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Short-term forecasting of the Limit Order Book (LOB) is challenging due to market noise. Traditionally, technical analysis using candlestick charts has been effective for market analysis and predictions. Inspired by this, we introduce a novel methodology. First, we preprocess the LOB data into long-term frame data resembling candlestick patterns to reduce noise interference. We then present the Long Short-Term Temporal Fusion Transformer (LSTFT), skillfully integrating both short-term and long-term information to capture complex dependencies and enhance prediction accuracy. Additionally, we propose a Temporal Attention Mechanism (TAM) that effectively distinguishes between long-term and short-term temporal relationships in LOB data. Our experimental results demonstrate the effectiveness of our approach in accurately forecasting the Limit Order Book in the short term. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We consider estimation of the spot volatility in a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices. Based on discrete, noisy observations of an Itô semimartingale with jumps and general stochastic volatility, we present a simple and explicit estimator using local order statistics. We establish consistency and stable central limit theorems as asymptotic properties. The asymptotic analysis builds upon an expansion of tail probabilities for the order statistics based on a generalized arcsine law. In order to use the involved distribution of local order statistics for a bias correction, an efficient numerical algorithm is developed. We demonstrate the finite-sample performance of the estimation in a Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at a few selected topics discussing recent literature. We moreover highlight and explain the important role played by some classical concepts of probability and statistics. We focus on three main aspects: Testing for jumps; rough fractional stochastic volatility; and limit order microstructure noise. We review jump tests based on extreme value theory and complement the literature proposing new statistical methods. They are based on asymptotic theory of order statistics and the Rényi representation. The second stage of our journey visits a recent strand of research showing that volatility is rough. We further investigate this and establish a minimax lower bound exploring frontiers to what extent the regularity of latent volatility can be recovered in a more general framework. Finally, we discuss a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices and its probabilistic and statistical foundation. [ABSTRACT FROM AUTHOR]

Summary: Modern 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. [ABSTRACT FROM AUTHOR]

We introduce a new matching design for financial transactions in an electronic market. In this mechanism, called ad hoc electronic auction design (AHEAD), market participants can trade between themselves at a fixed price and trigger an auction when they are no longer satisfied with this fixed price. In this context, we prove that a Nash equilibrium is obtained between market participants. Furthermore, we are able to assess quantitatively the relevance of ad hoc auctions and to compare them with periodic auctions and continuous limit order books. We show that from the investors' viewpoint, the microstructure of the asset is usually significantly improved when using AHEAD. [ABSTRACT FROM AUTHOR]

Understanding how price-volume information determines future price movement is important for market makers who frequently place orders on both buy and sell sides, and for traders to split meta-orders to reduce price impact. Given the complex non-linear nature of the problem, we consider the prediction of the movement direction of the mid-price on an option order book, using machine learning tools. The applicability of such tools on the options market is currently missing. On an intraday tick-level dataset of options on an exchange traded fund from the Chinese market, we apply a variety of machine learning methods, including decision tree, random forest, logistic regression, and long short-term memory neural network. As machine learning models become more complex, they can extract deeper hidden relationship from input features, which classic market microstructure models struggle to deal with. We discover that the price movement is predictable, deep neural networks with time-lagged features perform better than all other simpler models, and this ability is universal and shared across assets. Using an interpretable model-agnostic tool, we find that the first two levels of features are the most important for prediction. The findings of this article encourage researchers as well as practitioners to explore more sophisticated models and use more relevant features. [ABSTRACT FROM AUTHOR]

