We propose a microscopic model to describe the dynamics of the fundamental events in the limit order book (LOB): order arrivals and cancellations. It is based on an operator algebra for individual orders and describes their effect on the LOB. The model inputs are arrival and cancellation rate distributions that emerge from individual behavior of traders, and we show how prices and liquidity arise from the LOB dynamics. In a simulation study we illustrate how the model works and highlight its sensitivity with respect to assumptions regarding the collective behavior of market participants. Empirically, we test the model on a LOB snapshot of XETRA, estimate several linearized model specifications, and conduct in- and out-of-sample forecasts.The in-sample results based on contemporaneous information suggest that our model describes returns very well, resulting in an adjusted $R^2$ of roughly 80%. In the more realistic setting where only past information enters the model, we observe an adjusted $R^2$ around 15%. The direction of the next return can be predicted (out-of-sample) with an accuracy above 75% for time horizons below 10 minutes. On average, we obtain an RMSPE that is 10 times lower than values documented in the literature.
We discuss a concept denoted as Conformal Prediction (CP) in this paper. While initially stemming from the world of machine learning, it was never applied or analyzed in the context of short-term electricity price forecasting. Therefore, we elaborate the aspects that render Conformal Prediction worthwhile to know and explain why its simple yet very efficient idea has worked in other fields of application and why its characteristics are promising for short-term power applications as well. We compare its performance with different state-of-the-art electricity price forecasting models such as qua…
The large integration of variable energy resources is expected to shift a large part of the energy exchanges closer to real-time, where more accurate forecasts are available. In this context, the short-term electricity markets and in particular the intraday market are considered a suitable trading floor for these exchanges to occur. A key component for the successful renewable energy sources integration is the usage of energy storage. In this paper, we propose a novel modelling framework for the strategic participation of energy storage in the European continuous intraday market where exchange…
This paper proposes a forecast-centric adaptive learning model that engages with the past studies on the order book and high-frequency data, with applications to hypothesis testing. In line with the past literature, we produce brackets of summaries of statistics from the high-frequency bid and ask data in the CSI 300 Index Futures market and aim to forecast the one-step-ahead prices. Traditional time series issues, e.g. ARIMA order selection, stationarity, together with potential financial applications are covered in the exploratory data analysis, which pave paths to the adaptive learning mode…
We develop a tractable equilibrium model for price formation in intraday electricity markets in the presence of intermittent renewable generation. Using stochastic control theory, we identify the optimal strategies of agents with market impact and exhibit the Nash equilibrium in closed form for a finite number of agents as well as in the asymptotic framework of mean field games. Our model reproduces the empirical features of intraday market prices, such as increasing price volatility at the approach of the delivery date and the correlation between price and renewable infeed forecasts, and rela…
Optimal execution, i.e., the determination of the most cost-effective way to trade volumes in continuous trading sessions, has been a topic of interest in the equity trading world for years. Electricity intraday trading slowly follows this trend but is far from being well-researched. The underlying problem is a very complex one. Energy traders, producers, and electricity wholesale companies receive various position updates from customer businesses, renewable energy production, or plant outages and need to trade these positions in intraday markets. They have a variety of options when it comes t…
We propose a model for the dynamics of a limit order book in a liquid market where buy and sell orders are submitted at high frequency. We derive a functional central limit theorem for the joint dynamics of the bid and ask queues and show that, when the frequency of order arrivals is large, the intraday dynamics of the limit order book may be approximated by a Markovian jump-diffusion process in the positive orthant, whose characteristics are explicitly described in terms of the statistical properties of the underlying order flow. This result allows to obtain tractable analytical approximation…
University College London（伦敦大学学院）；UCL Centre for Blockchain Technologies（伦敦大学学院区块链技术中心）；London School of Economics（伦敦政治经济学院）；Systemic Risk Centre（系统风险中心）
This paper poses a few fundamental questions regarding the attributes of the volume profile of a Limit Order Books stochastic structure by taking into consideration aspects of intraday and interday statistical features, the impact of different exchange features and the impact of market participants in different asset sectors. This paper aims to address the following questions: 1. Is there statistical evidence that heavy-tailed sub-exponential volume profiles occur at different levels of the Limit Order Book on the bid and ask and if so does this happen on intra or interday time scales ? 2.In f…
