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This study uncovers how household investors intensify the effect of the 52-week high (52WH): increased volume and momentum-like returns at the 52WH price. Using daily household and institutional trading data, we find that households sharply increase their selling, particularly with limit orders at the 52WH price. This behavior is indicative of anchoring, as it is robust to past returns and intensified by proximity, market uncertainty, and salience of the 52WH. This uninformed limit order selling at and prior to the 52WH leads to a doubling of unconditional 52WH anomaly returns. Post-event returns benefit institutions, which act as counterparties. [ABSTRACT FROM AUTHOR]

Can order markets lead participants towards price-taking equilibrium? Viewing market sessions as steps of iterative algorithms, this paper indicates positive prospects for convergence. Mathematical arguments turn on convolution, efficiency and generalized gradients. Economic arguments revolve around reservation costs, derived from indifference or threshold payments for quantities supplied or demanded. [ABSTRACT FROM AUTHOR]

Limit Orders allow buyers and sellers to set a "limit price" they are willing to accept in a trade. On the other hand, market orders allow for immediate execution at any price. Thus, market orders are susceptible to slippage, which is the additional cost incurred due to the unfavorable execution of a trade order. As a result, limit orders are often preferred, since they protect traders from excessive slippage costs due to larger than expected price fluctuations. Despite the price guarantees of limit orders, they are more complex compared to market orders. Orders with overly optimistic limit prices might never be executed, which increases the risk of employing limit orders in Machine Learning (ML)-based trading systems. Indeed, the current ML literature for trading almost exclusively relies on market orders. To overcome this limitation, a Deep Reinforcement Learning (DRL) approach is proposed to model trading agents that use limit orders. The proposed method (a) uses a framework that employs a continuous probability distribution to model limit prices, while (b) provides the ability to place market orders when the risk of no execution is more significant than the cost of slippage. Extensive experiments are conducted with multiple currency pairs, using hourly price intervals, validating the effectiveness of the proposed method and paving the way for introducing limit order modeling in DRL-based trading. [ABSTRACT FROM AUTHOR]

We examine whether options exchanges' pricing schedules affect broker order routing behavior and limit order execution quality. We find that some brokers seemingly maximize the value of their order flow by selling marketable orders and sending nonmarketable orders to exchanges that offer large liquidity rebates. Other brokers appear to bypass liquidity rebates by routing both marketable and nonmarketable orders to exchanges that purchase order flow. Using a decision by the Philadelphia Stock Exchange (PHLX) to change its trading protocol, we provide empirical evidence that brokers can enhance limit order execution quality by routing nonmarketable limit orders to options exchanges that purchase order flow. [ABSTRACT FROM AUTHOR]

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 examine the effects of an order cancellation fee on limit order flow and execution quality in the PHLX options market. The cancellation fee on professional order flow effectively reduces the rate at which limit orders are canceled. Whereas the cancellation fee discourages the submission of nonmarketable orders, it encourages the submission of marketable orders. Consequently, nonmarketable order fill rates increase; marketable order fill speeds decrease; and bid-ask spreads widen. We also find slight increases in both dollar volume and market share. (JEL G11, G14, G18) Authors have furnished an Internet Appendix , which is available on the Oxford University Press Web site next to the link to the final published paper online. [ABSTRACT FROM AUTHOR]

Over-the-counter (OTC) markets attract substantial trading volume despite exhibiting frictions absent in centralized limit-order markets. We compare the efficiency of OTC and limit-order markets when traders' expertise is endogenous. We show that asymmetric access to counterparties in OTC markets yields increased rents from expertise acquisition for a few well-connected core traders. When the existence of gains to trade is uncertain, traders' higher expertise in OTC markets can improve allocative efficiency. In contrast, when expertise primarily causes adverse selection, competitive limit-order markets tend to dominate. Our model provides guidance for policy makers and empiricists evaluating the efficiency of market structures. [ABSTRACT FROM AUTHOR]

