RISK METRICS AND FINE TUNING OF HIGH‐FREQUENCY TRADING STRATEGIES

We propose risk metrics to assess the performance of high‐frequency (HF) trading strategies that seek to maximize profits from making the realized spread where the holding period is extremely short (fractions of a second, seconds, or at most minutes). The HF trader maximizes expected terminal wealth and is constrained by both capital and the amount of inventory that she can hold at any time. The risk metrics enable the HF trader to fine tune her strategies by trading off different metrics of inventory risk, which also proxy for capital risk, against expected profits. The dynamics of the midprice of the asset are driven by information flows which are impounded in the midprice by market participants who update their quotes in the limit order book. Furthermore, the midprice also exhibits stochastic jumps as a consequence of the arrival of market orders that have an impact on prices which can give rise to market momentum (expected prices to trend up or down). The HF trader's optimal strategy incorporates a buffer to cover adverse selection costs and manages inventories to maximize the expected gains from market momentum.     

Intraday Liquidity Provision by Trader Types in a Limit Order Market: Evidence from Taiwan Index Futures

This study examines the dynamic liquidity provision process by institutional and individual traders in the Taiwan index futures market, which is a pure limit order market. The empirical analysis obtains several interesting empirical results. We find that trader type affects liquidity provision in a number of interesting ways. First, although institutional traders use more limit orders than market orders, foreign institution (individual) traders use a relatively higher percentage of market (limit) orders in the early trading session and then switch to more limit (market) orders for the remainder of the day until close to the end of the trading day. Second, net limit order submissions by both institutional and individual traders are positively related to one‐period lagged transitory volatility and negatively related to informational volatility. Third, net limit order submissions by institutional traders are positively related to one‐period lagged spread. Finally, both the state of limit order book and order size significantly influence all types of traders’ strategy on submission of limit order versus market order during the intraday trading session. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 34:145–172, 2014     

GENERAL INTENSITY SHAPES IN OPTIMAL LIQUIDATION

The classical literature on optimal liquidation, rooted in Almgren–Chriss models, tackles the optimal liquidation problem using a trade‐off between market impact and price risk. It answers the general question of optimal scheduling but the very question of the actual way to proceed with liquidation is rarely dealt with. Our model, which incorporates both price risk and nonexecution risk, is an attempt to tackle this question using limit orders. The very general framework we propose to model liquidation with limit orders generalizes existing ones in two ways. We consider a risk‐averse agent, whereas the model of Bayraktar and Ludkovski only tackles the case of a risk‐neutral one. We consider very general functional forms for the execution process intensity, whereas Guéant, Lehalle and Fernandez‐Tapia are restricted to exponential intensity. Eventually, we link the execution cost function of Almgren–Chriss models to the intensity function in our model, providing then a way to see Almgren–Chriss models as a limit of ours.     

A Leland model for delta hedging in central risk books

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.     

Trader Survival: Evidence from the Energy Futures Markets

This study analyzes the adaptation of traders and the determinants of trader survival during a period of changing market structures. Our unique sample of transactions level data covers the introduction of electronic trading in the NYMEX energy futures market. The results show that most floor traders adapted to the side‐by‐side electronic and open outcry trading, although trader attrition increased and the profitability of surviving traders declined dramatically. It is also found that trading profits, trader experience and sophistication, and dual trading have a positive effect on the probability of trader survival. Scalpers are less likely to exit trading in pure open outcry trading, but are more likely to fail than traders who hold open positions longer in side‐by‐side trading. Finally, traders trading in multiple energy futures markets and those who use both the exchange floor and electronic trading appear to have a survival advantage in side‐by‐side trading. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:809–836, 2012     

Do brokers act in the best interests of their clients? New evidence from electronic trading systems

Prior research suggests brokers do not always act in the best interests of clients, although morally obligated to do so. We empirically investigated this issue focusing on trades executed at best execution price, before and after the introduction of electronic limit‐order trading, on the London Stock Exchange. As a result of limit‐order trading, the proportion of trades executed at the best execution price for the customer significantly increased. We attribute this to a sustained increase in the liquidity of stocks as a result of limit‐order trading, regardless of market capitalisation. We discuss the ethical implications of our findings and conclude that market structures that enhance market competitiveness may help reconcile broker and client interests.     

Order imbalances and market efficiency: New evidence from the Chinese stock market

This paper differentiates order imbalances based on trader categories. The daily order imbalances are highly persistent, especially for the number-measured imbalances. That the price pressure caused by imbalances cannot last beyond a trading day indicates that China's stock market is efficient enough to absorb the imbalances. We find that large individuals, small individuals and small institutions act frequently as market makers by submitting non-marketable limit orders, and the market making activities are profitable for small individuals and institutions. The evidence indicates that individuals are noise or liquidity traders, while institutions are more likely to be informed traders.     

