Limit Order Book

Deep Limit Order Book forecasting models capture nonlinear market dynamics, but their ability to quantify the effects of counterfactual order book messages has not been systematically validated. We introduce a model-agnostic framework that compares a trained forecaster's predictive distributions before and after injecting mechanically valid counterfactual messages, defining short-horizon model-implied market impact. A Transformer-based forecaster recovered scenario rankings with a Spearman correlation of 0.99 and 97.2% directional agreement with realized historical outcomes among non-neutral scenarios. Observation-level analysis further showed that estimated impacts captured incremental sequence-dependent variation beyond scenario identity and the pre-event forecast. These results provide evidence that pretrained Limit Order Book forecasters can be repurposed for scenario-conditioned response modeling without retraining.

Limit order book (LOB) simulators are most useful to practitioners when they combine realistic market dynamics, computationally efficient sampling, controllable scenario generation, and the ability to generalize beyond the instruments seen during training---properties that existing agent-based and deep generative simulators provide only partially. We present \textbf{FlowLOB}, a conditional \textbf{flow}-matching generator of \textbf{LOB} trajectories, trained on multiple Hong Kong Exchange (HKEX) symbols at three sampling frequencies ($0.1$s, $1$s, $10$s) in tick-relative representation that transfers to unseen instruments. Because flow and diffusion models admit a common formulation, we train both with identical data, architecture, and budget, and sample both through the same fixed-step ODE solvers, yielding a controlled comparison of sampling efficiency and fidelity. Flow matching attains its best quality with only $10$ ODE-solver steps, whereas diffusion needs many more function evaluations to approach the same fidelity. At this efficient operating point, FlowLOB improves realism over baselines, two learned and two agent-based models, in most distributional metrics at the two finer sampling frequencies. We evaluate counterfactual controllability with a distributional test that asks whether changing a scenario condition moves the generated statistic toward the corresponding real tail regime; FlowLOB satisfies this criterion in most tested settings. Both realism and control effects transfer zero-shot on a held-out symbol. We additionally conduct ablation studies on the network architecture and the learning rate.

Generative models of limit orderbook (LOB) data have advanced rapidly, but their evaluation often focuses on stylised facts and selected market statistics. These measures provide useful diagnostics but may not capture the joint temporal and cross-level structure of order-book trajectories. We introduce LOB-ID, an embedding-based framework that adapts the Fréchet Inception Distance (FID) and Monge Inception Distance (MIND) to LOB data. To obtain domain-specific embeddings, we train the DeepLOB architecture on four months of Level-2 order-book data for five equities. We show that LOB-ID is stable across time, instruments, and embedding checkpoints, and rises monotonically under controlled distortions. We then construct a moment-matching attack against FID and a deep-book perturbation that evades statistic-based evaluation. MIND remains substantially more sensitive to both distortions. Finally, we score five generative LOB models, spanning stochastic baselines and deep learning approaches, and find that LOB-ID ranks them in line with the joint temporal and cross-level structure each captures by construction.

Predicting extreme price movements in high-frequency financial markets is a challenging task due to non-stationarity, heavy-tailed return distributions, and severe class imbalance. In particular, rare but impactful events are often difficult to detect using conventional modeling approaches, which typically treat extreme movements as isolated observations. This study proposes a volatility-aware approach for extreme event detection using high-frequency Bitcoin limit order book (LOB) data. Motivated by empirical evidence of volatility clustering, the target formulation is extended to incorporate both large future returns and high-volatility regimes. This redefinition increases the proportion of informative samples and aligns the learning objective with the underlying market dynamics. Using a tree-based model (XGBoost) with time-series cross-validation and imbalance-aware evaluation, the proposed method achieves a Precision-Recall AUC of approximately 0.40, significantly outperforming the baseline formulation with a PR-AUC of around 0.06. This represents more than a sixfold improvement in detecting rare events. The results highlight that target design plays a critical role in financial machine learning, often exceeding the impact of model complexity. By incorporating volatility structure into the labeling process, the proposed approach provides a more effective and realistic framework for extreme event detection in high-frequency cryptocurrency markets.

Building event-conditioned market models requires separating macro-event labels from persistent microstructure state. We study this distinction in Binance BTCUSDT and ETHUSDT futures from 2023-2026, combining top-20 L2 order book data, trade-flow records, and macro-event windows. We define a supervised discrete L2 liquidity-state transition task, distinct from latent-regime detection and price-direction prediction, and evaluate models in rolling monthly out-of-sample folds with event-clustered validation and blocked permutation tests, admitting each feature layer only if it improves on the layer below it on the same panel. Within these event windows, the first-order predictive signal is the pre-event L2 liquidity state: a coarse pre-event state baseline strongly predicts post-event liquidity regimes, interpretable logit models over continuous L2 features fail to improve on it, and a shallow nonlinear L2 model adds a robust further gain of comparable size to the state baseline's own. The macro-event calendar enters only by locating the windows and supplying matched non-event controls; we use event timing but not the event's label content, so pre-event state competes against an uninformed within-window baseline, not against the event type. Order flow adds further value only when layered on top of the L2 state model, not as a replacement. This value is not robustly cross-symbol: for ETH it is present across calm, mixed, and stressed regimes and largest under stressed pre-event liquidity, whereas BTC shows only isolated five-minute passes and no regime that clears at both horizons. These findings motivate a state-first design principle for market microstructure models. We provide a liquidity-state transition baseline and evaluation protocol that reinforcement-learning, execution-policy, or LLM-based context layers should exceed before their added value is credited.

