Limit Order Book Research Articles

Limit Order Book Simulations: A Review

Limit Order Book Simulations: A Review

Limit Order Book Dynamics and Order Size Modelling Using Compound Hawkes Process

Limit Order Book Dynamics and Order Size Modelling Using Compound Hawkes Process

Thermodynamic Analysis of Financial Markets: Measuring Order Book Dynamics with Temperature and Entropy.

This study bridges finance and physics by applying thermodynamic concepts to model the limit order book (LOB) with high-frequency trading data on the Bitcoin spot. We derive the measures of Market Temperature and Market Entropy from the kinetic and potential energies in the LOB to provide a deeper understanding of order activities and market participant behavior. Market Temperature emerges as a robust indicator of market liquidity, correlating with liquidity measures such as Active Quote Volume, bid-ask spread and match volume. Market Entropy, on the other hand, quantifies the degree of disorder or randomness in the LOB, providing insights into the instantaneous volatility of price in the high-frequency trading market. Our empirical findings not only broaden the theoretical framework of econophysics but also enhance comprehensive understanding of the market microstructure and order book dynamics.

Continuous‐time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations

AbstractWe develop a new continuous‐time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an estimate for the gradient of the stationary distribution. The gradient estimate is simultaneously updated using forward propagation of the SDE state derivatives, asymptotically converging to the direction of steepest descent. We rigorously prove convergence of the online forward propagation algorithm for linear SDE models (i.e., the multidimensional Ornstein–Uhlenbeck process) and present its numerical results for nonlinear examples. The proof requires analysis of the fluctuations of the parameter evolution around the direction of steepest descent. Bounds on the fluctuations are challenging to obtain due to the online nature of the algorithm (e.g., the stationary distribution will continuously change as the parameters change). We prove bounds for the solutions of a new class of Poisson partial differential equations (PDEs), which are then used to analyze the parameter fluctuations in the algorithm. Our algorithm is applicable to a range of mathematical finance applications involving statistical calibration of SDE models and stochastic optimal control for long time horizons where ergodicity of the data and stochastic process is a suitable modeling framework. Numerical examples explore these potential applications, including learning a neural network control for high‐dimensional optimal control of SDEs and training stochastic point process models of limit order book events.

Short-term stock price trend prediction with imaging high frequency limit order book data

Predicting price movements over a short period is a challenging problem in high-frequency trading. Deep learning methods have recently been used to forecast short-term prices via limit order book (LOB) data. In this paper, we propose a framework to convert LOB data into a series of standard images in 2D matrices and predict the mid-price movements via an image-based convolutional neural network (CNN). The empirical study shows that the image-based CNN model outperforms other traditional machine learning and deep learning methods based on raw LOB data. Our findings suggest that the additional information implicit in LOB images contributes to short-term price forecasting.

A comparative study of the neural network models for the stock market data classification—A multicriteria optimization approach

The aim of this paper is to explore the potential of the class of recurrent neural networks in developing a classification model for the stock market. For this research, the data that replicates the entire Nasdaq stock market limit order book is used. After extracting order book attributes from the raw dataset, feature selection approaches based on conditional entropy and Stochastic Universal Sampling are proposed, in order to highlight potentially informative features for our data classification task. Furthermore, the performances of nine presented recurrent neural network models for classifying the stock market data vector into one of the labels from the set S = {buy, sell, idle} are examined. In this study, the performances of the models based on different networks, namely the gated recurrent unit, the long short-term memory, and the recurrent neural network, are compared. Using a multi-criteria approach it is concluded that the model based on the GRU topology fed with the features selected using the newly proposed feature selection method outperforms other examined models.