OPTIMAL TRADE EXECUTION AND PRICE MANIPULATION IN ORDER BOOKS WITH TIME‐VARYING LIQUIDITY

In financial markets, liquidity is not constant over time but exhibits strong seasonal patterns. In this paper, we consider a limit order book model that allows for time‐dependent, deterministic depth and resilience of the book and determine optimal portfolio liquidation strategies. In a first model variant, we propose a trading‐dependent spread that increases when market orders are matched against the order book. In this model, no price manipulation occurs and the optimal strategy is of the wait region/buy region type often encountered in singular control problems. In a second model, we assume that there is no spread in the order book. Under this assumption, we find that price manipulation can occur, depending on the model parameters. Even in the absence of classical price manipulation, there may be transaction triggered price manipulation. In specific cases, we can state the optimal strategy in closed form.     

Execution quality in open‐outcry futures markets

This study examines the composition of customer order .flow and the execution quality for different types of customer orders in six futures pits of the Chicago Mercantile Exchange (CME). It is shown that off‐exchange customers frequently provide liquidity to other traders by submitting limit orders. The determinants of customers' choice between limit and market orders are examined, and it is found that higher bid—ask spreads increase the limit‐order submission frequency, and increased price volatility makes limit‐order submission less likely. Effective spreads, trading revenues, and turnaround times for customer liquidity‐demanding and limit orders are also documented. Consistent with evidence from equity markets, the results show that limit‐order traders receive better executions than traders using liquidity‐demanding orders, but incur adverse selection costs. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:1067–1092, 2005     

What Influences Trader Choice of Electronic versus Intermediated Execution?

We examine the determinants of US equity trader choice of electronic versus intermediated execution. While traders exhibit a strong overall preference for automation, when the market is less liquid at order submission time, traders seek market maker automated and human order‐matching services more often. Traders' overall tendency to choose intermediaries is highly correlated with their demand for liquidity. Market maker participation rates are higher for more active and larger size traders. Traders who choose intermediaries more often trade more stocks, execute orders quicker, price orders more aggressively, and disperse their trading over longer periods of time. Although US stock intermediaries continue to lose market share, our results highlight the important role these firms can play in an increasingly automated, electronically driven marketplace.     

Trader networks and options risk management

We examine the effect of trading partner concentration and a matrix of variables which dictate the relative importance of a trader to the network on a set of large member proprietary traders’ risk. An increased closeness centrality and concentration of trading among network partners are found to reduce price, volatility and rebalancing risk. We further explore the nature of trading concentration established through traders’ recurring trading relationships to find that trading with an established and small network has a positive, yet costly, effect on inventory management. Relationships among market makers are important to managing their portfolio of risk.     

Exchange Market for Complex Goods: Theory and Experiments

The modern economy includes a variety of markets, and the Internet has opened opportunities for efficient on-line trading. Researchers have developed algorithms for various auctions, which have become a popular means of on-line sales. They have also designed algorithms for exchange markets, which support fast-paced trading of standardized goods. On the other hand, they have done little work on exchanges for complex nonstandard goods, such as used cars. We propose a formal model for trading complex goods, and present an exchange system that allows traders to describe desirable purchases and sales by multiple attributes; for example, a car buyer can specify a model, options, color, and other properties of a desirable vehicle. Furthermore, a trader can enter complex constraints on the acceptable items; for instance, a buyer can specify a set of desirable vehicles and their features. The system supports markets with up to 260,000 orders, and generates hundreds of trades per second.     

On commodity price limits

This paper examines the behavior of futures prices and trader positions around the occurrence of price limits in commodity futures markets. We ask whether limit events are the result of shocks to fundamental volatility or the result of temporary volatility induced by the trading of noncommercial market participants (speculators). We find little evidence that limits events are the result of speculative activity, but instead associated with shocks to fundamentals that lead to persistent price changes. When futures trading halts price discovery migrates to options markets, but option prices provide a biased estimate of subsequent future prices when trading resumes.     

Trading under the proof-of-stake protocol – A continuous-time control approach

We develop a continuous-time control approach to optimal trading in a Proof-of-Stake (PoS) blockchain, formulated as a consumption-investment problem that aims to strike the optimal balance between a participant's (or agent's) utility from holding/trading stakes and utility from consumption. We present solutions via dynamic programming and the Hamilton–Jacobi–Bellman (HJB) equations. When the utility functions are linear or convex, we derive close-form solutions and show that the bang-bang strategy is optimal (i.e., always buy or sell at full capacity). Furthermore, we bring out the explicit connection between the rate of return in trading/holding stakes and the participant's risk-adjusted valuation of the stakes. In particular, we show when a participant is risk-neutral or risk-seeking, corresponding to the risk-adjusted valuation being a martingale or a sub-martingale, the optimal strategy must be to either buy all the time, sell all the time, or first buy then sell, and with both buying and selling executed at full capacity. We also propose a risk-control version of the consumption-investment problem; and for a special case, the “stake-parity” problem, we show a mean-reverting strategy is optimal.     