Prediction markets aggregate dispersed beliefs into prices that act as probabilistic forecasts of uncertain events. Classical theory establishes a clean equivalence between forecasting accuracy and trading profit, but only for the specific automated market maker (AMM) design. However, the largest exchanges today are based on central limit order books in which informed forecasters routinely lose money while uninformed strategies can profit on simple heuristics. We resolve this discrepancy by establishing a formal equivalence between predictive accuracy and profitability. For any strictly proper scoring rule $S$, we exhibit a "proper" betting strategy that depends only on the forecaster's prediction $\mathbf{p}$ and the market price $\mathbf{q}$, and earns positive expected profit whenever $\mathbf{p}$ outperforms $\mathbf{q}$ under $S$ and the market has sufficient liquidity. Moreover, this proper betting is essentially the only strategy with such robust profitability guarantee. The proof rests on a decomposition of expected profit that strictly generalizes the classical AMM guarantee and also explains how strategies can profit without an accuracy edge. Empirically, across thousands of forecasts by AI models, proper betting is the only strategy that reliably converts accuracy into profit, and we further identify systematic forecasting personas and show how the optimal proper strategy varies across them. A month-long live deployment on Kalshi achieves $+80.33\%$ return on investment with a Sharpe ratio of $3.35$.

We propose Persona-Trained Monte Carlo (PTMC), a method for estimating distributions of market-outcome statistics by repeatedly simulating limit-order-book interaction among swarms of persona-conditioned neural-policy trading bots. Each run instantiates many bots sharing one trained policy network but conditioned on heterogeneous, individually sampled persona parameters drawn from a learned trader-heterogeneity distribution; the bots interact in a continuous double auction, and the resulting price path is one Monte Carlo sample. Repeating this over independent persona-population draws yields an ensemble from which a target market statistic is estimated. Randomness enters through persona draws, within-run action sampling, and optional exogenous shocks, not solely through price as in classical Monte Carlo. We distinguish PTMC from adjacent paradigms, including classical Monte Carlo, hand-coded agent-based models, single-agent reinforcement learning, and large-language-model-based generative agents. To justify the design, we survey cross-disciplinary foundations -- agent-based computational economics, market microstructure, behavioral finance, deep reinforcement learning, generative/LLM-based agents, news-driven trading, systemic risk, econophysics, and game theory -- connecting each literature to a specific design choice in the policy network, training data, or validation protocol. We formalize the PTMC estimator and its convergence properties, specify a candidate bot architecture and training objective, and propose a four-level validation methodology: stylized-fact matching, microstructure- and agent-level checks, and historical stress-test comparison against a zero-intelligence baseline. The framework is proposed but not implemented: we contribute a formal estimator, a cross-disciplinary design justification, and a validation roadmap, and conclude with open research questions.

We study whether a scaling-law-style inference-compute frontier appears in limit order book prediction. Using FI-2010 and a suite of models ranging from small decision trees to neural LOB architectures, we find that the realized empirical frontier of predictive loss versus structural forward work is well summarized by a power law. In particular, with MLPLOB held out as an architecture family, a power-law fit to the low- and mid-compute non-MLPLOB frontier extrapolates across multiple orders of magnitude and attains $R^2=0.941$ on the excluded high-compute MLPLOB target frontier. A similar exercise in latency space gives substantially weaker results, showing that latency is not merely noisy compute. We use this gap to motivate FastBiNLOB, a dense axis-separable LOB mixer built from hardware-friendly temporal and feature mixing operations. In a five-seed experiment, FastBiNLOB exceeds the published $y_{10}$ and $y_{100}$ macro-F1 targets at notably lower latency than existing published SOTA architectures.

This study addresses the optimal execution of large stock sell programs by introducing TT-DAC-PS (Twin-Target Deterministic Actor-Critic with Policy Smoothing), a deterministic actor-critic architecture that combines twin exponential-moving-average critic targets with pessimistic min backup, TD3-style target policy smoothing noise, delayed actor updates, and conservative Q regularisation to curb overestimation. Exploration uses Ornstein-Uhlenbeck (OU) noise with a hybrid schedule: deterministic episode-wise decay, variance-guided adjustment based on recent reward dispersion, and a Soft Actor-Critic (SAC)-style temperature that is learned and mapped to the noise scale. The environment integrates Almgren-Chriss (AC) trade impact with Limit Order Book (LOB) prices and volumes, normalised state features, per-step volume participation caps, and a utility-based reward. The trade execution algorithm is applied to LOB data for ten U.S. stocks. Performance is assessed against reinforcement-learning baseline algorithms, including Proximal Policy Optimisation (PPO), Soft Actor-Critic (SAC), and Advantage Actor-Critic (A2C), as well as alternative trade execution algorithms, including Time-Weighted Average Price (TWAP), Volume-Weighted Average Price (VWAP), and AC. The proposed model consistently reduces mean implementation shortfall percentage with competitive variance, outperforming classical baselines and standard reinforcement-learning benchmark models.

