Order Book Market Research Articles

Optimal execution with liquidity risk in a diffusive order book market

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, [Formula: see text], and optimal placement of limit order, [Formula: see text], 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.

Tick Size, Trading Strategies, and Market Quality

We investigate the effects of a tick-size reduction on market quality in a multiperiod limit order book market. For illiquid stocks, reducing the tick size facilitates undercutting and discourages liquidity provision, resulting in deteriorating market quality but higher volume. For liquid stocks, reducing the tick size curtails queues, resulting in lower depth and volume but narrower spread. With a competing crossing network, a tick-size reduction results in worse market quality for all stocks due to migration of order flows. We empirically test our model predictions and find support for recent tick-size reductions in Japan and the United States. This paper was accepted by Victoria Ivashina, finance. Supplemental Material: The data files and online appendices are available at https://doi.org/10.1287/mnsc.2022.4502 .

Manipulation of the Bitcoin market: an agent-based study

Fraudulent actions of a trader or a group of traders can cause substantial disturbance to the market, both directly influencing the price of an asset or indirectly by misinforming other market participants. Such behavior can be a source of systemic risk and increasing distrust for the market participants, consequences that call for viable countermeasures. Building on the foundations provided by the extant literature, this study aims to design an agent-based market model capable of reproducing the behavior of the Bitcoin market during the time of an alleged Bitcoin price manipulation that occurred between 2017 and early 2018. The model includes the mechanisms of a limit order book market and several agents associated with different trading strategies, including a fraudulent agent, initialized from empirical data and who performs market manipulation. The model is validated with respect to the Bitcoin price as well as the amount of Bitcoins obtained by the fraudulent agent and the traded volume. Simulation results provide a satisfactory fit to historical data. Several price dips and volume anomalies are explained by the actions of the fraudulent trader, completing the known body of evidence extracted from blockchain activity. The model suggests that the presence of the fraudulent agent was essential to obtain Bitcoin price development in the given time period; without this agent, it would have been very unlikely that the price had reached the heights as it did in late 2017. The insights gained from the model, especially the connection between liquidity and manipulation efficiency, unfold a discussion on how to prevent illicit behavior.

Queueing Dynamics and State Space Collapse in Fragmented Limit Order Book Markets

In modern equity markets, participants have a choice of many exchanges at which to trade, each of which typically operates as an electronic limit order book. This paper analyzes this setting as a multiclass queueing system. Taking into account the effect of investors’ order-routing decisions across exchanges, they find that the equilibrium of this decentralized market exhibits a state space collapse property, whereby the queues at different exchanges are coupled, and the overall behavior of the market is captured through a one-dimensional process that can be viewed as a weighted aggregate queue length across all exchanges. The key driver of this coupling phenomenon is anticipated delay as opposed to the queue lengths themselves.

Constrained Optimal Execution in Limit Order Book Market with Power-shaped Market Depth

Instead of using the classical block-shaped market depth to build the optimal execution model, this work studies the constrained optimal execution problem in a limit order book (LOB) market with a power-shaped market depth. Different from the linear price impact derived from the framework of block-shaped market depth, the price impact generated from the framework of our power-shaped market depth becomes a nonlinear function, which is consistent with the empirical studies. We also consider a class of state-dependent upper and lower bound constraints on trading strategies, which includes non-negative constraint (or non-short selling constraint) as its special case. Even though both the power-shaped market depth and trading strategy constraints make it hardly to solve such an optimal execution problem analytically, we still develop some significant properties on the optimal execution policy and optimal execution cost of our model. From some illustrative examples, we find that the optimal execution policy derived from our model is quite different from the one generated from the model with the block-shaped market depth when the market exhibits finite resiliency. However, when the market resilience is infinite, the obtained result becomes different, i.e., the optimal execution policies derived from these two kind of models are equivalent. For a special model with the stochastic block-shaped market depth and infinite market resilience, we successfully derive the analytical solution for such an optimal execution problem by utilizing the state separation property induced from its structure. The revealed optimal execution strategy is a piece-wise affine function with respect to the current remaining position, which can be computed off-line efficiently by solving two coupled equations. Finally, due to its explicit solution, we utilize this optimal execution model to demonstrate that the model admits no price magnification opportunity for the two-sided trading strategy.