Most of the existing literature on optimal trade execution in limit order book models assumes that resilience is positive. But negative resilience also has a natural interpretation, as it models self-exciting behaviour of the price impact, where trading activities of the large investor stimulate other market participants to trade in the same direction. In the paper we discuss several new qualitative effects on optimal trade execution that arise when we allow resilience to take negative values. We do this in a framework where both market depth and resilience are stochastic processes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper considers a Markovian model of a limit order book where time-dependent rates are allowed. With the objective of understanding the mechanisms through which a microscopic model of an orderbook can converge to more general diffusion than a Brownian motion with constant coefficient, a simple time-dependent model is proposed. The model considered here starts by describing the processes that govern the arrival of the different orders such as limit orders, market orders and cancellations. In this sense, this is a microscopic model rather than a "mesoscopic" model where the starting point is usually the point processes describing the times at which the price changes occur and aggregate in these all the information pertaining to the arrival of individual orders. Furthermore, several empirical studies are performed to shed some light into the validity of the modeling assumptions and to verify whether certain stocks satisfy the conditions for their price process to converge to a more complex diffusion. [ABSTRACT FROM AUTHOR]

One of the key decisions in execution strategies is the choice between a passive (liquidity providing) or an aggressive (liquidity taking) order to execute a trade in a limit order book (LOB). Essential to this choice is the fill probability of a passive limit order placed in the LOB. This paper proposes a deep learning method to estimate the filltimes of limit orders posted in different levels of the LOB. We develop a novel model for survival analysis that maps time-varying features of the LOB to the distribution of filltimes of limit orders. Our method is based on a convolutional-Transformer encoder and a monotonic neural network decoder. We use proper scoring rules to compare our method with other approaches in survival analysis, and perform an interpretability analysis to understand the informativeness of features used to compute fill probabilities. Our method significantly outperforms those typically used in survival analysis literature. Finally, we carry out a statistical analysis of the fill probability of orders placed in the order book (e.g. within the bid-ask spread) for assets with different queue dynamics and trading activity. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A core research area of computational behavioral finance investigates emergent price dynamics when heterogeneous traders follow a mix of rule-based strategies and interact indirectly through a limit order book. This paper offers a detailed specification of such a model in order to raise questions about some previous findings. The questions force a comprehensive reconsideration of the price dynamics of a well-known model. This leads to a surprising clarification of the contributions of various trading strategies to market outcomes: a popular characterization of chartism proves largely irrelevant for price dynamics. We also shed new light on the volume-volatility relationship, and provide improved visualizations to expose market behavior. [ABSTRACT FROM AUTHOR]

We introduce a class of Markov models to describe the bid–ask price dynamics in the presence of liquidity fluctuations. In a highly competitive regime, the spread evolution belongs to a class of Markov processes known as a population process with uniform catastrophes. Our mathematical analysis focuses on establishing the law of large numbers, the central limit theorem, and large deviations for this catastrophe-based model. Large deviation theory allows us to illustrate how huge deviations in the spread and prices can occur in the model. Moreover, our research highlights how these local trends and volatility are influenced by the typical values of the bid–ask spread. We calibrated the model parameters using available high-frequency data and conducted Monte Carlo numerical simulations to demonstrate its ability to reasonably replicate key phenomena in the presence of liquidity fluctuations. [ABSTRACT FROM AUTHOR]

Understanding how price-volume information determines future price movement is important for market makers who frequently place orders on both buy and sell sides, and for traders to split meta-orders to reduce price impact. Given the complex non-linear nature of the problem, we consider the prediction of the movement direction of the mid-price on an option order book, using machine learning tools. The applicability of such tools on the options market is currently missing. On an intraday tick-level dataset of options on an exchange traded fund from the Chinese market, we apply a variety of machine learning methods, including decision tree, random forest, logistic regression, and long short-term memory neural network. As machine learning models become more complex, they can extract deeper hidden relationship from input features, which classic market microstructure models struggle to deal with. We discover that the price movement is predictable, deep neural networks with time-lagged features perform better than all other simpler models, and this ability is universal and shared across assets. Using an interpretable model-agnostic tool, we find that the first two levels of features are the most important for prediction. The findings of this article encourage researchers as well as practitioners to explore more sophisticated models and use more relevant features.

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.

