MEAN REVERSION TRADING WITH SEQUENTIAL DEADLINES AND TRANSACTION COSTS

Yerkin Kitapbayev and Tim Leung
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Yerkin Kitapbayev: Questrom School of Business, Boston University, Boston MA 02215, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2018, vol. 21, issue 01, 1-22

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) A change-of-variable formula with local time on curves, Journal of Theoretical Probability 18, 499–535] to derive nonlinear integral equations of Volterra-type that uniquely characterize the trading boundaries. The numerical implementation of the integral equations provides examples of the optimal trading boundaries.

Keywords: Spread trading; optimal stopping; mean reversion; free-boundary problem; local time (search for similar items in EconPapers)
Date: 2018
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Working Paper: Mean Reversion Trading with Sequential Deadlines and Transaction Costs (2018)
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DOI: 10.1142/S0219024918500048

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