We exploit a discontinuity in the New York Stock Exchange Designated Market Maker (DMM) contract to identify causal effects of DMM participation on equilibrium market outcomes. We document that contractual features that enhance DMM participation are associated with increased depth, narrower bid-ask spreads, and higher rates of price improvement, with most of the improvements attributable to increases in liquidity provision on markets other than the NYSE. These results cannot be attributed to the mechanical effects of the contractual changes and support the interpretation that market making is characterized by strategic complementarity. Received October 7, 2017; editorial decision December 10, 2018 by Editor Itay Goldstein. [ABSTRACT FROM AUTHOR]

We examine the effect of selected limit order tools (stop loss, take profit, and trailing stop) on the disposition effect, a well-known behavioral bias, by using experimental trading data. Our presumption is that the limit orders should significantly eliminate this behavioral bias, which may lead to higher losses than feasible for a trader. The traders of our data sample can be considered as a sample of beginners or less informed traders. Based on our analysis it is possible to conclude that limit orders have a significant impact on the disposition effect. Traders using these tools were able not only to avoid this behavioral bias, but even reverse it, which is, as far as we know, a unique result within the existing literature. Moreover, we found out that the impact of eliminating of the disposition effect by limit orders use is positive, as it may lead to significant loss reduction. On the other hand, the effect on profits is insignificant. [ABSTRACT FROM AUTHOR]

Using a tractable extension of the model of Leland (1985), we study how a delta‐hedging strategy can realistically be implemented using market and limit orders in a centralized, automated market‐making desk that integrates trading and liquidity provision for both options and their underlyings. In the continuous‐time limit, the optimal limit‐order exposure can be computed explicitly by a pointwise maximization. It is determined by the relative magnitudes of adverse selection, bid–ask spreads, and volatilities. The corresponding option price—from which the option can be replicated using market and limit orders—is characterized via a nonlinear PDE. Our results highlight the benefit of tactical liquidity provision for contrarian trading strategies, even for a trading desk that is not a competitive market maker. More generally, the paper also showcases how reduced‐form models are competitive with "brute force" numerical approaches to market microstructure. Both the estimation of microstructure parameters and the simulation of the optimal trading strategy are made concrete and reconciled with real‐life high frequency data. [ABSTRACT FROM AUTHOR]

The optimal execution of stock trades is a relevant and interesting problem as it is key in maximizing profits and reducing risks when investing in the stock market. In the case of large orders, the problem becomes even more complex as the impact of the order in the market has to be taken into account. The usual solution is to split large orders into a set of smaller suborders that must be executed within a prescribed time window. This leads to the problem of deciding when in the time window execute each suborder. There are popular ways of executing the trading of these split orders like those which try to track the “Time Weighted Average Price” and the “Volume Weighted Average Price”, usually called TWAP and VWAP orders. This paper presents a strategy to optimize the splitting of large trade orders over a given time window. The strategy is based on the solution of an optimization problem that is applied following a receding horizon approach. This approach reduces the impact of prediction errors due to the uncertain market dynamics, by using new values of the price time series as they are available as time goes on. Suborder size constraints are taken into account in both market and limit orders. The strategy relies on price and traded volume forecast but it is independent of the prediction technique used. The performance index weighs not only the financial cost of the suborders, but also the impact on the market and the forecasting accuracy. A tailored optimization algorithm is proposed for efficiently solving the corresponding optimization problem. Most of the computations of the algorithm can be parallelized. Finally, the proposed approach has been tested through a case study composed by stocks of the Chinese A-share market.

The rise of computerized trading strategies in equity markets has spurred competition between trading venues. This paper shows that cross-venue strategies create highly interlinked markets: trades on one venue are followed by sizeable cancellations of limit orders on competing venues. These cancellations are explained in a simple model of competition between two limit order markets with fast and slow traders. Only the fast traders can access the liquidity of both venues simultaneously. Empirically, we confirm the predictions that the fraction of fast traders (1) reduces the equilibrium liquidity supply and (2) reduces the magnitude of the cancellations following a trade. [ABSTRACT FROM AUTHOR]