Is liquidity better when a trade counterparty's brokerage firm is unknown (anonymous) or known (transparent)? We examine a quasinatural experiment where some firms switched from transparent to anonymous trading and then, 1 year later, switched back. Our results for inside spread, price impact, and limit order book depth suggest that liquidity improves when anonymous post-trade reporting is introduced and liquidity worsens when anonymous post-trade reporting is reversed. [ABSTRACT FROM AUTHOR]

We study the optimal order placement strategy with the presence of a liquidity cost. In this problem, a stock trader wishes to clear her large inventory by a predetermined time horizon T. A trader uses both limit and market orders, and a large market order faces an adverse price movement caused by the liquidity risk. First, we study a single period model where the trader places a limit order and/or a market order at the beginning. We show the behavior of optimal amount of market order, m * , and optimal placement of limit order, y * , under different market conditions. Next, we extend it to a multi-period model, where the trader makes sequential decisions of limit and market orders at multiple time points. [ABSTRACT FROM AUTHOR]

Effectively forecasting the stock mid-price movements based on Limit Order Book (LOB) data is crucial for issuing the right trade instructions in an automated trading market. The LOB data contains much valuable information which reflects the microstructure of the stock market and investor trading behavior. However, there are bear several challenges when utilize LOB to built forecasting model, such as dealing with very large amounts of data with high-dimensional, high-frequency, and underlying nonlinear dependencies relationship. In this paper, we propose a novel deep learning architecture tailored to meet the needs of high-frequency mid-price movements forecasting using complex LOB. Specifically, we introduce dual-stage temporal attention mechanism to repeatedly highlight the most valuable time-dimension information. In the first stage, we adaptively assign the temporal attention weights for input data to emphasize the degree of importance of different moments. In the second stage, we adaptively assign the temporal attention weights for hidden states across all time steps to emphasize the degree of importance of different states. Moreover, the architecture utilizes stacked GRU network to enhance the ability of representation learning. Extensive experiments on two datasets demonstrate the validity and superiority of the proposed architecture. Furthermore, by feature importance analysis we find that the time-sensitive feature set is more important than other feature sets, where the derivation of price and volume is the most important feature in all features. The results provide evidence for further understanding the influence factors of the stock market and give a reference for processing financial time series data with high-frequency characteristics. [ABSTRACT FROM AUTHOR]

A novel approach is presented for predicting the mean-mid stock price by utilizing high-frequency and complex limit order book (LOB) data as inputs for machine learning algorithms. Specifically, the proposed approach uses rough path theory to extract signature path features from the LOB data and compresses them for training machine learning models. We compare the performance of this approach to standard autoregression methods and demonstrate its superior performance in terms of model prediction error. In addition, we use deep neural networks (DNN) and random forest (RF) to further test the proposed approach’s performance compared to standard approaches using raw LOB data. The findings show that Sig-DNN, DNN with signature features, outperforms DNN with raw LOB data in terms of prediction error and efficiency, while Sig-RF, RF with signature features, underperformed RF with raw LOB data in terms of prediction but not in efficiency. We evaluate the proposed approach on multiple exchanges, including the Johannesburg and New York Stock Exchanges, and the results demonstrate better prediction error and efficiency performance in developed markets compared to emerging markets. Overall, the study highlights the potential of using signature path features with machine learning techniques for predicting the mean-mid stock price.

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In quantitative finance, there have been numerous new aspects and developments related with the stochastic control and optimization problems which handle the controlled variables of performing the behavior of a dynamical system to achieve certain objectives. In this paper, we address the optimal trading strategies via price impact models using Heston stochastic volatility framework including jump processes either in price or in volatility of the price dynamics with the aim of maximizing expected return of the trader by controlling the inventories. Two types of utility functions are considered: quadratic and exponential. In both cases, the remaining inventories of the market maker are charged with a liquidation cost. In order to achieve the optimal quotes, we control the inventory risk and follow the influence of each parameter in the model to the best bid and ask prices. We show that the risk metrics including profit and loss distribution (PnL), standard deviation and Sharpe ratio play important roles for the trader to make decisions on the strategies. We apply finite differences and linear interpolation as well as extrapolation techniques to obtain a solution of the nonlinear Hamilton-Jacobi-Bellman (HJB) equation. Moreover, we consider different cases on the modeling to carry out the numerical simulations. [ABSTRACT FROM AUTHOR]

