Order Book Commonalities and Bond Return Predictability

An experimental approach to the study of limit order books lies in the availability of data. Most of the results presented in this book - in any case, those we have produced ourselves - use the Thomson Reuters Tick History (TRTH) database. All exchange-traded assets worldwide are present in the TRTH database, where they are identified by their Reuters Identification Code (RIC). Similar to most historical databases directly provided by the exchanges, the TRTH data come into the form of two separate files, a trade file recording all transactions, and an event file recording every change in the limit order book. Some very specific information, such as traders’ identities, cannot be publicly disclosed for obvious confidentiality reasons, but in theory, one could reconstruct the sequence of order arrivals of all types using this trade and event files. After explaining the algorithm used for the processing of limit order book data, we describe the specific data sets that have been used at various places in this book. That way, our results can be reproduced, extended and, of course, challenged, based on the very same data sets we have used. Limit Order Book Data Processing Because one cannot distinguish market orders from cancellations just by observing changes in the limit order book (the “event” file), and since, the timestamps of the “trade” and “event” files are asynchronous , we use a matching procedure to reconstruct the order book events. In a nutshell, we proceed as follows for each stock and each trading day: 1. Parse the “event” file to compute order book state variations: • If the variation is positive (volume at one or more price levels has increased), then label the event as a limit order. • If the variation is negative (volume at one or more price levels has decreased), then label the event as a “likely market order”. • If no variation—this happens when there is just a renumbering in the field “Level” that does not affect the state of the book—do not count an event. 2. Parse the “trade” file and for each trade: • Compare the trade price and volume to likely market orders whose timestamps are in, where t Tr is the trade timestamp and Δ t is a predefined, market-dependent time window.

Non-Parametric Prediction of the Mid-Price Dynamics in a Limit Order Book

Which is Limit Order Traders More Fearful of: Non-Execution Risk or Adverse Selection Risk'

Order Aggressiveness and Order Book Dynamics

Since Kalman Filter was first developed by Kalman (1960), it has been widely used in engineering, statistics and econometrics. Filtering is different from forecasting as forecasting is made for predicting the future while filtering aims the estimation of unobservable parameters in the same period. For techniques as Kalman filters, on one hand, it can help to filter away the “noisy order”, revealing the true state of limit order book. On the other hand, it can be also use for prediction of state for next time step. In this paper, we estimate the limit order book using gamma distribution. Then each order book snapshot can be described using four parameters. After that, the basic filter is introduced with applications to disclose the pattern in limit order book.

The modeling of the limit order book is directly related to the assumptions on the behavior of real market participants. This paper is two-fold. We first present empirical findings that lay the ground for two improvements to these models. The first one is concerned with market participants by adding the additional dimension of informed market makers, whereas the second, and maybe more original one, addresses the race in the book between informed traders and informed market makers leading to different shapes of the order book. Namely, we build an agent-based model for the order book with four types of market participants: informed trader, noise trader, informed market makers and noise market makers. We build our model based on the Glosten–Milgrom approach and the most recent Huang–Rosenbaum–Saliba approach. We introduce a parameter capturing the race between informed liquidity traders and suppliers after a new information on the fundamental value of the asset. We then derive the whole “static” limit order book and its characteristics, namely, the bid-ask spread and volumes available at each level price- from the interactions between the agents and compare it with the pre-existing model. We then discuss the case where noise traders have an impact on the fundamental value of the asset and extend the model to take into account many kinds of informed market makers.

The Bi-Channel Incorporation of Private Information

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.

ABSTRACTIn this article, we take an algorithmic approach to solve the problem of optimal execution under time-varying constraints on the depth of a limit order book (LOB). Our algorithms are within the resilience model proposed by Obizhaeva and Wang (2013) with a more realistic assumption on the order book depth; the amount of liquidity provided by an LOB market is finite at all times. For the simplest case where the order book depth stays at a fixed level for the entire trading horizon, we reduce the optimal execution problem into a one-dimensional root-finding problem which can be readily solved by standard numerical algorithms. When the depth of the order book is monotone in time, we apply the Karush-Kuhn-Tucker conditions to narrow down the set of candidate strategies. Then, we use a dichotomy-based search algorithm to pin down the optimal one. For the general case, we start from the optimal strategy subject to no liquidity constraints and iterate over execution strategy by sequentially adding more constraints to the problem in a specific fashion until primal feasibility is achieved. Numerical experiments indicate that our algorithms give comparable results to those of current existing convex optimization toolbox CVXOPT with significantly lower time complexity.

In this paper we show how to reconstruct the limit order book of the 30 stocks constituting the DAX30 index based on the trading protocol of the Xetra Trading System at the Frankfurt Stock Exchange. The algorithm used is innovative as it captures all trading phases, including auctions, and delivers a reconstruction of the orderbook either from a trader’s view or a supervisory view including hidden volume as well.Based on the rebuilt order book, liquidity dynamics are examined. In contrats to findings for dealer markets, past market returns play a minor role in the determination of liquidity and liquidity commonality in Xetra, a pure limit order book market. Consequently, we provide evidence that liquidity provision by multiple sources in Xetra mitigates systemic liquidity risk introduced by the interrelation of return and liquidity.

Liquidity Effects of Earnings Announcements in Stock Limit Order Markets: Empirical Evidence from NASDAQ Nordic

The authors model trades-through, i.e. transactions that reach at least the second level of limit orders in an order book. Using tick-by-tick data on Euronext-traded stocks, they show that a simple bivariate Hawkes process fits nicely their empirical observations of tradesthrough. The authors show that the cross-influence of bid and ask trades-through is weak.

We model the trading strategy of an investor who spoofs the limit order book (LOB) to increase the revenue obtained from selling a position in a security. The strategy employs, in addition to sell limit orders (LOs) and sell market orders (MOs), a large number of spoof buy LOs to manipulate the volume imbalance of the LOB. Spoofing is illegal, so the strategy trades off the gains that originate from spoofing against the expected financial losses due to a fine imposed by the financial authorities. As the fine increases, the investor relies less on spoofing, and if the fine is large, the investor does not spoof the LOB. The arrival rate of buy MOs increases because other traders interpret the spoofed buy-heavy LOB as an upward pressure on prices. When the fine is low, spoofing considerably increases the revenues from liquidating a position. Spoofing increases the PnL because (i) the investor employs fewer MOs to draw the inventory to zero and benefits from roundtrip trades, which stem from spoof buy LOs that are ‘inadvertently’ filled and subsequently unwound with sell LOs; and (ii) the midprice trends upward when the book is buy-heavy; therefore the spoofer sells the asset at better prices.

This paper concerns extracting knowledge from limit order books and using it to predict significant changes in the price of the financial asset under study. Limit order books are encoded in a feature-based data representation. A binary Support Vector Machine classifier is trained to predict whether a particular limit order book leads to a significant change in the price in a few successive time instants, or not. An Evolutionary Algorithm is used to find the optimal parameter setting of the feature-based data representation, so that the performance of the classifier was better. Computational experiments performed on financial ultra-high frequency time series coming from the London Stock Exchange Rebuild Order Book database confirmed that the optimization of the feature-based data representation is very effective in improving the performance of the classification.

Limit order books and liquidity around scheduled and non-scheduled announcements: Empirical evidence from NASDAQ Nordic