Mean Reversion Trading with Sequential Deadlines and Transaction Costs

Abstract

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. JEL Classification: C41, G11, G12 MSC2010: Primary 91G20, 60G40. Secondary 60J60, 35R35, 45G10.

High-dimensional Statistical Arbitrage with Factor Models and Stochastic Control

“…After the papers by Jurek and Yang (2007) and Mudchanatongsuk et al (2008), an increasing number of models have been proposed in this framework (see, for example, Chiu and Wong (2011), Tourin and Yan (2013), and Liu and Timmerman (2013)), in which generally they assume that some statistically-designed relation between the prices of two assets is a mean-reverting stochastic process and find a dynamic optimal allocation in continuous time in some version of the classical Merton framework. More recently, a number of papers have also studied the optimal entry and exit points when trading a couple of cointegrated assets, such as Leung and Li (2015), Lei and Xu (2015), Ngo and Pham (2016), and Kitapbayev and Leung (2018).…”