We develop an equilibrium model for market impact of trades when investors with private signals execute via a trading desk. Fat tails in the signal distribution lead to a power law for price impact, while the impact is logarithmic for lighter tails. Moreover, the tail distribution of the equilibrium trade volume obeys a power law. The spread decreases with the degree of noise trading and increases with the number of insiders. In case of a monopolistic insider, the last slice traded against the limit order book is priced at the fundamental value of the asset reminiscent of [17]. However, competition among insiders leads to aggressive trading, hence vanishing profit in the limit. The model also predicts that the order book flattens as the amount of noise trading increases converging to a model with proportional transactions costs with non-vanishing spread. [ABSTRACT FROM AUTHOR]

On 29 September 2020, JPMorgan was ordered to pay a settlement of $920.2 million for spoofing the metals and Treasury futures markets from 2008 to 2016. We examine these cases using a visualization method developed in particle physics (CERN) and the messages that the exchange receives about market activity rather than time‐based snapshots. This approach allows to examine multiple indicators related to market manipulation and complement existing research methods, thereby enhancing the identification and understanding of, as well as the motivation for, market manipulation. In the JPMorgan cases, we offer an alternative motivation for spoofing than moving the price. [ABSTRACT FROM AUTHOR]

We study the price impact of order flow in the world's largest soybean meal futures markets. Our intraday results indicate that incoming orders can be used to explain and predict future price changes. Our results are shown to be robust to various order flow measures, price aggregation approaches and data frequencies. We find that order flow imbalance (OFI) is a more all‐encompassing measure carrying greater information about price change relative to both trade imbalance (TI) and volume. Moreover, while both OFI and TI are shown to predict future price changes, this predictability diminishes over longer measure and price change frequency horizons. [ABSTRACT FROM AUTHOR]

Grid energy storage plays a key role in making carbon-free, renewable energy production a reality. Yet, when it comes to maximizing profit, owners of storage assets still struggle with coordinating their trading activities across time because of the complex nature of multisettlement electricity markets. In "Coordination of Multimarket Bidding of Grid-Energy Storage," Nils Löhndorf and David Wozabal propose a multistage stochastic programming model for market-oriented optimization of energy storage. To calculate lower and upper bounds on optimal values, they develop novel methods for scenario-tree generation and information relaxation. They show that a coordinated policy that reserves capacity for the short-term markets is optimal and that the gap to a sequential policy increases with short-term price volatility and market liquidity. The authors find that coordination is beneficial for all considered asset types and that flexible storages with high price impact benefit most. Their findings inform storage owners which markets contribute most value, how to organize trading across time, and how to calculate optimal bidding strategies. We consider the problem of a storage owner who trades in a multisettlement electricity market comprising an auction-based day-ahead market and a continuous intraday market. We show in a stylized model that a coordinated policy that reserves capacity for the intraday market is optimal and that the gap to a sequential policy increases with intraday price volatility and market liquidity. To assess the value of coordination in a realistic setting, we develop a multistage stochastic program for day-ahead bidding and hourly intraday trading along with a corresponding stochastic price model. We show how tight upper bounds can be obtained based on calculating optimal bilinear penalties for a novel information relaxation scheme. To calculate lower bounds, we propose a scenario tree generation method that lends itself to deriving an implementable policy based on reoptimization. We use these methods to quantify the value of coordination by comparing our policy with a sequential policy that does not coordinate day-ahead and intraday bids. In a case study, we find that coordinated bidding is most valuable for flexible storage assets with high price impact, like pumped-hydro storage. For small assets with low price impact, like battery storage, participation in the day-ahead auction is less important and intraday trading appears to be sufficient. For less flexible assets, like large hydro reservoirs without pumps, intraday trading is hardly profitable as most profit is made in the day-ahead market. A comparison of lower and upper bounds demonstrates that our policy is near-optimal for all considered assets. [ABSTRACT FROM AUTHOR]