Using transformer in stock trend prediction

Large transformer model had achieved good results in many tasks, such as computer vision (CV) and natural language processing (NLP). However, in financial domains, the application of large deep learning models is rarely observed. Stock Trend Prediction (STP) is a task that using Limit Order Books (LOBs) to predict the future stock price trend by the sequence of historical limit order information, the trend can be Current works are mostly based on the structure of Convolutional Neural Network (CNN) + Recurrent Neural Networks (RNN). This structure is hard to parallel and cannot make full use of GPU resources. It is also difficult to increase the dimension to fit more complex data and performs poor when time sequence is long. Recently, some works proposed that CNN + Transformer model can also work is solving this task. This paper verifies that Transformer can be directly used into STP task and gain a good result, and proposes a novel Transformer-based model, Transformer-LOB, to enhance the basic transformer model performance. This model uses attention mechanisms to extract temporal information rather than using RNN, which utilizes the GPU effectively. Since all the feature extractions are based on transformer modules, the model is scalable and easy to parallel. Transformer-LOB is tested on FI-2010 LOB dataset and SZ-2015 LOB dataset, and outputs ideal results on both datasets.

The profitability of lead–lag arbitrage at high frequency

Any lead–lag effect in an asset pair implies that future returns on the lagging asset have the potential to be predicted from past and present prices of the leader, thus creating statistical arbitrage opportunities. We utilize robust lead–lag indicators to uncover the origin of price discovery, and we propose an econometric model exploiting that effect with level 1 data of limit order books (LOBs). We also develop a high-frequency trading strategy based on the model predictions to capture arbitrage opportunities. The framework is then evaluated on six months of DAX 30 cross-listed stocks’ LOB data obtained from three European exchanges in 2013: Xetra, Chi-X, and BATS. We show that a high-frequency trader can profit from lead–lag relationships because of predictability, even when trading costs, latency, and execution-related risks are considered.

Asynchronous Deep Double Dueling Q-learning for trading-signal execution in limit order book markets.

We employ deep reinforcement learning (RL) to train an agent to successfully translate a high-frequency trading signal into a trading strategy that places individual limit orders. Based on the ABIDES limit order book simulator, we build a reinforcement learning OpenAI gym environment and utilize it to simulate a realistic trading environment for NASDAQ equities based on historic order book messages. To train a trading agent that learns to maximize its trading return in this environment, we use Deep Dueling Double Q-learning with the APEX (asynchronous prioritized experience replay) architecture. The agent observes the current limit order book state, its recent history, and a short-term directional forecast. To investigate the performance of RL for adaptive trading independently from a concrete forecasting algorithm, we study the performance of our approach utilizing synthetic alpha signals obtained by perturbing forward-looking returns with varying levels of noise. Here, we find that the RL agent learns an effective trading strategy for inventory management and order placing that outperforms a heuristic benchmark trading strategy having access to the same signal.

The impact of retail investor sentiment on the conditional volatility of stocks and bonds: Evidence from the Tel-Aviv stock exchange

We measured bond and stock conditional return volatility as a function of changes in sentiment, proxied by six indicators of the Tel-Aviv Stock Exchange. We found that changes in sentiment affect conditional volatilities at different magnitudes and often in an opposite manner in the two markets, subject to market states. We are the first to measure the bond conditional return volatility of retail investor sentiment, thanks to a unique dataset from a limit-order book with highly active retail traders. This market structure differs from the prevalent over-the-counter platforms, where institutional investors are active, yet less prone to sentiment.

Deep order flow imbalance: Extracting alpha at multiple horizons from the limit order book

AbstractWe employ deep learning in forecasting high‐frequency returns at multiple horizons for 115 stocks traded on Nasdaq using order book information at the most granular level. While raw order book states can be used as input to the forecasting models, we achieve state‐of‐the‐art predictive accuracy by training simpler “off‐the‐shelf” artificial neural networks on stationary inputs derived from the order book. Specifically, models trained on order flow significantly outperform most models trained directly on order books. Using cross‐sectional regressions, we link the forecasting performance of a long short‐term memory network to stock characteristics at the market microstructure level, suggesting that “information‐rich” stocks can be predicted more accurately. Finally, we demonstrate that the effective horizon of stock specific forecasts is approximately two average price changes.

