Optimal liquidation strategies for large-tick stocks

This thesis is devoted to study the optimal liquidation strategies in a limit order book for large-tick stocks. Two frameworks are proposed. In the first framework, we formulate a stylised limit order book that admits one-tick spread and fixed market depth cap, in which order flows arrive according to point processes with stochastic intensities. We consider an agent who wants to liquidate a position in this limit order book through market orders and pegged displayed/non-displayed limit orders within a fixed time horizon, and whose goal is to maximise the expected utility from the terminal wealth. For this optimal liquidation problem, we derive the associated Hamilton-Jacobi-Bellman quasi-variational inequality and prove a verification theorem giving sufficient conditions for the HJBQVI solution to be the value function. The optimal strategy is a combined stochastic and impulse control, and is then solved numerically using finite different scheme. In the second framework, we formulate a stylised level-I limit order book whose spread is constantly one tick and whose dynamics are driven by the queueing races at the best prices. Order book events occur according to independent Poisson processes, with parameters depending on the most recent price move direction. Our goal is to maximise the expected terminal wealth of an agent who needs to liquidate a position within a fixed time horizon. By assuming that the agent trades through both limit and market orders only when the price moves, we model her liquidation procedure as a semi-Markov decision process, and compute the semi-Markov kernel using Laplace method in the language of queueing theory. The optimal liquidation policy is then solved by dynamic programming, and illustrated numerically.Open Acces

We develop a sequential trade model of Iceberg order execution in a limit order book. The Iceberg-trader has the freedom to expose his trading intentions or (partially) shield the true order size against other market participants. Order exposure can cause drastic market reactions (“market impact”) in the end leading to higher transaction costs. On the other hand the Iceberg trader faces a loss-in-priority when he hides his intentions, as most electronic limit order books penalize the usage of hidden liquidity. Thus the Iceberg-trader is faced with the problem to find the right trade-off. Our model provides optimal exposure strategies for Iceberg traders in limit order book markets. In particular, we provide a range of analytical statements that are in line with recent empirical findings on the determinants of trader’s exposure strategies. In this framework, we also study the market impact also market impact of limit orders. We provide optimal exposure profiles for a range of hightech stocks from the US S&P500 and how they scale with the state-of-the-book. We finally test the Iceberg’s performance against the limit orders and find that Iceberg orders can significantly enhance trade performance by up to 60%.

Hidden Liquidity, Iceberg Orders, Limit Order Book, Market Impact of Limit Orders, Optimal Exposure, Trading Strategies, Iceberg versus Limit Order, Pre-trade transparency, Agency-Trading.

Research toward the Practical Application of Liquidity Risk Evaluation Methods

This paper proposes a practical framework for the quantification of Liquidity-adjusted Value at Risk ("L-VaR") incorporating the market liquidity of financial products. This framework incorporates the mechanism of the market impact caused by the investor's own dealings through adjusting Value-at-Risk according to the level of market liquidity and the scale of the investor's position. Specifically, the optimal execution strategy for liquidating the investor's entire position is first calculated taking the market impact into account. Then the maximum loss that may be incurred by price fluctuations under optimal execution strategy is calculated as L-VaR. This paper presents a specific model providing a closed-form solution for calculating L-VaR, and examines whether this framework can be applied to the practices of financial risk management by calculating numerical examples. It also demonstrates that this L-VaR calculation framework may be applied under more general conditions, such as (1) when the market impact is uncertain, (2) when the investor's portfolio consists of multiple financial assets, and (3) when there is a non-linear relationship between the market impact and the trading volume.

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 has the choice to trade via market orders or limit orders, which are represented respectively by impulse controls and regular controls. We model and discuss the consequences of the two main features of this particular microstructure: first, the limit orders sent by the high frequency trader are only partially executed, and therefore she has no control on the executed quantity. For this purpose, cumulative executed volumes are modelled by compound Poisson processes. Second, the high frequency trader faces the overtrading risk, which is the risk of brutal 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, which lead to a characterization of the value function in terms of an integro quasi-variational inequality. We then provide the associated numerical resolution procedure, and convergence of this computational scheme is proved. Next, we examine several situations where we can on one hand simplify the numerical procedure by reducing the number of state variables, and on the other hand focus on specific cases of practical interest. We examine both a market making problem and a best execution problem in the case where the mid-price process is a martingale. We also detail a high frequency trading strategy in the case where a (predictive) directional information on the mid-price is available. Each of the resulting strategies are illustrated by numerical tests

Modelling Asset Prices for Algorithmic and High-Frequency Trading

Algorithmic trading (AT) and high-frequency (HF) trading, which are responsible for over 70% of US stocks trading volume, have greatly changed the microstructure dynamics of tick-by-tick stock data. In this article, we employ a hidden Markov model to examine how the intraday dynamics of the stock market have changed and how to use this information to develop trading strategies at high frequencies. In particular, we show how to employ our model to submit limit orders to profit from the bid–ask spread, and we also provide evidence of how HF traders may profit from liquidity incentives (liquidity rebates). We use data from February 2001 and February 2008 to show that while in 2001 the intraday states with the shortest average durations (waiting time between trades) were also the ones with very few trades, in 2008 the vast majority of trades took place in the states with the shortest average durations. Moreover, in 2008, the states with the shortest durations have the smallest price impact as measured by the volatility of price innovations

Optimal Trade Execution under Endogenous Order Flow

We consider an optimal liquidation model in which an investor is required to execute meta-orders during intraday trading periods, and his trading activity triggers child orders and endogenously affects future order flow, both instantaneously and permanently. Under the assumptions of risk neutrality and deterministic constants of the impact parameters, we provide closed-form solutions and illustrate the relationship between trading strategies and feedback effects. The optimal trading strategy is of hyperbolic form if the feedback effect of current trading on future order flow is not too strong. If the feedback effect becomes too dominating, a cyclic strategy with possible beneficial round-trips may emerge. We set up an estimation framework so that parameter estimates can be made directly from public data and are consistent with the theoretical model. When implementing our model on 110 NASDAQ stocks, the empirical analysis shows that as the level of endogeneity increases, our strategy provides increasingly better performance than the commonly adopted trading strategy. The empirical analysis also shows that too strong feedback effects do not exist in practice, thus ruling out statistical arbitrage

How markets slowly digest changes in supply and demand

In this article we revisit the classic problem of tatonnement in price formation from a microstructure point of view, reviewing a recent body of theoretical and empirical work explaining how fluctuations in supply and demand are slowly incorporated into prices. Because revealed market liquidity is extremely low, large orders to buy or sell can only be traded incrementally, over periods of time as long as months. As a result order flow is a highly persistent long-memory process. Maintaining compatibility with market efficiency has profound consequences on price formation, on the dynamics of liquidity, and on the nature of impact. We review a body of theory that makes detailed quantitative predictions about the volume and time dependence of market impact, the bid-ask spread, order book dynamics, and volatility. Comparisons to data yield some encouraging successes. This framework suggests a novel interpretation of financial information, in which agents are at best only weakly informed and all have a similar and extremely noisy impact on prices. Most of the processed information appears to come from supply and demand itself, rather than from external news. The ideas reviewed here are relevant to market microstructure regulation, agent-based models, cost-optimal execution strategies, and understanding market ecologies.Comment: 111 pages, 24 figure