Limit order books (LOBs) match buyers and sellers in more than half of the world's financial markets. This survey highlights the insights that have emerged from the wealth of empirical and theoretical studies of LOBs. We examine the findings reported by statistical analyses of historical LOB data and discuss how severa…
JAX-LOB simulates thousands of LOBs for RL training.
problem Efficient simulation of large LOBs for RL training.
method GPU-accelerated JAX implementation of LOB simulator.
result JAX-LOB processes thousands of LOBs in parallel with reduced processing time.
Axial-LOB predicts stock prices from LOB data using attention layers.
problem Predicting stock price from LOB data with long-range dependencies.
method Axial-LOB uses gated position-sensitive axial attention layers to incorporate global interactions.
result Axial-LOB achieves state-of-the-art performance in stock price prediction.
LOB-Bench benchmarks generative AI for financial data, outperforming traditional models.
problem Lack of consensus on evaluating generative AI models for financial data.
method Python-based benchmark with LOB statistics and market impact metrics.
result Generative autoregressive models outperform traditional models in LOB data.
Model recreates LOB from TAQ data for small-tick stocks.
problem Lack of LOB data makes market analysis difficult.
method Combines GRU and ODE-RNN to predict LOB volumes.
result Model accurately recreates LOB with high precision.
Generative diffusion models improve financial LOB simulation and forecasting.
problem High noise and complexity in financial LOB data makes deep generative models ineffective.
method Convert LOB data to images, apply diffusion models with inpainting for long-term sequence generation.
result Our method achieves state-of-the-art performance on LOB-Bench, improving coherence over local details.
We have analyzed the statistical probabilities of limit-order book (LOB) shape through building the book using the ultra-high-frequency data from 23 liquid stocks traded on the Shenzhen Stock Exchange in 2003. We find that the averaged LOB shape has a maximum away from the same best price for both buy and sell LOBs. Th…
DSLOB creates synthetic LOB data for benchmarking forecasting algorithms under distributional shifts.
problem Challenges in dealing with out-of-distribution limit order book data.
method Multi-agent market simulator to create labeled synthetic LOB dataset with and without market stress.
result Demonstrates the need for robust forecasting algorithms to handle distributional shifts.
We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a n…
This paper uses deep RL to optimize market quotes from LOB data.
problem Optimizing quotes for market making from complex LOB data.
method Attn-LOB neural network with convolutional filters and attention mechanism for feature extraction; hybrid reward function for continuous action space.
result The RL agent outperforms traditional methods in market making tasks.
Paper uses K-NN resampling to simulate and evaluate LOB markets.
problem Simulating and evaluating limit order book (LOB) markets.
method Applies K-nearest neighbor (K-NN) resampling to LOB simulation and evaluation. result Demonstrates the effectiveness and efficiency of K-NN resampling in LOB simulation and evaluation. LOBRM model recreates limit order books from trade and quote data.
problem Lack of LOB data and limitations in LOBRM model.
method Extended LOBRM with time-weighted z-score standardization and exponential decay kernel, conducted in chronological order.
result LOBRM with decay kernel outperforms traditional models and module ensembling is effective.
Study develops advanced models to forecast complex LOB data.
problem Forecasting high-frequency data in a limit order book (LOB).
method Advanced multidimensional sequence-to-sequence models with compound multivariate embedding.
result Method outperforms other multivariate forecasting methods, achieving lowest forecasting error.
We propose a limit order book (LOB) model with dynamics that account for both the impact of the most recent order and the shape of the LOB. We present an empirical analysis showing that the type of the last order significantly alters the submission rate of immediate future orders, even after accounting for the state of…
Paper uses MBO data for high-frequency price forecasting.
problem Lack of predictive analysis on granular MBO data.
method Introduced normalisation scheme for MBO data, trained deep neural networks.
result Ensemble of MBO and LOB models improves forecasting accuracy.
DiffVolume generates realistic volume snapshots for LOBs.
problem Generating high-dimensional volume snapshots in LOBs is challenging.
method Conditional Diffusion model for volume generation.
result DiffVolume outperforms in realism, counterfactual generation, and downstream prediction.
