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.     

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.     

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 HIGH‐FREQUENCY TRADING IN A PRO RATA MICROSTRUCTURE WITH PREDICTIVE INFORMATION

We propose a framework to study optimal trading policies in a one‐tick pro rata limit order book, as typically arises in short‐term interest rate futures contracts. The high‐frequency trader chooses to post either market orders or limit orders, which are represented, respectively, by impulse controls and regular controls. We discuss the consequences of the two main features of this microstructure: first, the limit orders are only partially executed, and therefore she has no control on the executed quantity. Second, the high‐frequency trader faces the overtrading risk, which is the risk of large variations in her inventory. The consequences of this risk are investigated in the context of optimal liquidation. The optimal trading problem is studied by stochastic control and dynamic programming methods, and we provide the associated numerical resolution procedure and prove its convergence. We propose dimension reduction techniques in several cases of practical interest. We also detail a high‐frequency trading strategy in the case where a (predictive) directional information on the price is available. Each of the resulting strategies is illustrated by numerical tests.     

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.     

The contribution of a satellite market to price discovery: Evidence from the Singapore exchange

The Singapore Exchange (SGX), a small satellite market, successfully competes with a large home market, the Osaka Securities Exchange (OSE), in trading the Nikkei 225 futures index. In this paper, we investigate the contribution of the SGX to price discovery and shed light on the reasons for its continued success. Evidence is provided from information revelation and price discovery of three competing but informationally linked markets of the Nikkei 225 index—domestic spot (Tokyo Stock Exchange), domestic futures (OSE), and foreign futures (SGX), which represents the satellite market. Overall, the futures market contributes 77% to price discovery, with the satellite market contributing 42% of the futures and 33% of the total price discovery. These figures, surprisingly, far exceed the satellite market's share of trading volume. Support is provided for the extended trading hours on the SGX for three of the four non‐overlapping trading sub‐periods. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:981–1004, 2004     

Cash trading and index futures price volatility

This study examines the effect of cash market liquidity on the volatility of stock index futures. Two facets of cash market liquidity are considered: (1) the level of liquidity trading proxied by the expected New York Stock Exchange (NYSE) trading volume and (2) the noise composition of trading proxied by the average NYSE trading commission cost. Under the framework of spline–GARCH with a liquidity component, both the quarterly average commission cost and the quarterly expected NYSE volume are negatively associated with the ex ante daily volatility of S&P 500 and NYSE composite index futures. Conversely, liquidity and noise trading in the cash market both dampen futures price volatility, ceteris paribus. This negative association between secular cash trading liquidity and daily futures price volatility is amplified during times of market crisis. These results retain statistical significance and materiality after controlling for bid–ask bounce of futures prices and volume of traded futures contracts. This study establishes empirical evidence to affirm the conventional prediction of a liquidity–volatility relationship: the liquidity effect is secular and persistent across markets. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:465–486, 2011     

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.     

TRANSIENT LINEAR PRICE IMPACT AND FREDHOLM INTEGRAL EQUATIONS

We consider the linear‐impact case in the continuous‐time market impact model with transient price impact proposed by Gatheral. In this model, the absence of price manipulation in the sense of Huberman and Stanzl can easily be characterized by means of Bochner’s theorem. This allows us to study the problem of minimizing the expected liquidation costs of an asset position under constraints on the trading times. We prove that optimal strategies can be characterized as measure‐valued solutions of a generalized Fredholm integral equation of the first kind and analyze several explicit examples. We also prove theorems on the existence and nonexistence of optimal strategies. We show in particular that optimal strategies always exist and are nonalternating between buy and sell trades when price impact decays as a convex function of time. This is based on and extends a recent result by Alfonsi, Schied, and Slynko on the nonexistence of transaction‐triggered price manipulation. We also prove some qualitative properties of optimal strategies and provide explicit expressions for the optimal strategy in several special cases of interest.     

