Optimal high-frequency trading with limit and market orders

We propose a framework for studying optimal market-making policies in a limit order book (LOB). The bid–ask spread of the LOB is modeled by a tick-valued continuous-time Markov chain. We consider a small agent who continuously submits limit buy/sell orders at best bid/ask quotes, and may also set limit orders at best bid (resp. ask) plus (resp. minus) a tick for obtaining execution order priority, which is a crucial issue in high-frequency trading. The agent faces an execution risk since her limit orders are executed only when they meet counterpart market orders. She is also subject to inventory risk due to price volatility when holding the risky asset. The agent can then also choose to trade with market orders, and therefore obtain immediate execution, but at a less favorable price. The objective of the market maker is to maximize her expected utility from revenue over a short-term horizon by a trade-off between limit and market orders, while controlling her inventory position. This is formulated as a mixed regime switching regular/impulse control problem that we characterize in terms of a quasi-variational system by dynamic programming methods. Calibration procedures are derived for estimating the transition matrix and intensity parameters for the spread and for Cox processes modelling the execution of limit orders. We provide an explicit backward splitting scheme for solving the problem and show how it can be reduced to a system of simple equations involving only the inventory and spread variables. Several computational tests are performed both on simulated and real data, and illustrate the impact and profit when considering execution priority in limit orders and market orders.     

Market or limit orders?

In this paper we investigate the problem of optimal order placement of an asset listed on an exchange using both market and limit orders in a simple model of market dynamics. We seek to understand under which settings it is optimal to place limit or market orders. Limit orders typically lower transaction costs but increase the risk of incomplete order execution, whereas market orders typically have higher transaction costs but are guaranteed to be executed. Rather than considering order book dynamics to determine if a limit order is executed we rely on price dynamics for this. We look at implementation shortfall in this setup with market impact of trading and propose a dynamic program to find the optimal placement of both market and limit orders for risk-neutral and risk-averse traders. With this we find a bound on the expected cost of trading and show that a trader who behaves optimally should always expect to pay less to trade less. We then solve the dynamic program numerically and examine optimal order placement strategies. We find that the decision between market and limit orders is sensitive to price volatility, risk aversion, and trading costs.     

Is faster or slower trading better? An examination of order type execution speed and costs

We examine order type execution speed and costs for US equity traders. Marketable orders that execute slower exhibit lower execution costs. Those who remove liquidity faster and pay higher trading costs transact in smaller size, spread trading across more venues, take more liquidity, and are better informed. Nonmarketable limit orders that execute slower exhibit greater adverse selection; and larger, uninformed traders who concentrate their trading in fewer venues submit them. Our findings suggest that slowing down the trading process, when faster options exist, can benefit certain market participants who seek to cross the bid–ask spread.     

On the Feasibility of Automated Market Making by a Programmed Specialist

Securities trading is accomplished through the execution of orders. Admissible orders (e.g., market orders, limit orders) give rise to discontinuous aggregate demand functions, composed of many “steps.” Demand smoothing, or the balancing of excesses due to such discontinuities via intervention, is one of the most basic functions that could be assigned to a “specialist.” When the specialist's “affirmative obligation” is fully specified, his or her activity can in principle be automated. This paper is an attempt to assess, via simulation, some of the ramifications of using a “programmed specialist,” whose automated market making is limited to demand smoothing. A number of alternative rules of operation are simulated. Several of the rules performed well, especially the extremely simple rule that calls for the (computerized) specialist to minimize new absolute share holdings in each security at each trading point via “total” (as opposed to “local”) demand smoothing. Our results indicate that the underlying costs of demand smoothing are on the order of a fraction of a penny per share traded even in relatively thin markets.     

Order Preferencing and Market Quality on U.S. Equity Exchanges

We present a detailed view of market quality in the presenceof preferencing arrangements. A unique dataset provides theopportunity to measure trading costs of marketable orders andfill rates and ex post costs of limit orders across tradingvenues. For market orders, we find the primary exchange providesthe lowest execution costs. However, the preferencing exchangesare no worse than, and in most cases better than, the nonpreferencingregional exchanges. For limit orders, the regionals executelimit orders more frequently than the primary market and withan ex post execution cost that is not very different from theprimary market.     