The existing literature provides evidence that limit order book data can be used to predict short-term price movements in stock markets. This paper proposes a new neural network architecture for predicting return jump arrivals in equity markets with high-frequency limit order book data. This new architecture, based on Convolutional Long Short-Term Memory with Attention, is introduced to apply time series representation learning with memory and to focus the prediction attention on the most important features to improve performance. The data set consists of order book data on five liquid U.S. st…
This article presents a Hawkes process model with Markovian baseline intensities for high-frequency order book data modeling. We classify intraday order book trading events into a range of categories based on their order types and the price changes after their arrivals. To capture the stimulating effects between multiple types of order book events, we use the multivariate Hawkes process to model the self- and mutually-exciting event arrivals. We also integrate a Markovian baseline intensity into the event arrival dynamic, by including the impacts of order book liquidity state and time factor t…
Oxford-Man Institute of Quantitative Finance（牛津曼量化金融研究所）；University of Oxford（牛津大学）
We design multi-horizon forecasting models for limit order book (LOB) data by using deep learning techniques. Unlike standard structures where a single prediction is made, we adopt encoder-decoder models with sequence-to-sequence and Attention mechanisms to generate a forecasting path. Our methods achieve comparable performance to state-of-art algorithms at short prediction horizons. Importantly, they outperform when generating predictions over long horizons by leveraging the multi-horizon setup. Given that encoder-decoder models rely on recurrent neural layers, they generally suffer from slow…
Managing the prediction of metrics in high-frequency financial markets is a challenging task. An efficient way is by monitoring the dynamics of a limit order book to identify the information edge. This paper describes the first publicly available benchmark dataset of high-frequency limit order markets for mid-price prediction. We extracted normalized data representations of time series data for five stocks from the NASDAQ Nordic stock market for a time period of ten consecutive days, leading to a dataset of ~4,000,000 time series samples in total. A day-based anchored cross-validation experime…
Regarding the intraday sequence of high frequency returns of the S&P index as daily realizations of a given stochastic process, we first demonstrate that the scaling properties of the aggregated return distribution can be employed to define a martingale stochastic model which consistently replicates conditioned expectations of the S&P 500 high frequency data in the morning of each trading day. Then, a more general formulation of the above scaling properties allows to extend the model to the afternoon trading session. We finally outline an application in which conditioned forecasting is used to…
High frequency financial data is burdened by a level of randomness that is unavoidable and obfuscates the task of modelling. This idea is reflected in the intraday evolution of limit orders book data for many financial assets and suggests several justifications for the use of stochastic models. For instance, the arbitrary distribution of inter arrival times and the subsequent dependence structure between consecutive book events. This has lead to the development of many stochastic models for the dynamics of limit order books. In this paper we look to examine the adaptability of one family of su…
Ecole Polytechnique（巴黎综合理工学院）；Exoduspoint Capital Management France（法国Exoduspoint资本管理公司）；ENSAE Paris（巴黎国立统计与经济管理学院）
The existing publications demonstrate that the limit order book data is useful in predicting short-term volatility in stock markets. Since stocks are not independent, changes on one stock can also impact other related stocks. In this paper, we are interested in forecasting short-term realized volatility in a multivariate approach based on limit order book data and relational data. To achieve this goal, we introduce Graph Transformer Network for Volatility Forecasting. The model allows to combine limit order book features and an unlimited number of temporal and cross-sectional relations from di…
Northwestern University（西北大学）；UT Austin（德克萨斯大学奥斯汀分校）；University of Florida Conference on Machine Learning in Finance（佛罗里达大学金融机器学习会议）；Society of Quantitative Analyst Data Science in Finance Conference（金融量化分析师数据科学会议）；Cubist Systematic Strategies（Cubist系统策略）；Wolfe Research NLP Conference（Wolfe研究NLP会议）；Stony Brook Quantitative Finance Conference（石溪布鲁克量化金融会议）；Peking University（北京大学）；INFORMS Annual Meeting（INFORMS年度会议）；Institute for Mathematical and Statistical Innovation（数学与统计创新研究所）；CIBC（CIBC公司）
A limit order book provides information on available limit order prices and their volumes. Based on these quantities, we give an empirical result on the relationship between the bid-ask liquidity balance and trade sign and we show that liquidity balance on best bid/best ask is quite informative for predicting the future market order's direction. Moreover, we define price jump as a sell (buy) market order arrival which is executed at a price which is smaller (larger) than the best bid (best ask) price at the moment just after the precedent market order arrival. Features are then extracted relat…
