Book Description

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.