Managed futures,positive feedback trading,and futures price volatility

A major issue in recent years is the role that large, managed futures funds and pools play in futures markets. Many market participants argue that managed futures trading increases price volatility due to the size of managed futures trading and reliance on positive feedback trading systems. The purpose of this study is to provide new evidence on the impact of managed futures trading on futures price volatility. A unique data set on managed futures trading is analyzed for the period 1 December 1988 through 31 March 1989. The data set includes the daily trading volume of large commodity pools for 36 different futures markets. Regression results are unequivocal with respect to the impact of commodity pool trading on futures price volatility. For the 72 estimated regressions (two for each market), the coefficient on commodity pool trading volume is significantly different from zero in only four cases. These results constitute strong evidence that, at least for this sample period, commodity pool trading is not associated with increases in futures price volatility. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 759–776, 1999     

A Dynamic Volume–Return Relation and Investors' Positive Feedback Trading

With individual stocks, a larger increase in trading volume indicates a stronger short‐term return persistence. A reason for this short‐horizon ‘volume–return relation’ is that it can signal the existence of fundamental news, which can be gradually incorporated into stock price. In this study, we present another plausible explanation by considering investors' short‐term positive feedback trading. First, through empirical analysis, we show that the volume–return relation remains strong among stocks for which there is little fundamental news. Through a model‐based analysis, we demonstrate that positive feedback trading can cause this relation even when there is no news. Our findings raise the possibility that the short‐horizon volume–return relation is also caused by short‐term positive feedback trading.     

The determinants of price discovery on bitcoin markets

This paper investigates whether market quality, uncertainty, investor sentiment and attention, and macroeconomic news affect bitcoin price discovery in spot and futures markets. Over the period December 2017–March 2019, we find significant time variation in the contribution to price discovery of the two markets. Increases in price discovery are mainly driven by relative trading costs and volume, and uncertainty to a lesser extent. Additionally, medium-sized trades contain most information in terms of price discovery. Finally, higher news-based bitcoin sentiment increases the informational role of the futures market, while attention and macroeconomic news have no impact on price discovery.     

Expiration day effects: The case of Hong Kong

Regulators around the world often express concerns about the high volatility of stock markets due to index derivative expirations. Earlier studies of expiration day effects have found large volume effects, abnormal return volatility, and price effects during the last hour of trading on expiration days when the settlement is based on the closing price. This article examines the impact of the expiration of Hang Seng Index (HSI) derivatives on the underlying cash market in Hong Kong for the period from 1990 to 1999. The HSI derivative market is different from most other markets in the sense that the settlement price is computed by taking the average of 5‐minute quotations of the HSI on the last trading day, thus providing an alternative setting for testing expiration day effects. Our empirical findings indicate that expiration days in Hong Kong may be associated with a negative price effect and some return volatility on the underlying stock market, but there is no evidence of abnormal trading volume on the expiration day, or price reversal after expiration. Thus, the existence of expiration day effects cannot be confirmed in the Hong Kong market. [JEL classification: G13; G14; G15]. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:67–86, 2003     

Regulatory changes and information competition: The case of Taiwan index futures

This article examines the cross‐border competition in price discovery between the Taiwan Futures Exchange (TAIFEX) and the Singapore Exchange Derivatives Trading (SGX). We focused on the impact of market reforms on the information leadership of similar contracts traded on the two exchanges. Utilizing synchronized transaction data, it was found that reducing the futures transferring tax was the only policy change that enhanced TAIFEX's information role. Evidence supported the trading‐cost hypothesis that a lower transaction cost is associated with better price discovery. A brief linkage between trading volume and price discovery was found when data were broken down into subperiods according to the relative volume of TAIFEX and SGX. Evidence suggested that the SGX's information advantage reported in previous research had diminished as the rival market progressed. It also indicated that exchanges seeking to improve information efficiency should adopt policies that will reduce transaction costs or increase trading volume. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:399–412, 2004     

Option trading and the cross-listed stock returns: Evidence from Chinese A–H shares

We empirically investigate the effects of option trading on the cross-listed stock returns. Using dual-listed stocks in mainland China (A) and Hong Kong (H) stock exchanges, we show that option order imbalance (OI) positively and significantly predicts daily stock returns for both markets, controlling for risk factors and firm characteristics. Informed trading rather than price pressure better explain the predictability. High OI stocks have higher trading volume and present lottery-like properties. Three important events significantly affect the predictive power of OI, consistent with the improved market quality and the episode of speculative trading. Robustness checks support the main findings.     

