Optimal Mean Reversion Trading

The following sections are included:

• Preface
• Contents

In the financial markets, it has been widely observed that many asset prices exhibit mean reversion, including commodities, foreign exchange rates, volatility indices, as well as US and global equities. Mean-reverting processes are also used to model the dynamics of bond prices, interest rate, and default risk. In order to visualize a mean-reverting price path, we illustrate in Figure 1.1(a) the historical prices of an exchange-traded fund (ETF), the Vanguard Short-Term Bond ETF (BSV), from June 12, 2014 to June 11, 2015. This ETF is designed to track bond prices with short maturities, and is traded liquidly on NYSE and other exchanges. As another example, Figure 1.1(b) shows the time series of CBOE Volatility Index (VIX) from June 12, 2014 to June 11, 2015. Although the volatility index is not traded, investors can gain exposure to it by trading futures, options, or exchange-traded notes (ETNs) designed to track the index…

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. A number of extensions are also considered, such as incorporating a stop-loss constraint, or a minimum holding period. 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 stoploss 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 costs and stop-loss level…

Another widely used mean-reverting process is the exponential Ornstein-Uhlenbeck (XOU) process:

where X is the OU process defined in (2.1). In other words, X is the log-price of the positive XOU process ξ. In this chapter, 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. 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…

In this chapter, we study the problem of trading under the CIR model. We formulate an optimal double stopping problem and an optimal switching problem, and rigorously prove that the optimal starting and stopping strategies are of threshold type…

Futures are an integral part of the universe of derivatives. A futures is a contract that requires the buyer to purchase (seller to sell) a fixed quantity of an asset, such as a commodity, at a fixed price to be paid for on a prespecified future date. Commonly traded on exchanges, there are futures written on various underlying assets or references, including commodities, interest rates, equity indices, and volatility indices. Many futures stipulate physical delivery of the underlying asset, with notable examples of agricultural, energy, and metal futures. However, some, like the VIX futures, are settled in cash…

For decades, options have been widely used as a tool for investment and risk management. As of 2012, the daily market notional for S&P 500 options is about US$90 billion and the average daily volume has grown rapidly from 119,808 in 2002 to 839,108 as of Jan 2013. Empirical studies on options returns often assume that the options are held to maturity. For every liquidly traded option, there is an embedded timing flexibility to liquidate the position through the market prior to expiry. Hence, an important question for effective risk management is: When is the best time to sell an option? In this chapter, we propose a risk-adjusted optimal timing framework to address this problem for a variety of options under different underlying price dynamics…

In credit derivatives trading, one important question is how the market compensates investors for bearing credit risk. A number of related studies have examined analytically and empirically the structure of default risk premia inferred from the market prices of corporate bonds, credit default swaps, and multi-name credit derivatives. A major risk premium component is the mark-to-market risk premium which accounts for the fluctuations in default risk. In addition, there is the event risk premium (or jump-to-default risk premium) that compensates for the uncertain timing of the default event…

The following sections are included:

• Bibliography
• Index