Order dynamics: Recent evidence from the NYSE

We examine investor order choices using evidence from a recent period when the NYSE trades in decimals and allows automatic executions. We analyze the decision to submit or cancel an order or to take no action. For submitted orders, we distinguish order type (market vs. limit), order side (buy vs. sell), execution method (auction vs. automatic), and pricing aggressiveness. We find that the NYSE exhibits positive serial correlation in order type on an order-by-order basis, which suggests that follow-on order strategies dominate adverse selection or liquidity considerations at a moment in time. Aggregated levels of order flow also exhibit positive serial correlation in order type, but appear to be non-stationary processes. Overall, changes in aggregated order flow have an order-type serial correlation that is close to zero at short aggregation intervals, but becomes increasingly negative at longer intervals. This implies a liquidity exhaustion–replenishment cycle. We find that small orders routed to the NYSE's floor auction process are sensitive to the quoted spread, but that small orders routed to the automatic execution system are not. Thus, in addition to foregoing price improvement, traders selecting the speed of automatic executions on the NYSE do so with little regard for the quoted cost of immediacy. As quoted depth increases, traders respond by competing on price via limit orders that undercut existing bid and ask prices. Limit orders are more likely and market sells are less likely late in the trading day. These results are helpful in understanding the order arrival process at the NYSE and have potential applications in academics and industry for optimizing order submission strategies.     

The informational effect and market quality impact of upstairs trading and fleeting orders on the Australian Securities Exchange

This paper investigates the informational effect of trading and market segmentation on the Australian Securities Exchange (ASX) paying particular attention to the recent phenomenon: fleeting orders.¹ Confirming theoretical predictions, this study finds that permanent price effect (PPE) is significantly greater in the central limit order book (LOB) than in the upstairs market and that less informed institutional trades are routed to the upstairs market. It also finds that a well functioning upstairs market often results in lower transaction cost, higher volatility and larger trade size on the ASX. In the context of fleeting orders specifically, it finds the informational effect and market quality impact of upstairs market to be weaker after removing fleeting orders, which subsequently leads to the conclusion that recently introduced execution algorithms, which leave a trace of fleeting orders, often result in lower PPE and are mostly used my uninformed liquidity traders.     

A dynamic limit order market with fast and slow traders

This paper considers the role of high-frequency trading in a dynamic limit order market. Fast traders? ability to revise their quotes quickly after news arrivals helps to reduce the inefficiency that is rooted in the risk of being picked off, which increases trade. However, their presence induces slow traders to strategically submit limit orders with a lower execution probability, thereby reducing trade. Because speed is a source of market power, it enables fast traders to extract rents from other market participants and triggers a costly arms race that reduces social welfare. The model generates a number of testable implications concerning the effects of high-frequency trading in limit order markets.     

The self-financing equation in limit order book markets

The goal of this paper is to present a mathematical framework for trading on a limit order book, including its associated transaction costs, and to propose continuous-time equations which generalise the self-financing relationships of frictionless markets. These equations naturally differentiate between trading via limit and via market orders, as they include a price impact or adverse selection constraint. We briefly mention several possible applications, including hedging European options with limit orders, to illustrate their impact and how they can be used to the benefit of low-frequency traders. Two appendices include empirical evidence for facts which are not universally recognised in the current literature on the subject.

     

The Price of Immediacy

This paper models transaction costs as the rents that a monopolistic market maker extracts from impatient investors who trade via limit orders. We show that limit orders are American options. The limit prices inducing immediate execution of the order are functionally equivalent to bid and ask prices and can be solved for various transaction sizes to characterize the market maker's entire supply curve. We find considerable empirical support for the model's predictions in the cross-section of NYSE firms. The model produces unbiased, out-of-sample forecasts of abnormal returns for firms added to the S&P 500 index.     

Hybrid markets, tick size and investor trading costs

This paper shows how the tick size affects equilibrium outcomes in a hybrid stock market such as the NYSE that features both a specialist and a limit order book. Reducing the tick size facilitates the specialist's ability to step ahead of the limit order book, resulting in a reduction in the cumulative depth of the limit order book at prices above the minimum tick. If market demand is price-sensitive, and there are costs of limit order submission, the limit order book can be destroyed by tick sizes that are either too small or too large. We show that trading cost is minimized at larger tick sizes for larger market orders, creating an incentive to submit smaller orders when tick size is reduced. With a smaller tick size, specialist participation increases and specialist profit increases slightly for small market orders, and considerably for large market orders.     

An analysis of the economic justification for consolidation in a secondary security market

This paper considers whether all trading in a listed security should be required to go through an exchange. To this end, the incentives for a brokerage firm to offer in-house execution services are discussed, and an analytical framework is developed which shows that, under idealized conditions, fragmentation of the market through in-house execution services would not result in any overall deterioration of market performance characteristics. However, when some of the idealized conditions are relaxed, the market fragmentation arising from in-house execution causes the gains to some customers to be more than overcome by the losses to others. The analysis, which also takes account of the desirability of enforcing reasonable trading priority rules (such as priority by price and time) across all traders, yields several public policy implications. For some unlikely scenarios, it would be possible, through appropriate commission sharing and a perfectly operating intermarket trading system, for optimal overall market performance to be consistent with the market fragmentation inherent in in-house execution services. However, for most realistic scenarios, fragmentation would cause a deterioration in the quality of the market. Thus it seems desirable to require that all trading go through a central exchange with a consolidated limit order book.     

