Trading Under the Exponential OU Model

Tim Leung and Xin Li

Chapter 3 in Optimal Mean Reversion Trading:Mathematical Analysis and Practical Applications, 2016, pp 51-80 from World Scientific Publishing Co. Pte. Ltd.

Abstract: Another widely used mean-reverting process is the exponential Ornstein-Uhlenbeck (XOU) process:${\rm{\xi }}_t \, = \,e^{X_t } ,\,\,t \ge 0,\,\,\,\left( {3.1} \right)$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…

Keywords: Trading Strategies; Mean Reversion; Optimal Stopping; Optimal Switching; Stop-Loss; Stochastic Processes; Exchange-Traded Funds (ETFS); Ornstein–Uhlenbeck Model; Cox-Ingersoll-Ross (CIR) Model (search for similar items in EconPapers)
Date: 2016
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