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Optimal Execution Of Multiasset Block Orders Under Stochastic Liquidity
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Book Synopsis Optimal Execution of Multiasset Block Orders Under Stochastic Liquidity by : Naoki Makimoto
Download or read book Optimal Execution of Multiasset Block Orders Under Stochastic Liquidity written by Naoki Makimoto and published by . This book was released on 2010 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In this paper, we develop a multiasset model of market liquidity and derive the optimal strategy for block order execution under both liquidity and volatility risk. The market liquidity flowing into and out of an order book is modeled as a mean-reverting stochastic process. Given the shape of the order book for each asset, we express the market impact of an execution as a recursive impact that recovers gradually with associated uncertainty. We then derive the optimal execution strategy as a closed-form solution to the mean-variance problem that optimizes the trade-off between the market impact and the volatility/liquidity risk given investor risk aversion. Using our model, we analyze some implications of the optimal execution strategy with comparative statics and simulations. We also discuss whether we avoid price manipulation with our optimal execution strategy."--Prelim. p.
Book Synopsis Optimal Order Execution with Stochastic Liquidity by :
Download or read book Optimal Order Execution with Stochastic Liquidity written by and published by . This book was released on 2011 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Financial Mathematics of Market Liquidity by : Olivier Gueant
Download or read book The Financial Mathematics of Market Liquidity written by Olivier Gueant and published by CRC Press. This book was released on 2016-03-30 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is among the first to present the mathematical models most commonly used to solve optimal execution problems and market making problems in finance. The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making presents a general modeling framework for optimal execution problems-inspired from the Almgren-Chriss app
Book Synopsis Multi-Asset Optimal Execution and Statistical Arbitrage Strategies Under Ornstein-Uhlenbeck Dynamics by : Philippe Bergault
Download or read book Multi-Asset Optimal Execution and Statistical Arbitrage Strategies Under Ornstein-Uhlenbeck Dynamics written by Philippe Bergault and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, academics, regulators, and market practitioners have increasingly addressed liquidity issues. Amongst the numerous problems addressed, the optimal execution of large orders is probably the one that has attracted the most research works, mainly in the case of single-asset portfolios. In practice, however, optimal execution problems often involve large portfolios comprising numerous assets, and models should consequently account for risks at the portfolio level. In this paper, we address multi-asset optimal execution in a model where prices have multivariate Ornstein-Uhlenbeck dynamics and where the agent maximizes the expected (exponential) utility of her PnL. We use the tools of stochastic optimal control and simplify the initial multidimensional Hamilton-Jacobi-Bellman equation into a system of ordinary differential equations (ODEs) involving a Matrix Riccati ODE for which classical existence theorems do not apply. By using a priori estimates obtained thanks to optimal control tools, we nevertheless prove an existence and uniqueness result for the latter ODE, and then deduce a verification theorem that provides a rigorous solution to the execution problem. Using examples based on data from the foreign exchange and stock markets, we eventually illustrate our results and discuss their implications for both optimal execution and statistical arbitrage.
Book Synopsis Dynamic Portfolio Execution by : Gerry Tsoukalas
Download or read book Dynamic Portfolio Execution written by Gerry Tsoukalas and published by . This book was released on 2020 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze the optimal execution problem of a portfolio manager trading multiple assets. In addition to the liquidity and risk of each individual asset, we consider cross-asset interactions in these two dimensions, which substantially enriches the nature of the problem. Focusing on the market microstructure, we develop a tractable order book model to capture liquidity supply/demand dynamics in a multi-asset setting, which allows us to formulate and solve the optimal portfolio execution problem. We find that cross-asset risk and liquidity considerations are of critical importance in constructing the optimal execution policy. We show that even when the goal is to trade a single asset, its optimal execution may involve transitory trades in other assets. In general, optimally managing the risk of the portfolio during the execution process affects the time synchronization of trading in different assets. Moreover, links in the liquidity across assets lead to complex patterns in the optimal execution policy. In particular, we highlight cases where aggregate costs can be reduced by temporarily overshooting one's target portfolio.
Book Synopsis Optimal Execution with Uncertain Order Fills in Almgren-Chriss Framework by : Xue Cheng
Download or read book Optimal Execution with Uncertain Order Fills in Almgren-Chriss Framework written by Xue Cheng and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical price impact model of Almgren and Chriss is extended to incorporate the uncertainty of order fills. The extended model can be recast as alternatives to uncertain impact models and stochastic liquidity models. Optimal strategies are determined by maximizing the expected final P&L and various P&L-risk tradeoffs including utility maximization. Closed form expressions for optimal strategies are obtained in linear cases. The results suggest a type of adaptive VWAP, adaptive POV and adaptive Almgren-Chriss strategies. VWAP and classical Almgren-Chriss strategies are recovered as limiting cases with different characteristic time scale of liquidation for the latter.