Manipulation in Conditional Decision Markets

Conditional decision markets concurrently predict the future and decide on it. These markets price the impact of decisions, conditional on them being executed. After the markets close, a principal decides which decisions are executed based on the prices in the markets. As some decisions are not executed, the respective outcome cannot be observed, and the markets predicting the impact of non-executed decisions are void. This allows ex-post costless manipulation of such markets. We conduct two versions of an online experiment to explore scenarios in which a principal runs conditional decision markets to inform her choice among a set of a risky alternatives. We find that the level of manipulation depends on the simplicity of the market setting. When a trader is alone, has the power to move prices far enough, and the decision is deterministically tied to market prices or a very high correlation between prices and decision is implied, only then manipulation occurs. As soon as another trader is present to add risk to manipulation, manipulation is eliminated. Our results contrast theoretical work on conditional decision markets in two ways: First, our results suggest that manipulation may not be as meaningful an issue. Second, probabilistic decision rules are used to add risk to manipulation; when manipulation is not a meaningful issue, deterministic decisions provide the better decision with less noise. To the best of our knowledge, this is the first experimental analysis isolating the effects of the conditional nature of decision markets.     

PORTFOLIO LIQUIDATION IN DARK POOLS IN CONTINUOUS TIME

We consider an illiquid financial market where a risk averse investor has to liquidate a portfolio within a finite time horizon [0, T] and can trade continuously at a traditional exchange (the “primary venue”) and in a dark pool. At the primary venue, trading yields a linear price impact. In the dark pool, no price impact costs arise but order execution is uncertain, modeled by a multidimensional Poisson process. We characterize the costs of trading by a linear‐quadratic functional which incorporates both the price impact costs of trading at the primary exchange and the market risk of the position. The solution of the cost minimization problem is characterized by a matrix differential equation with singular boundary condition; by means of stochastic control theory, we provide a verification argument. If a single‐asset position is to be liquidated, the investor slowly trades out of her position at the primary venue, with the remainder being placed in the dark pool at any point in time. For multi‐asset liquidations this is generally not the case; for example, it can be optimal to oversize orders in the dark pool in order to turn a poorly balanced portfolio into a portfolio bearing less risk.     

LIQUIDATION IN LIMIT ORDER BOOKS WITH CONTROLLED INTENSITY

We consider a framework for solving optimal liquidation problems in limit order books. In particular, order arrivals are modeled as a point process whose intensity depends on the liquidation price. We set up a stochastic control problem in which the goal is to maximize the expected revenue from liquidating the entire position held. We solve this optimal liquidation problem for power‐law and exponential‐decay order book models explicitly and discuss several extensions. We also consider the continuous selling (or fluid) limit when the trading units are ever smaller and the intensity is ever larger. This limit provides an analytical approximation to the value function and the optimal solution. Using techniques from viscosity solutions we show that the discrete state problem and its optimal solution converge to the corresponding quantities in the continuous selling limit uniformly on compacts.     

A realistic model of market liquidity and depth

A model that realistically defines market liquidity and depth is introduced. Liquidity is the expected rate of order execution in shares per minute. Depth is the average density of the limit order book in shares per dollar. Illiquid markets tend to exhibit longer execution delays and indirectly higher risk related to price impact. Markets with low depth are characterized by high price sensitivity and larger risks. Deviations from fundamental value exist because arbitraging them away carries liquidity cost, entails impact risk, and generates negatively skewed profits. Premia include liquidity and transparency components. In order to avoid excessive frontrunning and liquidity withholding around their block trade, traders break their block orders into smaller orders. In anonymous markets, the trader discriminates against early liquidity providers, and is only compensated for liquidity. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:443–464, 2005     

OPTIMAL LIQUIDATION IN A LIMIT ORDER BOOK FOR A RISK‐AVERSE INVESTOR

In a limit order book model with exponential resilience, general shape function, and an unaffected stock price following the Bachelier model, we consider the problem of optimal liquidation for an investor with constant absolute risk aversion. We show that the problem can be reduced to a two‐dimensional deterministic problem which involves no buy orders. We derive an explicit expression for the value function and the optimal liquidation strategy. The analysis is complicated by the fact that the intervention boundary, which determines the optimal liquidation strategy, is discontinuous if there are levels in the limit order book with relatively little market depth. Despite this complication, the equation for the intervention boundary is fairly simple. We show that the optimal liquidation strategy possesses the natural properties one would expect, and provide an explicit example for the case where the limit order book has a constant shape function.     

OPTIMAL LIQUIDATION AND ADVERSE SELECTION IN DARK POOLS

We consider an investor who has access both to a traditional venue and a dark pool for liquidating a position in a single asset. While trade execution is certain on the traditional exchange, she faces linear price impact costs. On the other hand, dark pool orders suffer from adverse selection and trade execution is uncertain. Adverse selection decreases order sizes in the dark pool while it speeds up trading at the exchange. For small orders, it is optimal to avoid the dark pool completely. Adverse selection can prevent profitable round‐trip trading strategies that otherwise would arise if permanent price impact were included in the model.