A new algebraic framework models LOBs with physics and stochastic processes.
problem Capturing the dynamics of limit order books (LOBs).
method Algebraic framework using Dirac notation and generating functions.
result Exact simulations of market scenarios using the Gillespie algorithm.
This review examines various LOB simulation models in algorithmic trading.
problem Calibrating and fine-tuning automated trading strategies in financial markets.
method Classification and analysis of LOB simulation models based on methodology.
result Price impact is a crucial phenomenon to model in algorithmic trading.
Hybrid model simulates market dynamics using neural stochastic background traders.
problem Lack of realistic LOB simulations that combine historical data and dynamic interactions.
method Neural stochastic background trader trained on historical LOB data, embedded in multi-agent simulation.
result Hybrid model recreates stylised market facts and financial herding behaviors.
DeepFolio uses neural networks to predict stock price movements from LOB data.
problem Predicting price movements from LOB data.
method Convolutional Neural Networks (CNNs) for portfolio management.
result DeepFolio outperforms state-of-the-art models in various scenarios.
In this paper we consider classes of models that have been recently developed for quantitative finance that involve modelling a highly complex multivariate, multi-attribute stochastic process known as the Limit Order Book (LOB). The LOB is the primary data structure recorded each day intra-daily for all assets on every…
Paper proposes a deep learning method to estimate fill probabilities of limit orders in LOBs.
problem Estimating the fill probabilities of limit orders in different levels of a limit order book.
method Survival analysis model using a convolutional-Transformer encoder and a monotonic neural network decoder.
result The proposed method significantly outperforms other approaches in survival analysis.
Proposes a neural LOB model for market-making.
problem Capturing dynamic LOB events in financial markets.
method Neural Hawkes process for modeling LOB events.
result Model captures real market price fluctuations.
Study optimal market making in Hawkes LOB market using impulse control and RL.
problem Optimal market making in Hawkes LOB market with queue dynamics and endogenous price impact.
method Impulse control framework, RL approximation, deep learning method.
result Strong empirical performance and solution to HJB-QVI with deep learning.
Many commonly used liquidity measures are based on snapshots of the state of the limit order book (LOB) and can thus only provide information about instantaneous liquidity, and not regarding the local liquidity regime. However, trading in the LOB is characterised by many intra-day liquidity shocks, where the LOB genera…
This paper compares AMMs and LOBs in exchange mechanisms, formalizing complexity vs. expressiveness trade-offs.
problem Designing efficient exchange mechanisms between assets.
method Formalizes a complexity-approximation trade-off for CFMMs and LOBs, introducing an exchange complexity measure.
result Optimally expressive mechanisms can be designed with minimal complexity, allowing for arbitrary demand curves.
Adaptive market-making strategy improves profit by adjusting to order flow.
problem Optimizing market-making profits in a dynamic market environment.
method Closed-form solutions for optimal bid-ask spreads, modeling demand randomness, and adapting to market order behavior.
result Adaptive strategies outperform fixed and non-adaptive strategies.
This paper studies a limit order book (LOB) model, in which the order dynamics depend on both, the current best available prices and the current volume density functions. For the joint dynamics of the best bid price, the best ask price, and the standing volume densities on both sides of the LOB we derive a weak law of …
A novel Hawkes Process model captures order sizes in LOBs, improving fit quality and market impact studies.
problem Capturing the variability in order sizes in Limit Order Books (LOBs).
method Compound Hawkes Process with time-varying parameters and non-parametric calibration.
result Improved fit quality and empirical market impact function replication.
LOBDIF predicts limit order book events using a diffusion model.
problem Predicting the timing and type of events in a dynamic market system.
method LOBDIF uses a diffusion model to learn the complex time-event distribution in limit order book streams.
result LOBDIF significantly outperforms existing methods in real-world data experiments.
The paper develops Hawkes-based models for LOB and applies them to European, spread, and basket option pricing.
problem Developing accurate models for pricing options in the context of limit order books (LOB).
method Introduces multivariate Hawkes processes and their limit theorems, applies to European, spread, and basket options.
result Hawkes-based models provide more market forecast information than classical models.
DiffLOB models future market conditions for better decision-making.
problem Passive generative models cannot explore hypothetical market scenarios.
method Regime-conditioned diffusion model for counterfactual LOB generation.
result DiffLOB enables realistic and controllable generation of LOB trajectories.