We develop a game-theoretic framework that compares welfare efficiency across three market mechanisms: continuous double auctions with transparent order books (lit exchanges), opaque order books (dark pools), and periodic batch auctions. Each mechanism is modeled as a queuing system where heterogeneous traders face trade-offs between the execution price, waiting costs, and transaction costs. Our main result establishes that under moderate arrival rates and bounded adverse selection, dark pools dominate both alternatives in aggregate ex-ante welfare. Observable order books create costly strategic timing games in which traders delay or rush submissions to optimize their position in the queue, generating wasteful social waiting costs. Opaque order books eliminate these timing games through information design. We formally characterize the equilibrium strategies in each mechanism and prove the welfare ranking $W^{DARK} > W^{LIT} > W^{BATCH}$. Extensions incorporate asymmetric information and endogenous venue choice. The results demonstrate how the information structure and the discipline of the service jointly determine efficiency in strategic matching environments.

We study an online market-making problem in which a learner sequentially posts bid and ask prices for a single asset while interacting with traders holding private valuations. Unlike existing online learning formulations that assume fully censored feedback, we introduce an action-dependent feedback model inspired by real limit order books: when a trade occurs, the trader's valuation remains hidden, whereas when no trade occurs, informative feedback about supply and demand is revealed. We show that this additional information fundamentally changes the learnability of the problem. In the stochastic setting with i.i.d. market prices, we propose an elimination-based algorithm that achieves $O(\sqrt T)$ regret with high probability, without requiring any smoothness assumptions on the distribution of trader valuations. We then extend this result to a broad class of mean-reverting price processes by considering both local, autoregressive dynamics and a weaker global drift condition based on cumulative deviations from the mean. Under either assumption, we establish high-probability $O(\sqrt T)$ regret bounds, relying on a new concentration inequality of independent interest. Finally, in the adversarial setting with oblivious prices, we design an explore-then-perturb algorithm that guarantees $O(T^{2/3})$ regret in expectation. Our results quantify the value of observing the order book in online market making and demonstrate that even limited, action-dependent feedback can substantially improve regret guarantees compared to standard bandit feedback models.

We study the detection of transient liquidity erosion ("crumbling quotes") in electronic limit order books, where observable quote deterioration may reflect either mechanical liquidity withdrawal or informational repricing. Using the ABIDES agent-based simulator, we construct a multi-agent environment in which crumbling emerges from stochastic regime switches in a market maker, providing time-resolved ground truth unavailable in real market data. We develop a detection pipeline that identifies mechanically driven quote erosion using order book features, and train a neural model to produce calibrated crumbling probabilities. Experiments demonstrate that the proposed framework reliably identifies crumbling events against agent-level ground truth, with the neural model achieving +36% AUC improvement over rule-based baselines and robust performance across normal, high-volatility, bull, and bear market conditions. Ablation studies on temporal features and varying the dependence structure of the ground-truth mechanism confirm that the framework generalizes across both independent and autocorrelated liquidity withdrawal dynamics.

Limit order books can transition rapidly from stable to stressed conditions, yet standard early-warning signals such as order flow imbalance and short-term volatility are inherently reactive. We formalise this limitation via a three-regime causal data-generating process (stable $\to$ latent build-up $\to$ stress) in which a latent deterioration phase creates a prediction window prior to observable stress. Under mild assumptions on temporal drift and regime persistence, we establish identifiability of the latent build-up regime and derive guarantees for strictly positive expected lead-time and non-trivial probability of early detection. We propose a trigger-based detector combining MAX aggregation of complementary signal channels, a rising-edge condition, and adaptive thresholding. Across 200 simulations, the method achieves mean lead-time $+18.6 \pm 3.2$ timesteps with perfect precision and moderate coverage, outperforming classical change-point and microstructure baselines. A preliminary application to one week of BTC/USDT order book data shows consistent positive lead-times while baselines remain reactive. Results degrade in low signal-to-noise and short build-up regimes, consistent with theory.

Modeling the dynamics of financial Limit Order Books (LOB) at the message level is challenging due to irregular event timing, rapid regime shifts, and the reactions of high-frequency traders to visible order flow. Previous LOB models require cumbersome data representations and lack adaptability outside their original tasks, leading us to introduce LOBERT, a general-purpose encoder-only foundation model for LOB data suitable for downstream fine-tuning. LOBERT adapts the original BERT architecture for LOB data by using a novel tokenization scheme that treats complete multi-dimensional messages as single tokens while retaining continuous representations of price, volume, and time. With these methods, LOBERT achieves leading performance in tasks such as predicting mid-price movements and next messages, while reducing the required context length compared to previous methods.