Learning multi-market microstructure from order book data

In this paper, we investigate market behaviors at high-frequency using neural networks trained with order book data. Experiments are done intensively with 110 asset pairs covering 97% of spot-futures pairs in the Korea Exchange. An efficient training scheme that improves the performance and training stability is suggested, and using the proposed scheme, the lead–lag relationship between spot and futures markets are measured by comparing the performance gains of each market data set for predicting the other. In addition, the gradients of the trained model are analyzed to understand some important market features that neural networks learn through training, revealing characteristics of the market microstructure. Our results show that highly complex neural network models can successfully learn market features such as order imbalance, spread-volatility correlation, and mean reversion.     

The submission of limit orders or market orders: The role of timing and information in the Reuters D2000-2 system

Recent work in the market microstructure literature suggests that the speed with which orders arrive in the market impacts traders' order submission decisions. In this study we use an asymmetric autoregressive conditional duration (ACD) model to empirically investigate the influence on the submission of limit and market orders of changes in the time between the past submissions of different types of orders, changes in the slope of the limit order book, and changes in price uncertainty. We find that the expected time between the arrivals of successive orders in the foreign exchange market depends on the previous type of order submitted and the slope on both sides of the order book. Price uncertainty (volatility) plays a secondary role after accounting for the impact of changes in the slope of the order book. Lastly, we find that there are fundamental changes in the level of information contained in the submission of orders at the opening and closing of markets.     

Optimal execution strategies in limit order books with general shape functions

We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005 Obizhaeva, A and Wang, J. 2005. Optimal trading strategy and supply/demand dynamics, Preprint Available online at: http://www.rhsmith.umd.edu/faculty/obizhaeva/OW060408.pdf (accessed 16 February 2009)[Crossref] , [Google Scholar]) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modelling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e. of the volume of the LOB, or the exponential recovery of the bid–ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy of a risk-neutral investor, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005 Obizhaeva, A and Wang, J. 2005. Optimal trading strategy and supply/demand dynamics, Preprint Available online at: http://www.rhsmith.umd.edu/faculty/obizhaeva/OW060408.pdf (accessed 16 February 2009)[Crossref] , [Google Scholar]). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience-type.     

Electronic limit order book and order submission choice around macroeconomic news

We investigate the dynamics of the displayed part of the Island ECN limit order book for the equity-index-linked securities market around macroeconomic news releases. Our results indicate that the quality of the electronic market, measured by spread and depth, deteriorates during the releases. Furthermore, they show that traders appear to switch to more aggressive strategies as early as 3 min before an announcement and are most aggressive within the first minute after the announcement. Also, there is a noticeable difference in the response of the limit order book to the macroeconomic news during pre-market hours relative to regular trading hours.     

Latency and liquidity provision in a limit order book

We use a recent, high-quality data set from Nasdaq to perform an empirical analysis of order flow in a limit order book before and after the arrival of a market order. For each of the stocks that we study, we identify a sequence of distinct phases across which the net flow of orders differs considerably. We note that some of our results are consistent with the widely reported phenomenon of stimulated refill, but that others are not. We therefore propose alternative mechanical and strategic motivations for the behaviour that we observe. Based on our findings, we argue that strategic liquidity providers consider both adverse selection and expected waiting costs when deciding how to act.     

Modelling the shape of the limit order book

This article develops a parsimonious way to use the shape of the limit order book to produce an estimate of the asset price. The posited model captures and describes the evolution of the distribution of limit orders on the bid and ask sides of the LOB during the trading session and provides estimates of the execution asset price over time. The performance of the model is evaluated against some existing standards from the market microstructure literature during the trading session. Empirical evidence on listed companies confirm a strong contribution of our methodology to the innovation in asset prices, according to the information share coefficients. We also document a significant improvement relative to the Hasbrouck [J. Finance, 1991, 46, 179–207] model when our model estimates are included as regressors.     

Modelling intensities of order flows in a limit order book

We propose a parametric model for the simulation of limit order books. We assume that limit orders, market orders and cancellations are submitted according to point processes with state-dependent intensities. We propose new functional forms for these intensities, as well as new models for the placement of limit orders and cancellations. For cancellations, we introduce the concept of ‘priority index’ to describe the selection of orders to be cancelled in the order book. Parameters of the model are estimated using likelihood maximization. We illustrate the performance of the model by providing extensive simulation results, with a comparison to empirical data and a standard Poisson reference.     

