Mean Reversion Trading with Sequential Deadlines and Transaction Costs

摘要

We study the optimal timing strategies for trading a mean-reverting priceprocess with afinite deadline to enter and a separate finite deadline to exitthe market. The price process is modeled by a diffusion with an affine driftthat encapsulates a number of well-known models,including theOrnstein-Uhlenbeck (OU) model, Cox-Ingersoll-Ross (CIR) model, Jacobi model,andinhomogeneous geometric Brownian motion (IGBM) model.We analyze three types oftrading 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) thechooser strategy whereby the trader has the added flexibility to enter themarket by taking either a long or short position, and subsequently close theposition. For each strategy, we solve an optimal double stopping problem withsequential deadlines, and determine the optimal timing of trades. Our solutionmethodology utilizes the local time-space calculus of Peskir (2005) to derivenonlinear integral equations of Volterra-type that uniquely characterize thetrading boundaries. Numerical implementation ofthe integral equations providesexamples of the optimal trading boundaries.