The effects of trade size and market depth on immediate price impact in a limit order book market

We compare trade size to the prevailing market depth at the best level in the limit order book to detect and account for zero impact trades in an immediate price impact model. Our model also incorporates standard trade attributes (trade size, market capitalization and volatility) in a dynamic setting. The incorporation of market depth information reduces the mean absolute/squared forecast error of an immediate price impact prediction by about 60%. After controlling for trade attributes, market depth, price impact dynamics and intra-and inter- day periodicities (in order of relative importance) all improve the prediction of a trade’s price impact. We demonstrate the value of our model by showing that splitting a big order into a series of smaller trades results in a reduction of between 60% and 82% of the immediate price impact cost of the big order. We also find that our depth indicator helps with the prediction of order flow and permanent price impact.

An Agent‐Based model for Limit Order Book: Estimation and simulation

AbstractIn this article, we introduce an agent‐based model for a Limit Order Book (LOB) market with a price limit and simulate and estimate its parameters. In this framework, we have reached a linear relation between the percentage of the sellers in the market and the changes in the logarithm of the price. Moreover, we demonstrate that in this model if the supply and demand are equal and naturally if the demand is more than the supply, on the average, logarithm of the price strictly increases and this occurs while in the model argued, the inflation is assumed to be zero, no real factor exists in order to increase the value of stocks and no factor‐like rumors enters. This conclusion implies that merely the normal activities of the dealers to gain profit causes a false increase in the stock price. This fact, as being demonstrated in the simulation, has also been proved analytically. We call this phenomenon “the intrinsic bubble”. Finally, we show that if the rules of the market change in the way that the daily price of the stock is calculated by the median of the prices traded, instead of their mean, this intrinsic bubble will more or less disappear.

Trading strategy with stochastic volatility in a limit order book market

In this paper, we employ the Heston stochastic volatility model to describe the stock’s volatility and apply the model to derive and analyze trading strategies for dealers in a security market with price discovery. The problem is formulated as a stochastic optimal control problem, and the controlled state process is the dealer’s mark-to-market wealth. Dealers in the security market can optimally determine their ask and bid quotes on the underlying stocks continuously over time. Their objective is to maximize an expected profit from transactions with a penalty proportional to the variance of cumulative inventory cost. We provide an approximate, analytically tractable solution to the stochastic control problem. Numerical experiments are given to illustrate the effects of various parameters on the performances of trading strategies.

On Frequent Batch Auctions for Stocks

Abstract I show that frequent batch auctions for stocks have the potential to reduce the severity of stock price crashes when they occur. For a given sequence of orders from a continuous electronic limit order book market, matching orders using one-second apart batch auctions results in nearly the same trades and prices. Increasing the time interval between auctions to one minute significantly reduces the severity stock price crashes. In spite of this and other advantages pointed out in the literature, frequent batch auctions have not caught on. There is a need for carefully designed market experiments to understand why and what aspect of reality academic research may be missing.

Optimal execution with regime-switching market resilience

In this paper, we study the optimal placement of market orders in a limit order book (LOB) market when the market resilience rate, which is the rate at which market replenishes itself after each trade, is stochastic. More specifically, we establish a tractable extension to the optimal execution model in Obizhaeva and Wang (2013) by modelling the dynamics of the resilience rate to be driven by a Markov chain. When the LOB replenishes itself stochastically through time, the optimal execution strategy becomes state-dependent, and is driven linearly by the current remaining position and the current temporary price impact, with their linear dependence based on the expectation of the dynamics of future resilience rate. A trader would optimally place more aggressive (respectively, conservative) market orders when the limit order book switches from a low to a high resilience state, (respectively, from a high to a low resilience state). Our cost saving analysis indicates that the incremental execution costs can be substantial when the agent ignores the stochastic dynamics of the market resilience rate by adopting the state-independent strategies.

