Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit
Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit

Author: Tim Leung

Publisher:

Published: 2015

Total Pages: 26

ISBN-13:

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Motivated by the industry practice of pairs trading, we study the optimal timing strategies for trading a mean-reverting price spread. An optimal double stopping problem is formulated to analyze the timing to start and subsequently liquidate the position subject to transaction costs. Modeling the price spread by an Ornstein-Uhlenbeck process, we apply a probabilistic methodology and rigorously derive the optimal price intervals for market entry and exit. As an extension, we incorporate a stop-loss constraint to limit the maximum loss. We show that the entry region is characterized by a bounded price interval that lies strictly above the stop-loss level. As for the exit timing, a higher stop-loss level always implies a lower optimal take-profit level. Both analytical and numerical results are provided to illustrate the dependence of timing strategies on model parameters such as transaction cost and stop-loss level.

Optimal Mean Reversion Trading
Optimal Mean Reversion Trading

Author: Tim Leung (Professor of industrial engineering)

Publisher: World Scientific

Published: 2015-11-26

Total Pages: 221

ISBN-13: 9814725927

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"Optimal Mean Reversion Trading: Mathematical Analysis and Practical Applications provides a systematic study to the practical problem of optimal trading in the presence of mean-reverting price dynamics. It is self-contained and organized in its presentation, and provides rigorous mathematical analysis as well as computational methods for trading ETFs, options, futures on commodities or volatility indices, and credit risk derivatives. This book offers a unique financial engineering approach that combines novel analytical methodologies and applications to a wide array of real-world examples. It extracts the mathematical problems from various trading approaches and scenarios, but also addresses the practical aspects of trading problems, such as model estimation, risk premium, risk constraints, and transaction costs. The explanations in the book are detailed enough to capture the interest of the curious student or researcher, and complete enough to give the necessary background material for further exploration into the subject and related literature. This book will be a useful tool for anyone interested in financial engineering, particularly algorithmic trading and commodity trading, and would like to understand the mathematically optimal strategies in different market environments."--

Mean Reversion Trading with Sequential Deadlines and Transaction Costs
Mean Reversion Trading with Sequential Deadlines and Transaction Costs

Author: Yerkin Kitapbayev

Publisher:

Published: 2019

Total Pages: 22

ISBN-13:

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We study the optimal timing strategies for trading a mean-reverting price process with a finite deadline to enter and a separate finite deadline to exit the market. The price process is modeled by a diffusion with an affine drift that encapsulates a number of well-known models, including the Ornstein-Uhlenbeck (OU) model, Cox-Ingersoll-Ross (CIR) model, Jacobi model, and inhomogeneous geometric Brownian motion (IGBM) model. We analyze three types of trading strategies: (i) the long-short (long to open, short to close) strategy; (ii) the short-long (short to open, long to close) strategy, and (iii) the chooser strategy whereby the trader has the added flexibility to enter the market by taking either a long or short position, and subsequently close the position. For each strategy, we solve an optimal double stopping problem with sequential deadlines, and determine the optimal timing of trades. Our solution methodology utilizes the local time-space calculus of Peskir (2005) to derive nonlinear integral equations of Volterra-type that uniquely characterize the trading boundaries. Numerical implementation of the integral equations provides examples of the optimal trading boundaries.

Optimal Mean Reversion Trading
Optimal Mean Reversion Trading

Author: Tim Leung

Publisher:

Published: 2019

Total Pages: 1

ISBN-13:

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This book provides a systematic study on the optimal timing of trades in markets with mean-reverting price dynamics. We present a financial engineering approach that distills the core mathematical questions from different trading problems, and also incorporates the practical aspects of trading, such as model estimation, risk premia, risk constraints, and transaction costs, into our analysis. Self-contained and organized, the book not only discusses the mathematical framework and analytical results for the financial problems, but also gives formulas and numerical tools for practical implementation. A wide array of real-world applications are discussed, such as pairs trading of exchange-traded funds, dynamic portfolio of futures on commodities or volatility indices, and liquidation of options or credit risk derivatives.A core element of our mathematical approach is the theory of optimal stopping. For a number of the trading problems discussed herein, the optimal strategies are represented by the solutions to the corresponding optimal single/multiple stopping problems. This also leads to the analytical and numerical studies of the associated variational inequalities or free boundary problems. We provide an overview of our methodology and chapter outlines in the Introduction.Our objective is to design the book so that it can be useful for doctoral and masters students, advanced undergraduates, and researchers in financial engineering/mathematics, especially those who specialize in algorithmic trading, or have interest in trading exchange-traded funds, commodities, volatility, and credit risk, and related derivatives. For practitioners, we provide formulas for instant strategy implementation, propose new trading strategies with mathematical justification, as well as quantitative enhancement for some existing heuristic trading strategies.

Optimal Multiple Stopping Approach to Mean Reversion Trading
Optimal Multiple Stopping Approach to Mean Reversion Trading

Author:

Publisher:

Published: 2015

Total Pages:

ISBN-13:

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In other words, the continuation (waiting) region for entry is disconnected. A similar phenomenon is observed in the OU model with stop-loss constraint. Indeed, the entry region is again characterized by a bounded price interval that lies strictly above the stop-loss level. As for the exit timing, a higher stop-loss level always implies a lower optimal take-profit level. In all three models, numerical results are provided to illustrate the dependence of timing strategies on model parameters.

Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs
Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs

Author: Tim Leung

Publisher:

Published: 2017

Total Pages: 25

ISBN-13:

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This paper studies the timing of trades under mean-reverting price dynamics subject to fixed transaction costs. We solve an optimal double stopping problem to determine the optimal times to enter and subsequently exit the market, when prices are driven by an exponential Ornstein-Uhlenbeck process. In addition, we analyze a related optimal switching problem that involves an infinite sequence of trades, and identify the conditions under which the double stopping and switching problems admit the same optimal entry and/or exit timing strategies. Among our results, we find that the investor generally enters when the price is low, but may find it optimal to wait if the current price is sufficiently close to zero. In other words, the continuation (waiting) region for entry is disconnected. Numerical results are provided to illustrate the dependence of timing strategies on model parameters and transaction costs.

Pairs Trading
Pairs Trading

Author: Ganapathy Vidyamurthy

Publisher: John Wiley & Sons

Published: 2011-02-02

Total Pages: 295

ISBN-13: 111804570X

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The first in-depth analysis of pairs trading Pairs trading is a market-neutral strategy in its most simple form. The strategy involves being long (or bullish) one asset and short (or bearish) another. If properly performed, the investor will gain if the market rises or falls. Pairs Trading reveals the secrets of this rigorous quantitative analysis program to provide individuals and investment houses with the tools they need to successfully implement and profit from this proven trading methodology. Pairs Trading contains specific and tested formulas for identifying and investing in pairs, and answers important questions such as what ratio should be used to construct the pairs properly. Ganapathy Vidyamurthy (Stamford, CT) is currently a quantitative software analyst and developer at a major New York City hedge fund.

Optimal Mean-Reversion Strategy in the Presence of Bid-Ask Spread and Delays in Capital Allocations
Optimal Mean-Reversion Strategy in the Presence of Bid-Ask Spread and Delays in Capital Allocations

Author: Sergey Isaenko

Publisher:

Published: 2017

Total Pages: 31

ISBN-13:

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A portfolio optimization problem for an investor who trades T-bills and a mean-reverting stock in the presence of proportional and convex transaction costs is considered. The proportional transaction cost represents a bid-ask spread, while the convex transaction cost is used to model delays in capital allocations. I utilize the historical bid-ask spread in US stock market and assume that the stock reverts on yearly basis, while an investor follows monthly changes in the stock price. It is found that proportional transaction cost has a relatively weak effect on the expected return and the Sharpe ratio of the investor's portfolio. Meantime, the presence of delays in capital allocations has a dramatic impact on the expected return and the Sharpe ratio of investor's portfolio.I also find the robust optimal strategy in the presence of model uncertainty and show that the latter increases the effective risk aversion of the investor and makes her view the stock as more risky.

On the Profitability of Optimal Mean Reversion Trading Strategies
On the Profitability of Optimal Mean Reversion Trading Strategies

Author: Peng Huang

Publisher:

Published: 2016

Total Pages: 18

ISBN-13:

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We study the profitability of optimal mean reversion trading strategies in the US equity market. Different from regular pair trading practice, we apply maximum likelihood method to construct the optimal static pairs trading portfolio that best fits the Ornstein-Uhlenbeck process, and rigorously estimate the parameters. Therefore, we ensure that our portfolios match the mean-reverting process before trading. We then generate contrarian trading signals using the model parameters. We also optimize the thresholds and the length of in-sample period by multiple tests. In nine good pair examples, we can see that our pairs exhibit high Sharpe ratio (above 1.9) over in-sample period and out-of-sample period. In particular, Crown Castle International Corp. (CCI) and HCP, Inc. (HCP) achieve a Sharpe ratio of 2.326 during in-sample test and a Sharpe ration of 2.425 in out-of-sample test. Crown Castle International Corp. CCI and (Realty Income Corporation) O achieve a Sharpe ratio of 2.405 and 2.903 separately during in-sample period and out-of-sample period.

High-Frequency Trading
High-Frequency Trading

Author: Irene Aldridge

Publisher: John Wiley & Sons

Published: 2013-04-22

Total Pages: 326

ISBN-13: 1118343506

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A fully revised second edition of the best guide to high-frequency trading High-frequency trading is a difficult, but profitable, endeavor that can generate stable profits in various market conditions. But solid footing in both the theory and practice of this discipline are essential to success. Whether you're an institutional investor seeking a better understanding of high-frequency operations or an individual investor looking for a new way to trade, this book has what you need to make the most of your time in today's dynamic markets. Building on the success of the original edition, the Second Edition of High-Frequency Trading incorporates the latest research and questions that have come to light since the publication of the first edition. It skillfully covers everything from new portfolio management techniques for high-frequency trading and the latest technological developments enabling HFT to updated risk management strategies and how to safeguard information and order flow in both dark and light markets. Includes numerous quantitative trading strategies and tools for building a high-frequency trading system Address the most essential aspects of high-frequency trading, from formulation of ideas to performance evaluation The book also includes a companion Website where selected sample trading strategies can be downloaded and tested Written by respected industry expert Irene Aldridge While interest in high-frequency trading continues to grow, little has been published to help investors understand and implement this approach—until now. This book has everything you need to gain a firm grip on how high-frequency trading works and what it takes to apply it to your everyday trading endeavors.