Optimal Mean Reversion Trading: Mathematical Analysis and Practical Applications

World Scientific Publishing Co., Doi.org/10.1142/9839

Posted: 29 Sep 2015 Last revised: 23 Dec 2019

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Xin Li

Columbia University

Date Written: September 23, 2015

Abstract

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.

Keywords: Mean reversion, futures trading, pairs trading, options, credit derivatives, OU process, CIR process

JEL Classification: G11, G12, G13

Suggested Citation

Leung, Tim and Li, Xin, Optimal Mean Reversion Trading: Mathematical Analysis and Practical Applications (September 23, 2015). World Scientific Publishing Co., Doi.org/10.1142/9839, Available at SSRN: https://ssrn.com/abstract=2664588

Tim Leung (Contact Author)

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States

HOME PAGE: http://faculty.washington.edu/timleung/

Xin Li

Columbia University ( email )

345 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

HOME PAGE: http://www.columbia.edu/~xl2206/

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