We hypothesize that cognitive limitation may be manifested in a disproportionately large volume of limit orders submitted at round-number prices if investors use these numbers as cognitive shortcuts. Using detailed limit order data in the Taiwan Futures Exchange, we find that investors with lower cognitive abilities, defined as higher limit order submission ratios at round numbers, suffer greater losses in their round-numbered and non-round-numbered limit orders, market orders, and round-trip trades. The positive correlation between cognitive ability and investment performance is monotonic and robust across futures and options markets. In addition, past trading experience helps mitigate cognitive limitation. [ABSTRACT FROM PUBLISHER]

This paper deals with a fundamental subject that has seldom been addressed in recent years, that of market impact in the options market. Our analysis is based on a proprietary database of metaorders—large orders that are split into smaller pieces before being sent to the market—on one of the main Asian markets. In line with our previous work on the equity market [Said, E., Bel Hadj Ayed, A., Husson, A. and Abergel, F., Market impact: A systematic study of limit orders. Mark. Microstruct. Liq., 2018, 3(3&4), 1850008.], we propose an algorithmic approach to identify metaorders, based on some implied volatility parameters, the at the money forward volatility and at the money forward skew. In both cases, we obtain results similar to the now well-understood equity market: Square-Root Law, Fair Pricing Condition and Market Impact Dynamics. [ABSTRACT FROM AUTHOR]

The importance of incorporating an effective order placement strategy in the design of a stock market algorithmic trading system is evaluated. Although the types of order placements are fundamental to the success of any trading strategy, few studies testing the viability of algorithmic trading systems give attention to this critical issue. In this study a variety of order placements are investigated within a trading system including: limit and stop orders, trailing stops, and volume slicing. These placement orders are coupled with four popular technical trading rules to determine the entry and exit conditions. The selected technical indicators encompass well-known trend and momentum indicators including MACD, AROON, RSI and Stochastics. It is found that the success of an algorithmic trading strategy in achieving the risk and return preferences of an investor depend significantly on the types of order placements embodied in the system. [ABSTRACT FROM AUTHOR]

Competition among trading platforms has considerably reduced trading fees in stock markets. We show that this evolution is not necessarily beneficial to investors, Although they increase gains from trade when a trade happens, lower trading costs can induce investors to post limit orders with a smaller execution probability. In this case, gains from trade are realized less frequently and investors can be worse off. Our model has testable implications for the effects of trading fees and their breakdown between liquidity suppliers and liquidity demanders on limit order fill rates and bid-ask spreads. [ABSTRACT FROM AUTHOR]

This paper estimates a collection of high‐frequency informational efficiency metrics by constructing a unique Eurodollar futures data set with the complete messaging history. To capture price efficiency, this paper calculates the mid‐quote return autocorrelations following a full range of time intervals. The findings suggest the mid‐quote return autocorrelations are positive and gradually increase from the tick‐level to 30‐min. Then, I utilize a vector autoregression to estimate the pricing error, which shows the adjustment time of trade returns is completed in 1 s. Furthermore, trade prices are less sensitive about incorporating any available new information as the Eurodollar futures approaches its maturity. [ABSTRACT FROM AUTHOR]

We model a dynamic limit order market as a stochastic sequential game with rational traders. Since the model is analytically intractable, we provide an algorithm based on Pakes and McGuire (2001) to find a stationary Markov-perfect equilibrium. We then generate artificial time series and perform comparative dynamics. Conditional on a transaction, the midpoint of the quoted prices is not a good proxy for the true value. Further, transaction costs paid by market order submitters are negative on average, and negatively correlated with the effective spread. Reducing the tick size is not Pareto improving but increases total investor surplus. [ABSTRACT FROM AUTHOR]

For NYSE-listed IPOs, limit order submissions and depth relative to volume are unusually low on the first trading day. Initial buy-side liquidity is higher for IPOs with high-quality underwriters, large syndicates, low insider sales, and high premarket demand, while sell-side liquidity is higher for IPOs that represent a large fraction of outstanding shares and have low premarket demand. Our results suggest that uncertainty and offer design affect initial liquidity, though order flow stabilizes quickly. We also find that submission strategies are influenced by expected underwriter stabilization and preopening order flow contains information about both initial prices and subsequent returns. [ABSTRACT FROM AUTHOR]