The world's stock markets display a decades-long pattern of overnight and intraday returns seemingly consistent with only one explanation: one or more large, long-lived quant firms tending to expand its portfolio early in the day (when its trading moves prices more) and contract its portfolio later in the day (when its trading moves prices less), losing money on its daily round-trip trades to create mark-to-market gains on its large existing book. In the fourteen years since this extraordinary pattern of overnight and intraday returns was first noted in the literature, no plausible alternative…
The composition of natural liquidity has been changing over time. An analysis of intraday volumes for the S&P500 constituent stocks illustrates that (i) volume surprises, i.e., deviations from their respective forecasts, are correlated across stocks, and (ii) this correlation increases during the last few hours of the trading session. These observations could be attributed, in part, to the prevalence of portfolio trading activity that is implicit in the growth of ETF, passive and systematic investment strategies; and, to the increased trading intensity of such strategies towards the end of the…
Recurrent neural networks (RNNs) are types of artificial neural networks (ANNs) that are well suited to forecasting and sequence classification. They have been applied extensively to forecasting univariate financial time series, however their application to high frequency trading has not been previously considered. This paper solves a sequence classification problem in which a short sequence of observations of limit order book depths and market orders is used to predict a next event price-flip. The capability to adjust quotes according to this prediction reduces the likelihood of adverse price…
In an order-driven financial market, the price of a financial asset is discovered through the interaction of orders - requests to buy or sell at a particular price - that are posted to the public limit order book (LOB). Therefore, LOB data is extremely valuable for modelling market dynamics. However, LOB data is not freely accessible, which poses a challenge to market participants and researchers wishing to exploit this information. Fortunately, trades and quotes (TAQ) data - orders arriving at the top of the LOB, and trades executing in the market - are more readily available. In this paper, …
We showcase how Quantile Regression (QR) can be applied to forecast financial returns using Limit Order Books (LOBs), the canonical data source of high-frequency financial time-series. We develop a deep learning architecture that simultaneously models the return quantiles for both buy and sell positions. We test our model over millions of LOB updates across multiple different instruments on the London Stock Exchange. Our results suggest that the proposed network not only delivers excellent performance but also provides improved prediction robustness by combining quantile estimates.
We provide an explicit characterization of the optimal market making strategy in a discrete-time Limit Order Book (LOB). In our model, the number of filled orders during each period depends linearly on the distance between the fundamental price and the market maker's limit order quotes, with random slope and intercept coefficients. The high-frequency market maker (HFM) incurs an end-of-the-day liquidation cost resulting from linear price impact. The optimal placement strategy incorporates in a novel and parsimonious way forecasts about future changes in the asset's fundamental price. We show t…
The success of deep learning-based limit order book forecasting models is highly dependent on the quality and the robustness of the input data representation. A significant body of the quantitative finance literature focuses on utilising different deep learning architectures without taking into consideration the key assumptions these models make with respect to the input data representation. In this paper, we highlight the issues associated with the commonly-used representations of limit order book data from both a theoretical and practical perspectives. We also show the fragility of the repre…
We introduce a new model in order to describe the fluctuation of tick-by-tick financial time series. Our model, based on marked point process, allows us to incorporate in a unique process the duration of the transaction and the corresponding volume of orders. The model is motivated by the fact that the "excitation" of the market is different in periods of time with low exchanged volume and high volume exchanged. We illustrate our result by numerical simulations on foreign exchange data sampling in millisecond. By checking the main stylized facts, we show that the model is consistent with the e…
Oxford-Man Institute of Quantitative Finance, University of Oxford（牛津大学牛津曼量化金融研究院）
Market by order (MBO) data - a detailed feed of individual trade instructions for a given stock on an exchange - is arguably one of the most granular sources of microstructure information. While limit order books (LOBs) are implicitly derived from it, MBO data is largely neglected by current academic literature which focuses primarily on LOB modelling. In this paper, we demonstrate the utility of MBO data for forecasting high-frequency price movements, providing an orthogonal source of information to LOB snapshots and expanding the universe of alpha discovery. We provide the first predictive a…
Generative AI for End-to-End Limit Order Book Modelling: A Token-Level Autoregressive Generative Model of Message Flow Using a Deep State Space Network
University of Oxford（牛津大学）；Oxford-Man Institute of Quantitative Finance（牛津-曼量化金融研究院）；Alan Turing Institute（艾伦·图灵研究所）；Man Group（英仕曼集团）；Foerster Lab for AI Research（福斯特人工智能研究实验室）
