Limit Order Book Research Articles

Long short-term temporal fusion transformer for short-term forecasting of limit order book in China markets

Long short-term temporal fusion transformer for short-term forecasting of limit order book in China markets

High Price Impact Trade Identification and Its Implication for Volatility and Price Efficiency

We include limit order book (LOB) matchedness as a new trade attribute to identify high price impact trades (HPITs). HPITs are trades associated with large price changes relative to their volume proportion. We show that the inclusion of matchedness provides a finer analysis of the relationship between price contribution and trade categories. We further verify that a stronger presence of HPITs leads to a decline in volatility and improves price efficiency, which suggests a link between HPITs and informed trades.

Price predictability in limit order book with deep learning model

ABSTRACT This study explores the prediction of high-frequency price changes using deep learning models. Although state-of-the-art methods perform well, their complexity impedes the understanding of successful predictions. We found that an inadequately defined target price process may render predictions meaningless by incorporating past information. The commonly used three-class problem in asset price prediction can generally be divided into volatility and directional prediction. When relying solely on the price process, directional prediction performance is not substantial. However, volume imbalance improves directional prediction performance.

Limit Order Book dynamics and order size modelling using Compound Hawkes Process

Hawkes Process has been used to model Limit Order Book (LOB) dynamics in several ways in the literature however the focus has been limited to capturing the inter-event times while the order size is usually assumed to be constant. We propose a novel methodology of using Compound Hawkes Process for the LOB where each event has an order size sampled from a calibrated distribution. The process is formulated in a novel way such that the spread of the process always remains positive. Further, we condition the model parameters on time of day to support empirical observations. We make use of an enhanced non-parametric method to calibrate the Hawkes kernels and allow for inhibitory cross-excitation kernels. We showcase the results and quality of fits for an equity stock’s LOB in the NASDAQ exchange and compare them against several baselines. Finally, we conduct a market impact study of the simulator and show the empirical observation of a concave market impact function is indeed replicated.

An unbounded intensity model for point processes

We develop a model for point processes on the real line, where the intensity can be locally unbounded without inducing an explosion. In contrast to an orderly point process, for which the probability of observing more than one event over a short time interval is negligible, the bursting intensity causes an extreme clustering of events around the singularity. We propose a nonparametric approach to detect such bursts in the intensity. It relies on a heavy traffic condition, which admits inference for point processes over a finite time interval. With Monte Carlo evidence, we show that our testing procedure exhibits size control under the null, whereas it has high rejection rates under the alternative. We implement our approach on high-frequency data for the EUR/USD spot exchange rate, where the test statistic captures abnormal surges in trading activity. We detect a nontrivial amount of intensity bursts in these data and describe their basic properties. Trading activity during an intensity burst is positively related to volatility, illiquidity, and the probability of observing a drift burst. The latter effect is reinforced if the order flow is imbalanced or the price elasticity of the limit order book is large.

Risk-Averse Markov Decision Processes Through a Distributional Lens

By adopting a distributional viewpoint on law-invariant convex risk measures, we construct dynamic risk measures (DRMs) at the distributional level. We then apply these DRMs to investigate Markov decision processes, incorporating latent costs, random actions, and weakly continuous transition kernels. Furthermore, the proposed DRMs allow risk aversion to change dynamically. Under mild assumptions, we derive a dynamic programming principle and show the existence of an optimal policy in both finite and infinite time horizons. Moreover, we provide a sufficient condition for the optimality of deterministic actions. For illustration, we conclude the paper with examples from optimal liquidation with limit order books and autonomous driving. Funding: This work was supported by Natural Sciences and Engineering Research Council of Canada [Grants RGPAS-2018-522715 and RGPIN-2018-05705].

Equity auction dynamics: latent liquidity models with activity acceleration

Equity auctions display several distinctive characteristics in contrast to continuous trading. As the auction time approaches, the rate of events accelerates causing a substantial liquidity buildup around the indicative price. This, in turn, results in a reduced price impact and decreased volatility of the indicative price. In this study, we adapt the latent/revealed order book framework to the specifics of equity auctions. We provide precise measurements of the model parameters, including order submissions, cancelations, and diffusion rates. Our setup allows us to describe the full dynamics of the average order book during closing auctions in Euronext Paris. These findings support the relevance of the latent liquidity framework in describing limit order book dynamics. Lastly, we analyze the factors contributing to a sub-diffusive indicative price and demonstrate the absence of indicative price predictability.