Are auction markets or dealer markets better able to identify informed traders? Our analysis of firms that transfer to an alternative exchange structure indicates that traders are more anonymous in a competing dealer market than in an auction environment. Our evidence also shows that the associated changes in the probability of trading with an informed trader are related to changes in the bid-ask spread. The reduction in bid-ask spreads is more pronounced for firms with higher probability of transacting with an informed trader prior to the relocation from a dealer to an auction market. [ABSTRACT FROM AUTHOR]

We provide empirical evidence on order submission strategy of investors with similar commitments to trade by comparing the execution costs of market orders and marketable limit orders (i.e., limit orders with the same trading priority as market orders). The results indicate the unconditional trading costs of marketable limit orders are significantly greater than market orders. We attribute the difference in costs to a selection bias and provide evidence suggesting the order submission strategy decision is based on prevailing market conditions and stock characteristics. After correcting for the selection bias, the results show the average trader chooses the order type with lower conditional trading costs. [ABSTRACT FROM AUTHOR]

In this paper, we determine whether each bid (ask) quote reflects the trading interest of the specialist, limit order traders, or both for a sample of NYSE stocks in 1991. We then compare Nasdaq spreads with NYSE spreads that reflect the trading interest of the specialist. Our empirical results show that the average Nasdaq spread is significantly larger than the average NYSE specialist spread. We find that, on average, 49% of the difference between Nasdaq and specialist spreads is due to the differential use of even-eighth quotes between Nasdaq dealers and NYSE specialists. We also find that the NYSE specialist spread is significantly larger than the limit order spread, although NYSE specialists and limit order traders are similar in their use of even-eighth quotes. [ABSTRACT FROM AUTHOR]

We investigate the role of limit orders in the liquidity provision in a pure order-driven market. Results show that market depth rises subsequent to an increase in transitory volatility, and transitory volatility declines subsequent to an increase in market depth. We also examine how transitory volatility affects the mix between limit orders and market orders. When transitory volatility arises from the ask (bid) side, investors will submit more limit sell (buy) orders than market sell (buy) orders. This result is consistent with the existence of limit-order traders who enter the market and place orders when liquidity is needed. [ABSTRACT FROM AUTHOR]

We study order flow and liquidity around NYSE trading halts. We find that market and limit order submissions and cancellations increase significantly during trading halts, that a large proportion of the limit order book at the reopen is composed of orders submitted during the halt, and that the market-clearing price at the reopen is a good predictor of future prices. Depth near the quotes is unusually low around trading halts, though specialists and/or floor traders appear to provide additional liquidity at these times. Finally, specialists appear to "spread the quote" prior to imbalance halts to convey information to market participants. [ABSTRACT FROM AUTHOR]

We analyze the contribution to price discovery of market and limit orders by high‐frequency traders (HFTs) and non‐HFTs. While market orders have a larger individual price impact, limit orders are far more numerous. This results in price discovery occurring predominantly through limit orders. HFTs submit the bulk of limit orders and these limit orders provide most of the price discovery. Submissions of limit orders and their contribution to price discovery fall with volatility due to changes in HFTs' behavior. Consistent with adverse selection arising from faster reactions to public information, HFTs' informational advantage is partially explained by public information. [ABSTRACT FROM AUTHOR]

We show how the supply of liquidity in order-driven markets is affected if limit orders (LOs) are forced to rest in the limit order book for a minimum resting time (MRT) before they can be cancelled. The bid-ask spread increases as the MRT increases because market makers (MMs) increase the depth of their LOs to protect them from being picked off by other traders. We also show that the expected profits of the MMs increase when the MRT increases. The intuition is as follows. As the MRT increases, there are two opposing forces at work. One, the longer the MRT, the more likely the LOs are to be filled and, on average, shares are sold at a loss. Two, because the depth of the posted LOs increases, the probability that the LO is picked off by other traders before the end of the MRT decreases. The net effect is that a longer MRT leads to a higher expected profit. We also show that the depth of LOs increases when the volatility of the price of the asset increases. Also, the depth of LOs increases when the arrival rate of market orders increases because it is less likely that LOs will be picked off by the end of the MRT. Finally, our model also makes predictions about the overall liquidity of the market. We show that MMs choose to supply the minimum amount of shares per LO allowed by the exchange because expected profits are maximised when liquidity provided is lowest. [ABSTRACT FROM AUTHOR]