Paper develops models for better HFT and algorithmic trading.
problem Inaccurate LOB dynamics in financial markets.
method Semi-Markov and Hawkes jump-diffusion models for LOB dynamics.
result Improved trading strategies through precise model application.
A Hawkes process with state-dependent factor models order flows in limit order books.
problem Modeling order flows in limit order books for better market prediction.
method A Hawkes process with a state-dependent factor for conditional intensity estimation.
result State-dependent formulations improve the fit of LOB models to financial data.
An ability to postpone one's execution without penalty provides an important strategic advantage in high-frequency trading. To elucidate competition between traders one has to formulate to a quantitative theory of formation of the execution price from market expectations and quotes. This theory was provided in 2005 by …
ByteGen models LOB dynamics without tokenization, achieving realistic market metrics.
problem Modeling high-frequency LOB dynamics in finance.
method Autoregressive next-byte prediction on packed binary data, using H-Net architecture.
result Successfully reproduces stylized facts of financial markets.
Simpler models outperform deep architectures with proper preprocessing and tuning.
problem Signal extraction from noisy cryptocurrency LOB data.
method Benchmarked a range of models including deep architectures and interpretable baselines.
result Simpler models can match and exceed deep architectures' performance with proper preprocessing and tuning.
Model predicts stock returns from order arrivals and cancellations.
problem Forecasting intraday stock returns using limit order book dynamics.
method Microscopic model based on operator algebra for order arrivals and cancellations, estimating arrival and cancellation rate distributions.
result The model explains 80% of returns in in-sample forecasts and 15% in out-of-sample forecasts.
In this paper we study a continuous time equilibrium model of limit order book (LOB) in which the liquidity dynamics follows a non-local, reflected mean-field stochastic differential equation (SDE) with evolving intensity. Generalizing the basic idea of Ma et al. (2015), we argue that the frontier of the LOB (e.g., the…
Study identifies key metrics for small and large tick assets in LOBs.
problem Understanding microstructural properties of LOBs across different tick sizes.
method Hawkes Process model to fit LOBs of large and small tick assets.
result Model can transition stylized facts from large to small tick assets.
We showcase how Quantile Regression (QR) can be applied to forecast financial returns using Limit Order Books (LOBs), the canonical data source of high-frequency financial time-series. We develop a deep learning architecture that simultaneously models the return quantiles for both buy and sell positions. We test our mo…
Model simulates sparse order books in illiquid markets.
problem Inaccurate LOB models in illiquid markets.
method Inhomogeneous Poisson process for order arrivals and cancellations.
result Enhanced understanding of LOB dynamics in illiquid markets.
In order-driven markets, limit-order book (LOB) resiliency is an important microscopic indicator of market quality when the order book is hit by a liquidity shock and plays an essential role in the design of optimal submission strategies of large orders. However, the evolutionary behavior of LOB resilience around liqui…
Framework detects covert financial market manipulation using LOB representations.
problem Detecting covert financial market manipulation (spoofing) from complex anomaly patterns in multilevel prices.
method Cascaded contrastive representation learning of LOB data.
result Transformer-based architectures achieve state-of-the-art results in detection performance.
This paper focuses on an extension of the Limit Order Book (LOB) model with general shape introduced by Alfonsi, Fruth and Schied. Here, the additional feature allows a time-varying LOB depth. We solve the optimal execution problem in this framework for both discrete and continuous time strategies. This gives in partic…
We study an optimal execution problem in the presence of market impact where the security price follows a geometric Ornstein-Uhlenbeck process, which implies the mean-reverting property, and show that the optimal strategy is a mixture of initial/terminal block liquidation and gradual intermediate liquidation. The mean-…
Study forecasts cryptocurrency returns using LOB data and Hawkes model.
problem Predicting cryptocurrency returns due to their chaotic nature.
method Hawkes model applied to LOB data with COE model.
result Outperforms benchmarks in cryptocurrency return sign forecasting.
Paper analyzes fire sales in a network of banks using VWAP and LOB pricing.
problem Optimal asset liquidation and borrowing strategies in a network of banks.
method Nash equilibrium model with two market clearing mechanisms.
result Existence and uniqueness of clearing solutions for liquidations, borrowing, prices, and haircuts.