Trading mechanisms and market quality: Limit-order books versus dealership markets

We compare the market quality of the dealer market and limit order book (LOB) market in a unified framework. We find that, in terms of liquidity and gains from trade, dealer market performs better when the order size is small, while LOB market performs better when the order size is large. A competitive hybrid market where the dealer marker and the LOB market compete with each other dominates the two pure markets.

The role of volume in order book dynamics: a multivariate Hawkes process analysis

We show that multivariate Hawkes processes coupled with the nonparametric estimation procedure first proposed in Bacry and Muzy [IEEE Trans. Inform. Theory, 2016, 62, 2184–2202] can be successfully used to study complex interactions between the time of arrival of orders and their size observed in a limit order book market. We apply this methodology to high-frequency order book data of futures traded at EUREX. Specifically, we demonstrate how this approach is amenable not only to analyse interplay between different order types (market orders, limit orders, cancellations) but also to include other relevant quantities, such as the order size, into the analysis, showing also that simple models assuming the independence between volume and time are not suitable to describe the data.

Strategic Foundation for the Tail Expectation in Limit Order Book Markets

In an environment with noise traders and informed traders trading on news, we model competition in schedules by liquidity suppliers quoting on a limit order book. We show that there is an equilibrium featuring quoters using mixed strategies; each quoter employs a step function, offering the same quantity of shares at random prices (and, of course, random bid prices). These random prices with their associated quantities form the market quotes and the depth of book, or price schedule. There are equilibria with a smaller number of quoters quoting a larger number of shares and equilibria with a larger number of quoters quoting a smaller number of shares. Considering a sequence of equilibria with the number of quoters becoming large, we establish that the stochastic equilibrium price schedule converges to the zero-profit deterministic competitive price schedule.

Trading strategies of institutional investors in a limit order book market

The study aims to examine the trading strategies of institutional investors in limit order book market. The study modifies assumptions of prior studies [1,2] to match actual situations or facilitate calculations. First, to match actual situations or facilitate calculations. First, the investors’ objective in the study is profit maximization rather than minimization of trading costs. Second, time is continuous rather than discrete. Third, price impact functions are non-linear and take the quadratic form that features increasing prices. Study results indicate that institutional investors adopt the increasing trading strategy if the permanent price impact dominate whereas they adopt the decreasing trading strategy if the transient price impact dominates. In addition, the average trading strategy is adopted if and only if the permanent and transient price impacts are combined in some fixed proportions.

The High-Frequency Trading Arms Race: Frequent Batch Auctions as a Market Design Response *

AbstractThe high-frequency trading arms race is a symptom of flawed market design. Instead of the continuous limit order book market design that is currently predominant, we argue that financial exchanges should use frequent batch auctions: uniform price double auctions conducted, for example, every tenth of a second. That is, time should be treated as discrete instead of continuous, and orders should be processed in a batch auction instead of serially. Our argument has three parts. First, we use millisecond-level direct-feed data from exchanges to document a series of stylized facts about how the continuous market works at high-frequency time horizons: (i) correlations completely break down; which (ii) leads to obvious mechanical arbitrage opportunities; and (iii) competition has not affected the size or frequency of the arbitrage opportunities, it has only raised the bar for how fast one has to be to capture them. Second, we introduce a simple theory model which is motivated by and helps explain the empirical facts. The key insight is that obvious mechanical arbitrage opportunities, like those observed in the data, are built into the market design—continuous-time serial-processing implies that even symmetrically observed public information creates arbitrage rents. These rents harm liquidity provision and induce a never-ending socially wasteful arms race for speed. Last, we show that frequent batch auctions directly address the flaws of the continuous limit order book. Discrete time reduces the value of tiny speed advantages, and the auction transforms competition on speed into competition on price. Consequently, frequent batch auctions eliminate the mechanical arbitrage rents, enhance liquidity for investors, and stop the high-frequency trading arms race.