Reducing transaction costs using intraday forecasts of limit order book slopes

AbstractMarket participants who need to trade a significant number of securities within a given period can face high transaction costs. In this paper, we document how improvements in intraday liquidity forecasts can help reduce total transaction costs. We compare various approaches for forecasting intraday transaction costs, including autoregressive and machine learning models, using comprehensive ultra‐high‐frequency limit order book data for a sample of NYSE stocks from 2002 to 2012. Our results indicate that improved liquidity forecasts can significantly decrease total transaction costs. Simple models capturing seasonality in market liquidity tend to outperform alternative models.

Who can see the iceberg's peak? How icebergs are used by information and liquidity traders

AbstractIceberg orders are partially disclosed limit orders that only reveal a small portion of their hidden volume at any time. Once traded, the iceberg order automatically replenishes until all its hidden volume executes. Consistent with theory, icebergs appeal to both information and liquidity traders. Information traders place orders at aggressive prices in the limit order book, which transact immediately as marketable orders. Liquidity traders use non‐aggressive orders, which sit on the book as limit orders. Iceberg traders adjust the aggressiveness of their orders as market conditions change. We find the market discovers iceberg orders through repeated replenishments.

Deep Hawkes process for high-frequency market making

AbstractHigh-frequency market making is a liquidity-providing trading strategy that simultaneously generates many bids and asks for a security at ultra-low latency while maintaining a relatively neutral position. The strategy makes a profit from the bid-ask spread for every buy and sell transaction, against the risk of adverse selection, uncertain execution and inventory risk. We design realistic simulations of limit order markets and develop a high-frequency market making strategy in which agents process order book information to post the optimal price, order type and execution time. By introducing the Deep Hawkes process to the high-frequency market making strategy, we allow a feedback loop to be created between order arrival and the state of the limit order book, together with self- and cross-excitation effects. Our high-frequency market making strategy accounts for the cancellation of orders that influence order queue position, profitability, bid-ask spread and the value of the order. The experimental results show that our trading agent outperforms the baseline strategy, which uses a probability density estimate of the fundamental price. We investigate the effect of cancellations on market quality and the agent’s profitability. We validate how closely the simulation framework approximates reality by reproducing stylised facts from the empirical analysis of the simulated order book data.

Lob-based deep learning models for stock price trend prediction: a benchmark study

The recent advancements in Deep Learning (DL) research have notably influenced the finance sector. We examine the robustness and generalizability of fifteen state-of-the-art DL models focusing on Stock Price Trend Prediction (SPTP) based on Limit Order Book (LOB) data. To carry out this study, we developed LOBCAST, an open-source framework that incorporates data preprocessing, DL model training, evaluation, and profit analysis. Our extensive experiments reveal that all models exhibit a significant performance drop when exposed to new data, thereby raising questions about their real-world market applicability. Our work serves as a benchmark, illuminating the potential and the limitations of current approaches and providing insight for innovative solutions.

Algorithmic trading and market efficiency around the introduction of the NYSE Hybrid Market

I study the effect of algorithmic trading on market efficiency, taking into account past market and limit order flows alike. I find that an exogenous increase in algorithmic trading around the introduction of the NYSE Hybrid Market leads to a significant decrease in the predictive power of surprises in market order imbalance and limit order book imbalances, especially at the outer levels of the limit order book. However, the predictive power of past returns remains largely unchanged. This suggests that algorithmic trading improves market efficiency by facilitating the incorporation of information embedded in both market and limit order flows.