This paper discusses performance measures for market and limit orders. We suggest two measures: one for precommitted traders (who must trade) and another for passive traders (who are indifferent to trading). We compute these measures for a sample of NYSE SuperDOT orders. The results suggest that the limit order placement strategies most commonly used by NYSE SuperDOT traders do in fact perform best. Limit orders placed at or better than the prevailing quote perform better than do market orders, even after imputing a penalty for unexecuted orders, and after taking into account market order price improvement. Unconditional order submission strategies that use SuperDOT to offer liquidity in competition with the specialist do not appear to be profitable. [ABSTRACT FROM AUTHOR]

This paper employs a "transaction" data-base to study whether observed quote-revisions are consistent with those predicted by the adverse selection and inventory cost theories of the bid-ask spread. We find that actual quote-revisions are consistent with the theoretical prediction in only 25% of the cases. Furthermore, quote-revision patterns are found to be strongly dependent on the level of the outstanding spread and, to a lesser extent, on the transaction size. These systematic patterns, unrelated to the inventory cost and adverse selection theories, are consistent with the effect on quote-revisions of the limit order book and the minimum 1/8 price-change rule. [ABSTRACT FROM AUTHOR]

In the Black and Scholes system, the underlying asset price model follows geometric Brownian motion (GBM) with no bankruptcy risk. While GBM is a commonly used model in financial markets, bankruptcy risk should be considered in the case of a severe economic crisis, such as that caused by the COVID-19 pandemic. The omission of bankruptcy risk could considerably influence the setting of a trading strategy. In this article, we adopt an extended GBM model that considers the bankruptcy risk and study its optimal limit price problem. A limit order is a classical trading strategy for investing in stocks. First, we construct the explicit expressions of the expected discounted profit functions for sell and buy limit orders and then derive their optimal limit prices. Furthermore, via sensitivity analysis, we discuss the influence of the omission of bankruptcy risk in executing limit orders.

A correction to the online version of the article in this issue entitled "Over-the-Counter versus Limit-Order Markets: The Role of Traders’ Expertise” by Vincent Glode and Christian C. Opp, is noted and was corrected in the print version.

We develop a trading strategy that employs limit and market orders in a multiasset economy where the assets are not only correlated, but can also be structurally dependent. To model the structural dependence, the mid-price processes follow a multivariate reflected Brownian motion on the closure of a no-arbitrage region which is dictated by the bid–ask spreads of the assets. We provide a mathematical framework for such an economy and solve for the value function and optimal control for an investor who takes positions in these assets. The optimal strategy exhibits two dominant features which depend on how far the vector of mid-prices is from the no-arbitrage bounds. When mid-prices are sufficiently far from the no-arbitrage edges, the strategy behaves as that of a market maker who posts buy and sell limit orders. And when the mid-price vector is close to the edge of the no-arbitrage region, the strategy executes a combination of market orders and limit orders to profit from statistical arbitrages. We discuss a numerical scheme to solve for the value function and optimal control, and perform a simulation study to discuss the main characteristics of the optimal strategy. [ABSTRACT FROM AUTHOR]

High-frequency trading dominates trading in financial markets. How it affects the low-frequency trading, however, is still unclear. Using NASDAQ order book data, the authors investigate this question by categorizing orders as either high or low frequency, and examining several measures. They find that high-frequency trading enhances liquidity by increasing the trade frequency and quantity of low-frequency orders. High-frequency trading also reduces the waiting time of low-frequency limit orders and improves their likelihood of execution. The results indicate that high-frequency trading has a liquidity provision effect and improves the execution quality of low-frequency orders. [ABSTRACT FROM AUTHOR]

