-adaptive strategy and those that quote limit orders at a fixed distance from the midprice. ...

Beyond the Bid-Ask: Strategic Insights into Spread Prediction and the Global Mid-Price Phenomenon ArXiv ID: 2404.11722 “View on arXiv” Authors: Unknown Abstract This research extends the conventional concepts of the bid–ask spread (BAS) and mid-price to include the total market order book bid–ask spread (TMOBBAS) and the global mid-price (GMP). Using high-frequency trading data, we investigate these new constructs, finding that they have heavy tails and significant deviations from normality in the distributions of their log returns, which are confirmed by three different methods. We shift from a static to a dynamic analysis, employing the ARMA(1,1)-GARCH(1,1) model to capture the temporal dependencies in the return time-series, with the normal inverse Gaussian distribution used to capture the heavy tails of the returns. We apply an option pricing model to address the risks associated with the low liquidity indicated by the TMOBBAS and GMP. Additionally, we employ the Rachev ratio to evaluate the risk–return performance at various depths of the limit order book and examine tail risk interdependencies across spread levels. This study provides insights into the dynamics of financial markets, offering tools for trading strategies and systemic risk management. ...