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Author: Patrick Cheridito
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
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.
Author: Patrick Cheridito
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
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.
Author: Naoki Makimoto
Publisher:
ISBN:
Category : Liquidity (Economics)
Languages : en
Pages : 33
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Book Description
"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.
Author: Antje Fruth
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
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Book Description
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.
Author: Patrick Cheridito
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
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Book Description
We consider the problem of optimally acquiring a position in a financial asset by submitting orders to a standard exchange and a dark pool. We assume that volatility is stochastic and trading at the standard exchange causes a price impact. Orders sent to the dark pool do not generate price impact. But they are not always filled and are exposed to adverse selection risk. Therefore, an optimal strategy has to find the right balance between favorable transaction prices and guaranteed execution. We consider two different optimality criteria: the expected implementation cost and an expected exponential of the implementation cost. In the first case, the optimal strategy can be given in closed form by a forward-backward system of stochastic equations. In the expected exponential case we characterize the optimal strategy by a Bellman equation that can be solved numerically.Our simulation experiments show that the presence of a dark pool lowers the average implementation cost and that the performance is improving if crossing probabilities in the dark pool increase.
Author: Álvaro Cartea
Publisher: Cambridge University Press
ISBN: 1316453650
Category : Mathematics
Languages : en
Pages : 360
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Book Description
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.
Author: Jean-Pierre Fouque
Publisher: Cambridge University Press
ISBN: 113950245X
Category : Mathematics
Languages : en
Pages : 456
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Book Description
Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.
Author: Olivier Gueant
Publisher: CRC Press
ISBN: 1498725481
Category : Business & Economics
Languages : en
Pages : 302
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Book Description
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
Author: Charles-albert Lehalle
Publisher: World Scientific
ISBN: 9813231149
Category : Business & Economics
Languages : en
Pages : 366
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Book Description
This book exposes and comments on the consequences of Reg NMS and MiFID on market microstructure. It covers changes in market design, electronic trading, and investor and trader behaviors. The emergence of high frequency trading and critical events like the'Flash Crash' of 2010 are also analyzed in depth.Using a quantitative viewpoint, this book explains how an attrition of liquidity and regulatory changes can impact the whole microstructure of financial markets. A mathematical Appendix details the quantitative tools and indicators used through the book, allowing the reader to go further independently.This book is written by practitioners and theoretical experts and covers practical aspects (like the optimal infrastructure needed to trade electronically in modern markets) and abstract analyses (like the use on entropy measurements to understand the progress of market fragmentation).As market microstructure is a recent academic field, students will benefit from the book's overview of the current state of microstructure and will use the Appendix to understand important methodologies. Policy makers and regulators will use this book to access theoretical analyses on real cases. For readers who are practitioners, this book delivers data analysis and basic processes like the designs of Smart Order Routing and trade scheduling algorithms.In this second edition, the authors have added a large section on orderbook dynamics, showing how liquidity can predict future price moves, and how High Frequency Traders can profit from it. The section on market impact has also been updated to show how buying or selling pressure moves prices not only for a few hours, but even for days, and how prices relax (or not) after a period of intense pressure.Further, this edition includes pages on Dark Pools, Circuit Breakers and added information outside of Equity Trading, because MiFID 2 is likely to push fixed income markets towards more electronification. The authors explore what is to be expected from this change in microstructure. The appendix has also been augmented to include the propagator models (for intraday price impact), a simple version of Kyle's model (1985) for daily market impact, and a more sophisticated optimal trading framework, to support the design of trading algorithms.
Author: Frédéric Abergel
Publisher: John Wiley & Sons
ISBN: 1119952417
Category : Business & Economics
Languages : en
Pages : 257
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Book Description
The latest cutting-edge research on market microstructure Based on the December 2010 conference on market microstructure, organized with the help of the Institut Louis Bachelier, this guide brings together the leading thinkers to discuss this important field of modern finance. It provides readers with vital insight on the origin of the well-known anomalous "stylized facts" in financial prices series, namely heavy tails, volatility, and clustering, and illustrates their impact on the organization of markets, execution costs, price impact, organization liquidity in electronic markets, and other issues raised by high-frequency trading. World-class contributors cover topics including analysis of high-frequency data, statistics of high-frequency data, market impact, and optimal trading. This is a must-have guide for practitioners and academics in quantitative finance.
Author: Alexander Shapiro
Publisher: SIAM
ISBN: 0898718759
Category : Mathematics
Languages : en
Pages : 447
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Book Description
Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. Readers will find coverage of the basic concepts of modeling these problems, including recourse actions and the nonanticipativity principle. The book also includes the theory of two-stage and multistage stochastic programming problems; the current state of the theory on chance (probabilistic) constraints, including the structure of the problems, optimality theory, and duality; and statistical inference in and risk-averse approaches to stochastic programming.