We show how the position of a limit order (LO) in the queue influences the decision of whether to cancel the order or let it rest. Using ultra-high-frequency data from the Nasdaq exchange, we perform empirical analysis on various LO book events and propose novel ways for modelling some of these events, including cancellation of LOs in various positions and size of market orders. Based on our empirical findings, we develop a queuing model that captures stylized facts on the data. This model includes a distinct feature which allows for a potentially random effect due to the agent’s impulse control. We apply the queuing model in an algorithmic trading setting by considering an agent maximizing her expected utility through placing and cancelling of LOs. The agent’s optimal strategy is presented after calibrating the model to real data. A simulation study shows that for the same level of standard deviation of terminal wealth, the optimal strategy has a 2.5% higher mean compared to a strategy which ignores the effect of position, or an 8.8% lower standard deviation for the same level of mean. This extra gain stems from posting an LO during adverse conditions and obtaining a good queue position before conditions become favourable. [ABSTRACT FROM AUTHOR]

In modern markets, limit order traders can no longer be characterized as passive traders, which has led some researchers to argue that limit orders, rather than trades, are the informational unit in today's markets. If this is true, measures such as order imbalance, which uses signed trades and captures the information from liquidity demanders, may not be as valid as they once were. We calculate two measures of limit order imbalance and examine the relation between limit order imbalances and returns. We find evidence that limit order imbalances explain returns, but conclude that traditional order imbalance has more explanatory power. Thus, our results suggest that limit orders have not trumped trades as the informational unit in today's markets. [ABSTRACT FROM AUTHOR]

This paper is devoted to the important yet little explored subject of the market impact of limit orders. Our analysis is based on a proprietary database of metaorders — large orders that are split into smaller pieces before being sent to the market. We first address the case of aggressive limit orders and then that of passive limit orders. In both cases, we provide empirical evidence of a power law behavior for the temporary market impact. The relaxation of the price following the end of the metaorder is also studied, and the long-term impact is shown to stabilize at a level of approximately two-thirds of the maximum impact. Finally, a fair pricing condition during the life cycle of the metaorders is empirically validated. [ABSTRACT FROM AUTHOR]

We identify and analyze statistical regularities and irregularities in the recent order flow of different NASDAQ stocks, focusing on the positions where orders are placed in the order book. This includes limit orders being placed outside of the spread, inside the spread and (effective) market orders. Based on the pairwise comparison of the order flow of different stocks, we perform a clustering of stocks into groups with similar behavior. This is useful to assess systemic aspects of stock price dynamics. We find that limit order placement inside the spread is strongly determined by the dynamics of the spread size. Most orders, however, arrive outside of the spread. While for some stocks order placement on or next to the quotes is dominating, deeper price levels are more important for other stocks. As market orders are usually adjusted to the quote volume, the impact of market orders depends on the order book structure, which we find to be quite diverse among the analyzed stocks as a result of the way limit order placement takes place. [ABSTRACT FROM AUTHOR]

Iceberg orders, which allow traders to hide a portion of their order size, have become prevalent in many electronic limit order markets. This paper investigates, via a real options analysis, whether small traders, who have no use for submitting iceberg orders, are better off submitting their orders to fully transparent markets which have low depth, or to more liquid markets which do permit the placement of iceberg orders by large traders. Surprisingly, we find that in the context of our model, small traders are better off submitting to fully transparent markets in spite of them being less liquid. [ABSTRACT FROM AUTHOR]

By introducing a genetic algorithm with a classifier system as a learning mechanism for uninformed traders into a dynamic limit order market with asymmetric information, this paper examines the effect of the learning on traders’ trading behavior, market liquidity and efficiency. We show that the learning is effective and valuable with respect to information acquisition, forecasting, buy–sell order choice accuracies, and profit opportunity for uninformed traders. It improves information dissemination efficiency and reduces the information advantage of informed traders and hence the value of the private information. In particular, the learning and information become more valuable with higher volatility, less informed traders, and longer information lag. Furthermore, the learning makes not only uninformed but also informed traders submit more limit orders and hence increases market liquidity supply. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