Correlated Trading and Returns

A German broker's clients place similar speculative trades and therefore tend to be on the same side of the market in a given stock during a given day, week, month, and quarter. Aggregate liquidity effects, short sale constraints, the systematic execution of limit orders (coordinated through price movements) or the correlated trading of other investors who pick off retail limit orders do not fully explain why retail investors trade similarly. Correlated market orders lead returns, presumably due to persistent speculative price pressure. Correlated limit orders also predict subsequent returns, consistent with executed limit orders being compensated for accommodating liquidity demands.     

Technology and liquidity provision: The blurring of traditional definitions

Limit orders are usually viewed as patiently supplying liquidity. We investigate the trading of one hundred Nasdaq-listed stocks on INET, a limit order book. In contrast to the usual view, we find that over one-third of nonmarketable limit orders are cancelled within two seconds. We investigate the role these “fleeting orders” play in the market and test specific hypotheses about their uses. We find evidence consistent with dynamic trading strategies whereby traders chase market prices or search for latent liquidity. We show that fleeting orders are a relatively recent phenomenon, and suggest that they have arisen from a combination of factors that includes improved technology, an active trading culture, market fragmentation, and an increasing utilization of latent liquidity.     

Order submission strategies,liquidity supply,and trading in pennies on the New York Stock Exchange

We use NYSE system order data to conduct a controlled experiment examining changes in trader behavior, displayed liquidity supply, and execution quality around the reduction in the minimum price variation to $0.01. Although traders do not substantially reduce their use of traditional limit orders in favor of market orders or non-displayed orders, they do decrease limit order size and cancel limit orders more frequently after decimals than before. These changes in order submission strategy appear to result in less displayed liquidity throughout the limit order book more than 15 cents from the quote midpoint. This reduction in displayed liquidity, however, does not manifest itself in poor execution quality. Even for large system orders, traditional execution quality is not worse with decimals than with fractions.     

Limit order books and trade informativeness

In the microstructure literature, information asymmetry is an important determinant of market liquidity. The classic setting is that uninformed dedicated liquidity suppliers charge price concessions when incoming market orders are likely to be informationally motivated. In limit order book (LOB) markets, however, this relationship is less clear, as market participants can switch roles, and freely choose to immediately demand or patiently supply liquidity by submitting either market or limit orders. We study the importance of information asymmetry in LOBs based on a recent sample of 30 German Deutscher Aktienindex (DAX) stocks. We find that Hasbrouck's (1991) measure of trade informativeness Granger causes book liquidity, in particular that required to fill large market orders. Picking-off risk due to public news-induced volatility is more important for top-of-the book liquidity supply. In our multivariate analysis, we control for volatility, trading volume, trading intensity and order imbalance to isolate the effect of trade informativeness on book liquidity.     

A simulation analysis of the microstructure of double auction markets

Abstract

We introduce an order-driven market model with heterogeneous agents trading via a central order matching mechanism. Traders set bids and asks and post market or limit orders according to exogenously fixed rules. We investigate how different trading strategies may affect the dynamics of price, bid-ask spreads, trading volume and volatility. We also analyse how some features of market design, such as tick size and order lifetime, affect market liquidity. The model is able to reproduce many of the complex phenomena observed in real stock markets.     

Why Do Traders Split Orders?

We examine factors that influence decisions by U.S. equity traders to execute a string of orders, in the same stock, in the same direction, around the same time. Order splitting is more likely to occur when traders submit larger‐size orders and when market depth and trading activity are lower. Order splitters demand liquidity more and pay higher trading costs, but their overall performance is better. When controlling for execution time, split orders are more informative than single orders. Our results suggest that order splitting arises from a variety of factors, including informational differences, order and trader characteristics, and market conditions.     

Speed,distance, and electronic trading: New evidence on why location matters

We examine the execution quality of electronic stock traders who are geographically dispersed throughout the United States. Traders who are located near market central computers in the New York City area experience faster order execution. Moreover, the time to execute orders rises as a trader’s actual distance (mileage) to NYC widens. In electronic market settings, data transfer limitations and transmission slowdowns result in geographically-dispersed electronic traders having different access to trading speed. We find that speed differences are costly to traders and that speed-advantaged traders engage in strategies that are more conducive to speed.     

Informed trading and order type

Each trader must choose between a limit order, a market order, or using a floor broker. We hypothesize that informed investors will: (1) concentrate their trading in floor broker orders and (2) sometimes trade patiently. Consistent with our hypotheses, empirical results suggest that most informed trading occurs through orders executed by floor brokers and that informed floor brokers are sometimes patient. Regardless of their patience, however, quote revisions following trade executions are consistent with the hypothesis that markets recognize that floor traders are more likely to be informed than other traders. As a result, informed trading moves equilibrium security values.