Neural stochastic agent‐based limit order book simulation with neural point process and diffusion probabilistic model

SummaryModern financial exchanges use an electronic limit order book (LOB) to store bid and ask orders for a specific financial asset. As the most fine‐grained information depicting the demand and supply of an asset, LOB data are essential in understanding market dynamics. Therefore, realistic LOB simulations offer a valuable methodology for explaining the empirical properties of markets. Mainstream simulation models include agent‐based models (ABMs) and stochastic models (SMs). However, ABMs tend not to be grounded on real historical data, whereas SMs tend not to enable dynamic agent‐interaction. More recently, deep generative approaches have been successfully implemented to tackle these issues, whereas its black‐box essence hampers the explainability and transparency of the system. To overcome these limitations, we propose a novel hybrid neural stochastic agent‐based model (NS‐ABM) for LOB simulation that incorporates a neural stochastic trader in agent‐based simulation, characterised by (1) representing the aggregation of market events' logic by a neural stochastic background trader that is pre‐trained on historical LOB data through a neural point process model; (2) learning the complex distribution for order‐related attributes conditioned on various market indicators through a non‐parametric diffusion probabilistic model; and (3) embedding the background trader in a multi‐agent simulation platform to enable interaction with other strategic trading agents. We instantiate this hybrid NS‐ABM model using the ABIDES platform. We first run the background trader in isolation and show that the simulated LOB can recreate a comprehensive list of stylised facts that demonstrate realistic market behaviour. We then introduce a population of ‘trend’ and ‘value’ trading agents, which interact with the background trader. We show that the stylised facts remain and we demonstrate order flow impact and financial herding behaviours that are in accordance with empirical observations of real markets.

The Intraday Dynamics Predictor: A TrioFlow Fusion of Convolutional Layers and Gated Recurrent Units for High-Frequency Price Movement Forecasting

This paper introduces a novel deep learning approach for intraday stock price direction prediction, motivated by the need for more accurate models to enable profitable algorithmic trading. The key problems addressed are effectively modelling complex limit order book (LOB) and order flow (OF) microstructure data and improving prediction accuracy over current state-of-the-art models. The proposed deep learning model, TrioFlow Fusion of Convolutional Layers and Gated Recurrent Units (TFF-CL-GRU), takes LOB and OF features as input and consists of convolutional layers splitting into three channels before rejoining into a Gated Recurrent Unit. Key innovations include a tailored input representation incorporating LOB and OF features across recent timestamps, a hierarchical feature-learning architecture leveraging convolutional and recurrent layers, and a model design specifically optimised for LOB and OF data. Experiments utilise a new dataset (MICEX LOB OF) with over 1.5 million LOB and OF records and the existing LOBSTER dataset. Comparative evaluation against the state-of-the-art models demonstrates significant performance improvements with the TFF-CL-GRU approach. Through simulated trading experiments, the model also demonstrates practical applicability, yielding positive returns when used for trade signals. This work contributes a new dataset, performance improvements for microstructure-based price prediction, and insights into effectively applying deep learning to financial time-series data. The results highlight the viability of data-driven deep learning techniques in algorithmic trading systems.

Modeling of limit order book data with ordered fuzzy numbers

This paper presents a novel approach to representing the Limit Order Book data at a given timestamp using the Ordered Fuzzy Numbers concept. The limit order book contains all buy and sell orders placed by investors, updated in real-time, for the most liquid securities, even several hundred times a minute. Due to its irregular nature (different and dynamic changes in the number of buy and sell orders), direct calculations on the order book data are not feasible without transforming it into feature vectors. Currently, most studies use a price level-based data representation scheme when applying deep learning models on limit order book data. However, this scheme has limitations, particularly its sensitivity to subtle perturbations that can negatively impact model performance. On the other hand, the ordered fuzzy number is a mathematical object (a pair of two functions) used to process imprecise and uncertain data. Ordered Fuzzy Numbers possess well-defined arithmetic properties. Converting the limit order book data to ordered fuzzy numbers allows the creation of a time series of ordered fuzzy numbers (order books) and use them for further calculations, e.g., to represent input data for deep learning models or employing the concept of fuzzy time series in various domains, such as defining liquidity measures based on limit order book data. In this paper, the proposed approach is tested using one-year market data from the Polish Stock Exchange for the five biggest companies. The DeepLOB model is employed to predict mid-price movement using different input data representations. The proposed representation of Limit Order Book data demonstrated remarkably stable out-of-sample prediction accuracy, even when subjected to data perturbation.