Optimal control models for limit order trading often assume that the underlying asset price is a Brownian motion since they deal with relatively short time scales. The resulting optimal bid and ask limit order prices tend to track the underlying price as one might expect. This is indeed the case with the model of Avellaneda and Stoikov [Quantitative Finance 8(3) (2008), 217-224], which has been studied extensively. We consider here this model under the condition when the underlying price is mean reverting. Our main result is that when time is far from the terminal, the optimal price for bid and ask limit orders is constant, which means that it does not track the underlying price. Numerical simulations confirm this behavior. When the underlying price is mean reverting, then for times sufficiently far from terminal, it is more advantageous to focus on the mean price and ignore fluctuations around it. Mean reversion suggests that limit orders will be executed with some regularity, and this is why they are optimal. We also explore intermediate time regimes where limit order prices are influenced by the inventory of outstanding orders. The duration of this intermediate regime depends on the liquidity of the market as measured by specific parameters in the model. [ABSTRACT FROM AUTHOR]

A model is proposed to study the risk management problem of designing optimal trading strategies in a limit order book. The execution of limit orders is uncertain, which leads to a stochastic control problem. In contrast to previous literature, we allow the agents to choose both the quotes and the sizes of their submitted orders. Attention is paid to how the trading strategy is affected by an order book's characteristics, market volatility and the trader's risk attitude. We prescribe an optimal splitting of the order size for the trades with limit orders, while the existing literature offers a solution to this problem with market orders, and, at the same time, we provide guidelines to optimally place orders further behind the best price or to (re)position them more aggressively. Thus this paper is an attempt towards a more realistic modeling of optimal liquidation throughout limit orders. [ABSTRACT FROM AUTHOR]

Using a version of the ITCH data set time stamped to the millisecond, O'Hara, Yao and Ye find that odd-lot trades are highly informed. However, NASDAQ reports trades based on the size of the resting limit order, creating a bias in the count of odd-lot trades. Using ITCH data from 2013, time stamped to the nanosecond, we find that roughly 50% of odd-lot trades are created by the resting limit order and are part of larger marketable orders. We show that odd-lot marketable orders are not more informed than round/mixed lot marketable orders. [ABSTRACT FROM AUTHOR]

To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by characteristics of the order flows and queue sizes in each limit order book, as well as the structure of transaction fees and rebates across exchanges. We propose a quantitative framework for studying thisorder placementproblem by formulating it as a convex optimization problem. This formulation allows the study of how the optimal order placement decision depends on the interplay between the state of order books, the fee structure, order flow properties and the aversion to execution risk. In the case of a single exchange, we derive an explicit solution for the optimal split between limit and market orders. For the general case of order placement across multiple exchanges, we propose a stochastic algorithm that computes the optimal routing policy and study the sensitivity of the solution to various parameters. Our algorithm does not require an explicit statistical model of order flow but exploits data on recent order fills across exchanges in the numerical implementation of the algorithm to acquire this information through a supervised learning procedure. [ABSTRACT FROM PUBLISHER]

By incorporating behavioural sentiment in a model of a limit order market, we show that behavioural sentiment not only helps to replicate most of the stylized facts in limit order markets simultaneously, but it also plays a unique role in explaining those stylized facts that cannot be explained by noise trading, such as fat tails in the return distribution, long memory in the trading volume, an increasing and non-linear relationship between trade imbalance and mid-price returns, as well as the diagonal effect, or event clustering, in order submission types. The results show that behavioural sentiment is an important driving force behind many of the well-documented stylized facts in limit order markets. [ABSTRACT FROM PUBLISHER]

We explore the relation between limit order price clustering and price efficiency. We find that executed sell limit orders cluster more frequently on round increments than buy limit orders and that this asymmetry in clustering is consistent with the well-documented asymmetry in price response to marketable orders. In addition, we find that the degree of clustering is positively related to volatility and that asymmetry in clustering depends on whether stock prices are rising or falling-sell limit orders cluster more frequently as prices are rising, although buy limit orders cluster more as prices are declining. Our results indicate that predictable patterns in limit order pricing contribute to short-run deviations from price efficiency. [ABSTRACT FROM AUTHOR]