Volatility and market structure

This study examines volatility within three related intra-day series – transaction returns, quote midpoint returns, and limit order book midpoint returns – for a set of NYSE-listed stocks. We document statistically significant GARCH effects both overall and surrounding earnings announcements in all three series for the majority of stocks in the sample. We then compare the extent of volatility clustering among the series. In addition, the relation between volatility and market structure is examined via a set of cross-sectional regressions, and relations among the series over time are studied in a vector autoregressive framework.     

Quasi-centralized limit order books

A quasi-centralized limit order book (QCLOB) is a limit order book (LOB) in which financial institutions can only access the trading opportunities offered by counterparties with whom they possess sufficient bilateral credit. In this paper, we perform an empirical analysis of a recent, high-quality data set from a large electronic trading platform that utilizes QCLOBs to facilitate trade. We argue that the quote-relative framework often used to study other LOBs is not a sensible reference frame for QCLOBs, so we instead introduce an alternative, trade-relative framework, which we use to study the statistical properties of order flow and LOB state in our data. We also uncover an empirical universality: although the distributions that describe order flow and LOB state vary considerably across days, a simple, linear rescaling causes them to collapse onto a single curve. Motivated by this finding, we propose a semi-parametric model of order flow and LOB state for a single trading day. Our model provides similar performance to that of parametric curve-fitting techniques but is simpler to compute and faster to implement.     

The information content of a limit order book: The case of an FX market

In this paper we examine the question of whether knowledge of the information contained in a limit order book helps to provide economic value in a simple trading scheme. Given the greater information content of the order book, over simple price information, it might naturally be expected that the order book would dominate. Using Dollar Sterling tick data, we find that despite the in-sample statistical significance of variables describing the structure of the limit order book in explaining tick-by-tick returns, they do not consistently add significant economic value out-of-sample. We show this using a simple linear model to determine trading activity, as well as a model-free genetic algorithm based on price, order flow, and order book information. We also find that the profitability of all trading rules based on genetic algorithms dropped substantially in 2008 compared to 2003 data.     

The price impact of order book events: market orders,limit orders and cancellations

While the long-ranged correlation of market orders and their impact on prices has been relatively well studied in the literature, the corresponding studies of limit orders and cancellations are scarce. We provide here an empirical study of the cross-correlation between all these different events, and their respective impact on future price changes. We define and extract from the data the ‘bare’ impact these events would have if they were to happen in isolation. For large tick stocks, we show that a model where the bare impact of all events is permanent and non-fluctuating is in good agreement with the data. For small tick stocks, however, bare impacts must contain a history-dependent part, reflecting the internal fluctuations of the order book. We show that this effect can be accurately described by an autoregressive model of the past order flow. This framework allows us to decompose the impact of an event into three parts: an instantaneous jump component, the modification of the future rates of the different events, and the modification of the jump sizes of future events. We compare in detail the present formalism with the temporary impact model that was proposed earlier to describe the impact of market orders when other types of events are not observed. Finally, we extend the model to describe the dynamics of the bid–ask spread.     

Scheduled macro-news effects on a Euro/US dollar limit order book around the 2008 financial crisis

Characteristics of a complete limit order book (LOB) for Euro/US dollar in 2006-09, are asymmetrically affected by scheduled macro news announcements during the financial crisis. Depth is the most responsive characteristic followed by spread, volatility and slope. Depth and volatility respond more to expansion surprises, while spread and slope are more sensitive to recession. The effect of the announcement’s occurrence without surprise is overwhelmingly positive (negative) for depth and volatility (spread) in both regimes. This effect is mitigated by the surprise. More than half of US scheduled news surprises have state dependent depth coefficients, most with opposing signs between recession and expansion. Using all quote levels generates stronger characteristic response, indicating the existence of information outside of the best quotes.     

Algorithmic trading in a microstructural limit order book model

We propose a microstructural modeling framework for studying optimal market-making policies in a FIFO (first in first out) limit order book (order book). In this context, the limit orders, market orders, and cancel orders arrivals in the order book are modeled as point processes with intensities that only depend on the state of the order book. These are high-dimensional models which are realistic from a micro-structure point of view and have been recently developed in the literature. In this context, we consider a market maker who stands ready to buy and sell stock on a regular and continuous basis at a publicly quoted price, and identifies the strategies that maximize their P&L penalized by their inventory. An extension of the methodology is proposed to solve market-making problems where the orders arrivals are modeled using Hawkes processes with exponential kernel.

We apply the theory of Markov Decision Processes and dynamic programming method to characterize analytically the solutions to our optimal market-making problem. The second part of the paper deals with the numerical aspect of the high-dimensional trading problem. We use a control randomization method combined with quantization method to compute the optimal strategies. Several computational tests are performed on simulated data to illustrate the efficiency of the computed optimal strategy. In particular, we simulated an order book with constant/ symmetric/ asymmetrical/ state dependent intensities, and compared the computed optimal strategy with naive strategies. Some codes are available on https://github.com/comeh.     

