Optimal Mean Reversion Strategy In The Presence Of Bid Ask Spread And Delays In Capital Allocations

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.

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.

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.

"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."--

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.

This publication aims to fill the void between books providing an introduction to derivatives, and advanced books whose target audience are members of quantitative modelling community. In order to appeal to the widest audience, this publication tries to assume the least amount of prior knowledge. The content quickly moves onto more advanced subjects in order to concentrate on more practical and advanced topics. "A master piece to learn in a nutshell all the essentials about volatility with a practical and lively approach. A must read!" Carole Bernard, Equity Derivatives Specialist at Bloomberg "This book could be seen as the 'volatility bible'!" Markus-Alexander Flesch, Head of Sales & Marketing at Eurex "I highly recommend this book both for those new to the equity derivatives business, and for more advanced readers. The balance between theory and practice is struck At-The-Money" Paul Stephens, Head of Institutional Marketing at CBOE "One of the best resources out there for the volatility community" Paul Britton, CEO and Founder of Capstone Investment Advisors "Colin has managed to convey often complex derivative and volatility concepts with an admirable simplicity, a welcome change from the all-too-dense tomes one usually finds on the subject" Edmund Shing PhD, former Proprietary Trader at BNP Paribas "In a crowded space, Colin has supplied a useful and concise guide" Gary Delany, Director Europe at the Options Industry Council

Academic finance has had a remarkable impact on many financial services. Yet long-term investors have received curiously little guidance from academic financial economists. Mean-variance analysis, developed almost fifty years ago, has provided a basic paradigm for portfolio choice. This approach usefully emphasizes the ability of diversification to reduce risk, but it ignores several critically important factors. Most notably, the analysis is static; it assumes that investors care only about risks to wealth one period ahead. However, many investors—-both individuals and institutions such as charitable foundations or universities—-seek to finance a stream of consumption over a long lifetime. In addition, mean-variance analysis treats financial wealth in isolation from income. Long-term investors typically receive a stream of income and use it, along with financial wealth, to support their consumption. At the theoretical level, it is well understood that the solution to a long-term portfolio choice problem can be very different from the solution to a short-term problem. Long-term investors care about intertemporal shocks to investment opportunities and labor income as well as shocks to wealth itself, and they may use financial assets to hedge their intertemporal risks. This should be important in practice because there is a great deal of empirical evidence that investment opportunities—-both interest rates and risk premia on bonds and stocks—-vary through time. Yet this insight has had little influence on investment practice because it is hard to solve for optimal portfolios in intertemporal models. This book seeks to develop the intertemporal approach into an empirical paradigm that can compete with the standard mean-variance analysis. The book shows that long-term inflation-indexed bonds are the riskless asset for long-term investors, it explains the conditions under which stocks are safer assets for long-term than for short-term investors, and it shows how labor income influences portfolio choice. These results shed new light on the rules of thumb used by financial planners. The book explains recent advances in both analytical and numerical methods, and shows how they can be used to understand the portfolio choice problems of long-term investors.

A limit order book is essentially a file on a computer that contains all orders sent to the market, along with their characteristics such as the sign of the order, price, quantity and a timestamp. The majority of organized electronic markets rely on limit order books to store the list of interests of market participants on their central computer. A limit order book contains all the information available on a specific market and it reflects the way the market moves under the influence of its participants. This book discusses several models of limit order books. It begins by discussing the data to assess their empirical properties, and then moves on to mathematical models in order to reproduce the observed properties. Finally, the book presents a framework for numerical simulations. It also covers important modelling techniques including agent-based modelling, and advanced modelling of limit order books based on Hawkes processes. The book also provides in-depth coverage of simulation techniques and introduces general, flexible, open source library concepts useful to readers studying trading strategies in order-driven markets.