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. • We propose a novel formulation of the Hawkes Process to maintain positive spread. • We augment the non-parametric methods proposed in Kirchner 2017 to work with slow decaying kernels and to be more stable. • We make use of calibrated distributions for sampling the order sizes of the events rather than assuming unit order-size. • We formulate the in-spread order arrivals as a function of the current spread — utilizing the well known fact that spreads are mean-reverting. • We perform a MI study on this simulator along with testing against several baselines and comparing against empirical data. [ABSTRACT FROM AUTHOR]

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.

We introduce a class of Markov models to describe the bid–ask price dynamics in the presence of liquidity fluctuations. In a highly competitive regime, the spread evolution belongs to a class of Markov processes known as a population process with uniform catastrophes. Our mathematical analysis focuses on establishing the law of large numbers, the central limit theorem, and large deviations for this catastrophe-based model. Large deviation theory allows us to illustrate how huge deviations in the spread and prices can occur in the model. Moreover, our research highlights how these local trends and volatility are influenced by the typical values of the bid–ask spread. We calibrated the model parameters using available high-frequency data and conducted Monte Carlo numerical simulations to demonstrate its ability to reasonably replicate key phenomena in the presence of liquidity fluctuations.

At subsecond horizons, bids and offers in U.S. equity markets are more volatile than what would be implied by long-term fundamentals. To assess costs and consequences, this paper suggests that traders’ random delays (latencies) interact with quote volatility to generate execution price risk and relative latency costs. Analysis of the behavior of quote setters suggests that this volatility is more likely to arise from recurrent cycles of undercutting similar to the Edgeworth cycles found in product markets rather than mixed strategies of limit-order placement. [ABSTRACT FROM PUBLISHER]

Deciding between the use of market orders and limit orders is an important question in practical optimal trading problems. A key ingredient in making this decision is understanding the uncertainty of the execution of a limit order, that is, the fill probability or the probability that an order will be executed within a certain time horizon. Equivalently, one can estimate the distribution of the time-to-fill. We propose a data-driven approach based on a recurrent neural network to estimate the distribution of time-to-fill for a limit order conditional on the current market conditions. Using a historical data set, we demonstrate the superiority of this approach to several benchmark techniques. This approach also leads to significant cost reductions while implementing a trading strategy in a prototypical trading problem. [ABSTRACT FROM AUTHOR]

Abstract We propose an empirical behavioral order-driven (EBOD) model with price limit rules, which consists of an order placement process and an order cancellation process. All the ingredients of the model are determined based on the empirical microscopic regularities in the order flows of stocks traded on the Shenzhen Stock Exchange. The model can reproduce the main stylized facts in real markets. Computational experiments unveil that asymmetric setting of price limits will cause the stock price to diverge exponentially when the up price limit is higher than the down price limit and to vanish vice versa. We also find that asymmetric price limits have little influence on the correlation structure of the return series and the volatility series, but cause remarkable changes in the average returns and the tail exponents of returns. Our EBOD model provides a suitable computational experiment platform for academics, market participants, and policy makers.

We extend a Discrete Time Random Walk (DTRW) numerical scheme to simulate the anomalous diffusion of financial market orders in a simulated order book. Here using random walks with Sibuya waiting times to include a time-dependent stochastic forcing function with non-uniformly sampled times between order book events in the setting of fractional diffusion. This models the fluid limit of an order book by modelling the continuous arrival, cancellation and diffusion of orders in the presence of information shocks. We study the impulse response and stylised facts of orders undergoing anomalous diffusion for different forcing functions and model parameters. Concretely, we demonstrate the price impact for flash limit-orders and market orders and show how the numerical method generates kinks in the price impact. We use cubic spline interpolation to generate smoothed price impact curves. The work promotes the use of non-uniform sampling in the presence of diffusive dynamics as the preferred simulation method. [ABSTRACT FROM AUTHOR]

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.