Tick size, liquid stocks and market quality: Evidence from a natural experiment in a unique setting

We study the causal impacts of a tick size reduction policy in highly liquid stocks, exploiting a unique experiment in Borsa Istanbul leading to substantial exogenous variation in the tick size. Adapting a differences-in-differences strategy with a novel limit order and trade book data with intraday calculations, we find evidence that the tick size reduction improves market quality for the liquid stocks by significantly lowering quoted, effective, and realized spread yet reducing the depth at the best bid offer and aggregate depth. Moreover, results indicate a lower price impact for the treated stocks while there is no significant impact on trading volume, however, the number of trades increases but trade and order sizes get smaller significantly. Estimates show null effects on the submission of market orders, volatility, and returns. Our study departs from the existing literature with no dark pool trading and internalization of orders in the Turkish Stock Markets.

Predicting High-Frequency Stock Movement with Differential Transformer Neural Network

Predicting stock prices has long been the holy grail for providing guidance to investors. Extracting effective information from Limit Order Books (LOBs) is a key point in high-frequency trading based on stock-movement forecasting. LOBs offer many details, but at the same time, they are very noisy. This paper proposes a differential transformer neural network model, dubbed DTNN, to predict stock movement according to LOB data. The model utilizes a temporal attention-augmented bilinear layer (TABL) and a temporal convolutional network (TCN) to denoise the data. In addition, a prediction transformer module captures the dependency between time series. A differential layer is proposed and incorporated into the model to extract information from the messy and chaotic high-frequency LOB time series. This layer can identify the fine distinction between adjacent slices in the series. We evaluate the proposed model on several datasets. On the open LOB benchmark FI-2010, our model outperforms other comparative state-of-the-art methods in accuracy and F1 score. In the experiments using actual stock data, our model also shows great stock-movement forecasting capability and generalization performance.

Price Impact Without Averaging

ABSTRACT We present a method to estimate price impact in order-driven markets that does not require averaging over executions or scenarios. Given order book data associated with one single execution of a sell metaorder, we estimate its contribution to price decrease during the trade. We do so by modelling the limit order book using a state-dependent Hawkes process, and by defining the price impact profile of the execution as a function of the compensator of the state-dependent Hawkes process. We apply our method to a dataset from NASDAQ, and we conclude that the scheduling of sell child orders has a bigger impact on price than their sizes.

A generative model of a limit order book using recurrent neural networks

In this work, a generative model based on recurrent neural networks for the complete dynamics of a limit order book is developed. The model captures the dynamics of the limit order book by decomposing the probability of each transition into a product of conditional probabilities of order type, price level, order size and time delay. Each such conditional probability is modelled by a recurrent neural network. Several evaluation metrics for generative models related to trading execution are introduced. Using these metrics, it is demonstrated that the generative model can be successfully trained to fit both synthetic and real data from the Nasdaq Stockholm exchange.

Ensemble of supervised and unsupervised deep neural networks for stock price manipulation detection

Illegal practices that cause stock prices to vary from their fair values are known as stock price manipulations. Our prior study used unsupervised deep learning to detect these unlawful activities, in which the autoencoder model could catch five out of six cases in the Stock Exchange of Thailand (SET). Trading actions of good governance equities in a limit order book format were used to train the model, and abnormalities were viewed as manipulation. This unsupervised technique has the strength of discovering never-before-seen patterns, although it has a low recall rate. In this work, the findings were improved by incorporating knowledge about the popular pump-and-dump pattern into another supervised deep learning model, which has a strength in catching known patterns. To combine the advantages of both models, an ensemble of supervised and unsupervised deep neural networks was proposed. The main contribution of this paper is to demonstrate that the new ensemble model achieved a higher detection rate than the unsupervised model alone. The supervised learning model used was a long short-term memory (LSTM) network, the unsupervised learning model used was an LSTM-based autoencoder, and the stack classifier in the ensemble model was a support vector machine (SVM). The proposed method was evaluated on six real manipulation cases from the SET. The empirical results showed that our ensemble model could improve the detection strength, achieved high accuracy on pump-and-dump unseen data, and could identify six out of six real manipulation cases with low false alarm rates.