Book Synopsis Optimal Execution with Hidden Orders Under Self-Exciting Dynamics by : Ying Chen
Download or read book Optimal Execution with Hidden Orders Under Self-Exciting Dynamics written by Ying Chen and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hidden liquidity is attracting significant volume share in modern order-driven markets, providing exposure risk reduction and mitigating adverse selection risk. In a continuous-time framework, we show there is a switching in the optimal liquidation strategy for a risk-neutral agent who uses both hidden and displayed limit orders controlling the order sizes. When market order arrivals are modeled as the Poisson process, we derive a closed-form solution that contains a switching time, at which the agent changes from a pure-hidden-order phase to a mixed-orders phase until termination. Under the Hawkes process with self-exciting dynamics, a numerical solution is provided. We show that the optimal strategy exhibits a similar two-phase pattern, except that the switching time becomes a function of the market order intensity. Simulation experiments show that the use of hidden order reduces liquidation cost, accompanied by an increase in liquidity. Given event-level limit order book data of 100 NASDAQ stocks, we test the liquidation strategies, where our strategy (with mixed type under the self-exciting dynamics) leads to cost reduction up to 57% to the pure limit order strategy and 15% to the strategy with both order types under the Poisson process.
Book Synopsis Optimal Conic Execution Strategies with Stochastic Liquidity by : Markus Leippold
Download or read book Optimal Conic Execution Strategies with Stochastic Liquidity written by Markus Leippold and published by . This book was released on 2018 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we develop the conic finance framework for optimal execution of a large portfolio in an illiquid market. We extend the classical optimal execution results by considering stochastic exogenous liquidity effects as well as temporary price impact functions. We depart from the traditionally assumed linear impact function and introduce both stochastic liquidity and volatility effects and nonlinear temporary market impact. Moreover, we allow for an additional stochastic exogenous liquidity effect, used to capture the base illiquidity of a market. We analyze various aspects of our model using a stylized example.
Book Synopsis Optimal Trade Execution Under Stochastic Volatility and Liquidity by : Patrick Cheridito
Download or read book Optimal Trade Execution Under Stochastic Volatility and Liquidity written by Patrick Cheridito and published by . This book was released on 2014 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the problem of optimally liquidating a financial position in a discrete-time model with stochastic volatility and liquidity. We consider the three cases where the objective is to minimize the expectation, an expected exponential and a mean-variance criterion of the implementation cost. In the first case, the optimal solution can be fully characterized by a forward-backward system of stochastic equations depending on conditional expectations of future liquidity. In the other two cases we derive Bellman equations from which the optimal solutions can be obtained numerically by discretizing the control space. In all three cases we compute optimal strategies for different simulated realizations of prices, volatility and liquidity and compare the outcomes to the ones produced by the deterministic strategies of Bertsimas and Lo and Almgren and Chriss.
Book Synopsis Optimal Trade Execution and Price Manipulation in Order Books with Time-Varying Liquidity by : Antje Fruth
Download or read book Optimal Trade Execution and Price Manipulation in Order Books with Time-Varying Liquidity written by Antje Fruth and published by . This book was released on 2015 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: In financial markets, liquidity is not constant over time but exhibits strong seasonal patterns. In this article 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.
Book Synopsis Large Orders in Small Markets by : Agostino Capponi
Download or read book Large Orders in Small Markets written by Agostino Capponi and published by . This book was released on 2019 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: We solve a Stackelberg game where a large uninformed seller executes optimally, fully cognizant of the response of Cournot-competitive market makers. The game therefore endogenizes both demand and supply of liquidity. The closed-form solution yields several insights. First, stealth trading is both privately and socially costly because market makers incur additional cost not knowing when execution ends. Second, the presence of a large seller does not unambiguously benefit other participants. Market makers benefit only if there is enough risk-absorption capacity or if the execution period is short. Other investors benefit only when the seller sells at high enough intensity.