Liquidity,information, strategic trading in an electronic order book: New insights from the European carbon markets

The electronic limit order book (LOB hereafter) has rapidly become the primary way of trading European carbon assets over the 4 years of the EU ETS programme (2008–2012). In this first attempt of examining the informational content of an electronic order book, we evidence that order flow imbalances have a moderate capacity to predict short term price changes. However, we find that both LOB slope and immediacy costs help to forecast quote improvements and volatility in the next 30 min. Further, we explain why informed trading is highly influential and show that it consists in mixing order splitting strategies and posting fleeting orders once the asymmetric information is reduced (Rosu, 2009). Overall, the consolidated status of the order book mirrors a high level of market uncertainty and a low degree of informational efficiency. In this way, strategic trading can in itself explain some of order book properties, independently of the degree of traders’ sophistication and market competition.     

Characteristics of the order flow through an electronic open limit order book

We estimate and examine certain characteristics of the order flow through an electronic open limit order book, using order (not trade) data. In doing this, we bring out new evidence on order flow from a market with microstructure different from that of the NYSE. We find that the proportion of informed orders is less than 10%, lower than previous estimates. Informed traders choose smaller orders than uninformed traders, but do not materially differ in their choice of limit or market orders. The proportion of informed investors is similar between good and bad news days. Finally, there are U-shaped intraday patterns in order arrival, and the information content of the order flow appears to follow this pattern across the day.     

Reduced form modeling of limit order markets

This paper proposes a parametric approach for stochastic modeling of limit order markets. The models are obtained by augmenting classical perfectly liquid market models with a few additional risk factors that describe liquidity properties of the order book. The resulting models are easy to calibrate and to analyse using standard techniques for multivariate stochastic processes. Despite their simplicity, the models are able to capture several properties that have been found in microstructural analysis of limit order markets. Calibration of a continuous-time three-factor model to Copenhagen Stock Exchange data exhibits, for example, mean reversion in liquidity as well as the so-called crowding out effect, which influences subsequent mid-price moves. Our dynamic models are also well suited for analysing market resilience after liquidity shocks.     

A fully consistent,minimal model for non-linear market impact

We propose a minimal theory of non-linear price impact based on the fact that the (latent) order book is locally linear, as suggested by reaction–diffusion models and general arguments. Our framework allows one to compute the average price trajectory in the presence of a meta-order that consistently generalizes previously proposed propagator models. We account for the universally observed square-root impact law, and predict non-trivial trajectories when trading is interrupted or reversed. We prove that our framework is free of price manipulation and that prices can be made diffusive (albeit with a generic short-term mean-reverting contribution). Our model suggests that prices can be decomposed into a transient ‘mechanical’ impact component and a permanent ‘informational’ component.     

Estimation of slowly decreasing Hawkes kernels: application to high-frequency order book dynamics

We present a modified version of the non parametric Hawkes kernel estimation procedure studied in Bacry and Muzy [arXiv:1401.0903, 2014] that is adapted to slowly decreasing kernels. We show on numerical simulations involving a reasonable number of events that this method allows us to estimate faithfully a power-law decreasing kernel over at least six decades. We then propose a eight-dimensional Hawkes model for all events associated with the first level of some asset order book. Applying our estimation procedure to this model, allows us to uncover the main properties of the coupled dynamics of trade, limit and cancel orders in relationship with the mid-price variations.     

The impact of short-selling and margin-buying on liquidity: Evidence from the Chinese stock market

We propose a framework based on limit order book to analyze the impact of short-selling and margin-buying on liquidity. We show that when short-sellers are perceived as informed, adverse selection may lead to uninformed traders withdrawing their limit orders. Given that the Chinese stock market has strong information asymmetry and a high proportion of uninformed traders, we predict that the pilot program launched in March 2010, which lifts restrictions on short-selling and margin-buying for a designated list of stocks, may have a negative impact on liquidity. We perform difference-in-differences tests and show evidence that allowing for short-selling and margin-buying indeed has a significantly negative impact on liquidity for stocks on the designated list. In particular, the negative impact on liquidity is more pronounced for stocks with high information asymmetry. Nevertheless, when short-selling volume dries up due to regulation changes in August 2015, i.e., the “T+1” trading rule on short-selling, we show that consistent with model predictions, lifting restrictions on short-selling and margin-buying has a positive effect on liquidity.