On the quadratic variation in limit order markets

This paper explores the quadratic variation (QV) as an alternative measure to the bid-ask spread in limit order markets when observed at high resolution. Although the spread cannot be precisely estimated because of microstructure noise, the QV of the price series, consisting of the transaction prices and midquotes (an expanded filtration of transaction prices), in limit order markets is an important property of high-frequency datasets. An empirical examination of a sample of stocks from the NASDAQ 100 is used to estimate and examine the QV. The examination is done at high resolution (subsecond timescale). The QV of our sample best fits a log-normal distribution with higher skewness. The QV of trades (29.73E–05) is distant from the QV measured with pretrade and posttrade price series, as they are characterized by a high range in QV. Similarly, the QV is generally lower with pretrades than posttrades. Using a high resolution, the revealed state of the limit order book presents a solution that reduced the impact cost of trading. The QV is higher with the limit order book (68.5E–05) than with trades. A measure called the limit-to-market order signal shows a consistent pattern of decline in stocks with increasing activity. The limit-to-market signal ranged from an average of 3.55 in the first quartile of stocks based on messages to 1.84 in the third quartile. This signal decreases because of a relatively larger decline in uncertainty in QV using the limit order book.

Mesoscale effects of trader learning behaviors in financial markets: A multi-agent reinforcement learning study.

Recent advances in the field of machine learning have yielded novel research perspectives in behavioural economics and financial markets microstructure studies. In this paper we study the impact of individual trader leaning characteristics on markets using a stock market simulator designed with a multi-agent architecture. Each agent, representing an autonomous investor, trades stocks through reinforcement learning, using a centralized double-auction limit order book. This approach allows us to study the impact of individual trader traits on the whole stock market at the mesoscale in a bottom-up approach. We chose to test three trader trait aspects: agent learning rate increases, herding behaviour and random trading. As hypothesized, we find that larger learning rates significantly increase the number of crashes. We also find that herding behaviour undermines market stability, while random trading tends to preserve it.

Bid-ask spread dynamics: large upward jump with geometric catastrophes

We propose a simple continuous-time stochastic model for capturing the dynamics of a limit order book in the presence of liquidity fluctuations, manifested by gaps in filled price levels within the OB. Inspired by [D. Farmer, L. Gillemot, F. Lillo, S. Mike and A. Sen, Quant. Finance 4 (2004) 383–397.], we define a model for the dynamics of spread that incorporates liquidity fluctuations and undertake a comprehensive theoretical study of the model’s properties, providing rigorous proofs of several key asymptotic theorems. Furthermore, we show how large deviations manifest in the spread under this regime.

MULTIVARIATE HAWKES-BASED MODELS IN LIMIT ORDER BOOK: EUROPEAN AND SPREAD OPTION PRICING

In this paper, we consider the pricing problem of European options and spread options for the Hawkes-based model in the limit order book (LOB). We introduce a variant of Hawkes process and consider its limit theorems, namely the exponential multivariate general compound Hawkes process (EMGCHP). We also consider a special case of one-dimensional EMGCHP and its limit theorems. Option pricing with one-dimensional EMGCHP in LOB and numerical examples are presented. We also discuss implied volatility and implied order flow. It reveals the relationship between stock volatility and the order flow in the LOB system. In this way, the Hawkes-based model can provide more market forecast information than the classical Black–Scholes model. Margrabe’s spread options valuations with two one-dimensional and one two-dimensional Hawkes-based models for two assets are presented.

Optimal Incentives in a Limit Order Book: A SPDE Control Approach

With the fragmentation of electronic markets, exchanges are now competing in order to attract trading activity on their platform. Consequently, they developed several regulatory tools to control liquidity provision/consumption on their liquidity pool. In this paper, we study the problem of an exchange using incentives in order to increase market liquidity. We model the limit order book as the solution of a stochastic partial differential equation (SPDE) as in [R. Cont and M. S. Müller, 2021, A stochastic partial differential equation model for limit order book dynamics, SIAM Journal on Financial Mathematics 12(2), 744–787]. The incentives proposed to the market participants are functions of the time and the distance of their limit order to the mid-price. We formulate the control problem of the exchange who wishes to modify the shape of the order book by increasing the volume at specific limits. Due to the particular nature of the SPDE control problem, we are able to characterize the solution with a classic Feynman–Kac representation theorem. Moreover, when studying the asymptotic behavior of the solution, a specific penalty function enables the exchange to obtain closed-form incentives at each limit of the order book. We study numerically the form of the incentives and their impact on the shape of the order book, and analyze the sensitivity of the incentives to the market parameters.