Book Synopsis Market Liquidity by : Thierry Foucault
Download or read book Market Liquidity written by Thierry Foucault and published by Oxford University Press. This book was released on 2023 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The process by which securities are traded is very different from the idealized picture of a frictionless and self-equilibrating market offered by the typical finance textbook. This book offers a more accurate and authoritative take on this process. The book starts from the assumption that not everyone is present at all times simultaneously on the market, and that participants have quite diverse information about the security's fundamentals. As a result, the order flow is a complex mix of information and noise, and a consensus price only emerges gradually over time as the trading process evolves and the participants interpret the actions of other traders. Thus, a security's actual transaction price may deviate from its fundamental value, as it would be assessed by a fully informed set of investors. The book takes these deviations seriously, and explains why and how they emerge in the trading process and are eventually eliminated. The authors draw on a vast body of theoretical insights and empirical findings on security price formation that have come to form a well-defined field within financial economics known as "market microstructure." Focusing on liquidity and price discovery, the book analyzes the tension between the two, pointing out that when price-relevant information reaches the market through trading pressure rather than through a public announcement, liquidity may suffer. It also confronts many striking phenomena in securities markets and uses the analytical tools and empirical methods of market microstructure to understand them. These include issues such as why liquidity changes over time and differs across securities, why large trades move prices up or down, and why these price changes are subsequently reversed, and why we observe temporary deviations from asset fair values"--
Book Synopsis Incorporating Order-Flow Into Optimal Execution by : Álvaro Cartea
Download or read book Incorporating Order-Flow Into Optimal Execution written by Álvaro Cartea and published by . This book was released on 2016 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: We provide an explicit closed-form strategy for an investor who executes a large order when market order-flow from all agents, including the investor's own trades, has a permanent price impact. The strategy is found in closed-form when the permanent and temporary price impacts are linear in the market's and investor's rates of trading. We do this under very general assumptions about the stochastic process followed by the order-flow of the market. The optimal strategy consists of an Almgren-Chriss execution strategy adjusted by a weighted-average of the future expected net order-flow (given by the difference of the market's rate of buy and sell market orders) over the execution trading horizon and proportional to the ratio of permanent to temporary linear impacts. We use historical data to calibrate the model to Nasdaq traded stocks and use simulations to show how the strategy performs.
Book Synopsis Algorithmic and High-Frequency Trading by : Álvaro Cartea
Download or read book Algorithmic and High-Frequency Trading written by Álvaro Cartea and published by Cambridge University Press. This book was released on 2015-08-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The design of trading algorithms requires sophisticated mathematical models backed up by reliable data. In this textbook, the authors develop models for algorithmic trading in contexts such as executing large orders, market making, targeting VWAP and other schedules, trading pairs or collection of assets, and executing in dark pools. These models are grounded on how the exchanges work, whether the algorithm is trading with better informed traders (adverse selection), and the type of information available to market participants at both ultra-high and low frequency. Algorithmic and High-Frequency Trading is the first book that combines sophisticated mathematical modelling, empirical facts and financial economics, taking the reader from basic ideas to cutting-edge research and practice. If you need to understand how modern electronic markets operate, what information provides a trading edge, and how other market participants may affect the profitability of the algorithms, then this is the book for you.
Book Synopsis A Study on the Optimal Order Execution Problem for Stochastic Market Depth Models by : 黃冠智
Download or read book A Study on the Optimal Order Execution Problem for Stochastic Market Depth Models written by 黃冠智 and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Design of Sell-Side Limit and Market Order Tactics by : Vladimir Markov
Download or read book On the Design of Sell-Side Limit and Market Order Tactics written by Vladimir Markov and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This article provides a novel framework to evaluate limit order tactics that highlights expected fill price, adverse price selection cost, and opportunity cost. We formulate the problem of optimal execution of market orders with nonlinear market impact, power law decay kernel, and stochastic and deterministic liquidity constraints. We demonstrate how these tactics can be incorporated in the uncertainty bands framework.
Book Synopsis Optimal Execution in a Limit Order Book and an Associated Microstructure Market Impact Model by : Costis Maglaras
Download or read book Optimal Execution in a Limit Order Book and an Associated Microstructure Market Impact Model written by Costis Maglaras and published by . This book was released on 2015 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: We model an electronic limit order book as a multi-class queueing system under fluid dynamics, and formulate and solve a problem of limit and market order placement to optimally buy a block of shares over a short, predetermined time horizon. Using the structure of the optimal execution policy, we identify microstructure variables that affect trading costs over short time horizons and propose a resulting microstructure-based model of market impact costs. We use a proprietary data set to estimate this cost model, and highlight its insightful structure and increased accuracy over conventional (macroscopic) market impact models that estimate the cost of a trade based on its normalized size but disregarding measurements of limit order book variables.