Designating Market Maker Behaviour in Limit Order Book Markets

Designating Market Maker Behaviour in Limit Order Book Markets

Optimal Trading with Limit Orders on a Dynamic Limit Order Book

I develop a theory of optimal trading by an institutional trader who receives a parent order (i.e., an overall trading request) from a fund manager to buy a specific quantity of a particular stock over a specified time horizon. The trader selects child orders to be submitted each period over the allotted time horizon to a limit order book market. Child orders can be either market orders or limit orders. Limit order prices can be selected from any price on a penny price grid. An unexecuted limit order can be cancelled at any time. The trader’s objective is to minimize the disutility of the fund manager. In the base version of the theory, all child orders are of unit size. I derive an analytic solution for the optimal trading strategy and show that it involves “dynamic aggressiveness.” This means that if the current period limit order executes (doesn’t execute), then the next limit order optimally has a weakly less (weakly more) aggressive price. Next, I extend the theory to: (1) permit child orders of any size, (2) allow the fund manager to have private information about future stock prices, (3) allow the fund manager to be risk averse, and (4) allow four alternative metrics for computing execution cost. I calibrate the model to real-world data and optimize it numerically. I find that if the fund manager has a large disutility parameter for underfills, then the optimal strategy involves a sequence of limit orders early on and switches to a sequence market orders later on to guarantee purchasing the parent order. Conversely, if the fund manager has a zero disutility parameter for underfills, then the optimal strategy involves a sequence of limit orders with low price aggressiveness, such that each individual trade will earn the spread. If a fund manager is relatively informed and/or highly risk averse, then the optimal strategy is relatively front-loaded in time and switches to market orders relatively early so as to trade before price moves in the predicted direction and/or to reduce risk. Conversely, if the fund manager is uninformed and has low risk aversion, then the optimal strategy is spread out over time and switches to market orders later. I find that the optimal trading strategy frequently involves dynamic aggressiveness and frequently beats two benchmark trading strategies from the existing literature. Finally, I discuss empirical predictions of the theory and how they can be tested.

Queueing Dynamics and State Space Collapse in Fragmented Limit Order Book Markets

In modern equity markets, participants have a choice of many exchanges at which to trade. Exchanges typically operate as electronic limit order books operating under a “price-time” priority rule and, in turn, can be modeled as multi-class FIFO queueing systems. A market with multiple exchanges can be thought as a decentralized, parallel queueing system. Heterogeneous traders that submit limit orders select the exchange, i.e., the queue, in which to place their orders by trading off delays until their order may fill against financial considerations. These limit orders can be thought as jobs waiting for service. Simultaneously, traders that submit market orders select the exchange, i.e., the queue, to direct their order. These market orders trigger instantaneous service completions of queued limit orders. In this way, the “server” is the aggregation of self-interested, atomistic traders submitting market orders. Taking into account the effect of investors’ order routing decisions across exchanges, we find that the equilibrium of this decentralized market exhibits a state space collapse property, whereby: (a) the queue lengths at different exchanges are coupled in an intuitive manner; (b) the behavior of the market is captured through a one-dimensional process that can be viewed as a weighted aggregate queue length across all exchanges; and (c) the behavior at each exchange can be inferred via a mapping of the aggregated market depth process that takes into account the heterogeneous trader characteristics. This predicted dimension reduction is the result of high-frequency order routing decisions that essentially couple the dynamics across exchanges. We derive a characterization of the market equilibrium and the associated aggregated depth process. Analyzing a TAQ dataset for a sample of stocks over a one month period, we find empirical support for the predicted state space collapse.

The Simplicity of Optimal Trading in Order Book Markets

The Simplicity of Optimal Trading in Order Book Markets

The Role of Visual Analysis in the Regulation of Electronic Order Book Markets

Electronic markets and automated trading have resulted in a drastic increase in the quantity and complexity of regulatory data. Reconstructing the limit order book and analyzing order flow is an emerging challenge for financial regulators. New order types, intra-market behavior and other exchange functionality further complicate the task of understanding market behavior at multiple levels. Data visualizations have proven to be a fundamental tool for building intuition and enabling exploratory data analysis in many fields. In this paper, we propose the incorporation of visualizations in the workflow of multiple financial regulatory roles, including market surveillance, enforcement, and supporting academic research.