Information and optimal trading strategies with dark pools

This paper examines the effects of the competition between asset trading venues with different levels of transparency: an opaque dark pool alongside a transparent exchange organized as a limit order book (two-venue market). In a model with asymmetric information, we compare traders’ strategies and market performance in the two-venue market with that of a single-venue market (trading only in the exchange). We show that price informativeness is lower in the two-venue market when informed traders migrate to the dark pool and uninformed investors remain in the exchange. We also find that when orders migrate to the dark pool in the first period, market liquidity is lower (higher) in the two-venue market for high (low) fundamental volatility stocks as traders migrating to the dark pool would have demanded (supplied) liquidity in the exchange. Finally, the expected profits of informed traders are never lower in the two-venue market, but this may not always be true for uninformed traders.

Online Hybrid Neural Network for Stock Price Prediction: A Case Study of High-Frequency Stock Trading in the Chinese Market

Time-series data, which exhibit a low signal-to-noise ratio, non-stationarity, and non-linearity, are commonly seen in high-frequency stock trading, where the objective is to increase the likelihood of profit by taking advantage of tiny discrepancies in prices and trading on them quickly and in huge quantities. For this purpose, it is essential to apply a trading method that is capable of fast and accurate prediction from such time-series data. In this paper, we developed an online time series forecasting method for high-frequency trading (HFT) by integrating three neural network deep learning models, i.e., long short-term memory (LSTM), gated recurrent unit (GRU), and transformer; and we abbreviate the new method to online LGT or O-LGT. The key innovation underlying our method is its efficient storage management, which enables super-fast computing. Specifically, when computing the forecast for the immediate future, we only use the output calculated from the previous trading data (rather than the previous trading data themselves) together with the current trading data. Thus, the computing only involves updating the current data into the process. We evaluated the performance of O-LGT by analyzing high-frequency limit order book (LOB) data from the Chinese market. It shows that, in most cases, our model achieves a similar speed with a much higher accuracy than the conventional fast supervised learning models for HFT. However, with a slight sacrifice in accuracy, O-LGT is approximately 12 to 64 times faster than the existing high-accuracy neural network models for LOB data from the Chinese market.

LOB modeling using Hawkes processes with a state-dependent factor

A point process model for order flows in limit order books is proposed, in which the conditional intensity is the product of a Hawkes component and a state-dependent factor. In the LOB context, state observations may include the observed imbalance or the observed spread. Full technical details for the computationally-efficient estimation of such a process are provided, using either direct likelihood maximization or EM-type estimation. Applications include models for bid and ask market orders, or for upwards and downwards price movements. Empirical results on multiple stocks traded in Euronext Paris underline the benefits of state-dependent formulations for LOB modeling, e.g. in terms of goodness-of-fit to financial data.

Augmented bilinear network for incremental multi-stock time-series classification

Deep Learning models have become dominant in tackling financial time-series analysis problems, overturning conventional machine learning and statistical methods. Most often, a model trained for one market or security cannot be directly applied to another market or security due to differences inherent in the market conditions. In addition, as the market evolves over time, it is necessary to update the existing models or train new ones when new data is made available. This scenario, which is inherent in most financial forecasting applications, naturally raises the following research question: How to efficiently adapt a pre-trained model to a new set of data while retaining performance on the old data, especially when the old data is not accessible? In this paper, we propose a method to efficiently retain the knowledge available in a neural network pre-trained on a set of securities and adapt it to achieve high performance in new ones. In our method, the prior knowledge encoded in a pre-trained neural network is maintained by keeping existing connections fixed, and this knowledge is adjusted for the new securities by a set of augmented connections, which are optimized using the new data. The auxiliary connections are constrained to be of low rank. This not only allows us to rapidly optimize for the new task but also reduces the storage and run-time complexity during the deployment phase. The efficiency of our approach is empirically validated in the stock mid-price movement prediction problem using a large-scale limit order book dataset. Experimental results show that our approach enhances prediction performance as well as reduces the overall number of network parameters.