LIQUIDATION OF A LARGE BLOCK OF STOCK WITH REGIME SWITCHING

In the literature, stock‐selling rules are mainly concerned with liquidation of the security within a short period of time. In practice, this is feasible only when a relatively smaller number of shares of a stock is involved. Selling a large position in a market place normally depresses the market if sold in a short period of time, which would result in poor filling prices. Comparing to the existing results in the literature, this work has two distinct features. First, the underlying stock price is modeled using a geometric Brownian motion formulation with regime switching in which the jump rate depends on the selling intensity. A larger selling intensity makes the regime more likely to change from a higher return mode to a lower one or forces the return mode to stay in the lower one longer. Secondly, we consider the liquidation strategy for selling a large block of stock by selling much smaller number of shares over a longer period of time. By using a fluid model, in which the number of shares is treated as fluid (continuous), we treat the selling rule problem where the corresponding liquidation is dictated by the rate of selling over time. Our objective is to maximize the expected overall return. Thus it may be formulated as a stochastic control problem with state constraints. Method viscosity solution is used to characterize the dynamics governing the optimal reward function and the associated boundary conditions. Numerical examples are reported to illustrate the results.     

Price discovery in bitcoin spot or futures?

In December 2017, both the Chicago Board Options Exchange and the Chicago Mercantile Exchange introduced futures contracts on bitcoin. We investigate to what extent they provide useful information for the price discovery of bitcoin. We rely on the information share methodology of Hasbrouck (1995, J Finance, 50, pp. 1175–1199) and Gonzalo and Granger (1995, J Bus Econ Stat, 13, pp. 27–35) and find that the spot price leads the futures price. We attribute this result to the higher trading volume and the longer trading hours of the globally distributed bitcoin spot market, compared to the relatively restricted access to the US-based futures markets.     

Optimal investment,derivative demand,and arbitrage under price impact

This paper studies the optimal investment problem with random endowment in an inventory‐based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading and nonlinear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is generically neither closed nor convex. Regarding hedging, nonlinear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only for limited position sizes, and may be ignored if outweighed by hedging considerations. We also show that arbitrage‐inducing prices may arise endogenously in equilibrium, and that equilibrium positions are inversely proportional to the market makers' representative risk aversion. Therefore, large positions endogenously arise in the limit of either market maker risk neutrality, or a large number of market makers.     

Can the Indicative Price System Mitigate Expiration‐Day Effects?

We investigate whether the indicative price system, introduced in the Korean derivatives market on July 1, 2003, has helped mitigate the options and futures expiration‐day effects. Prior to introduction of this system, we find evidence of high trading volume and significant price reversals during the first half hour of trading for the day immediately following the expiration day. These effects decline significantly after July 1, 2003. Our evidence suggests that the indicative price system can mitigate the expiration‐day effects.     

A、B股市场信息价值的比较研究

中国证券市场具有在全世界资本市场都堪称独特的A、B、H股市场分割体制 ,对这一问题的研究具有重要的学术价值和现实意义。从会计盈余信息价值的角度研究我国证券市场分割 ,即通过比较A、B股市场中双重上市公司的股价和成交量对不同会计准则下盈余信息的反应 ,发现两个市场在信息传递、信息评价、信息反应模式等方面体现出明显的信息价值差异 ,同时就证券市场分割下信息价值差异的成因及解决对策进行了探讨。