  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. As an
extension, we incorporate a stop-loss constraint to limit the maximum loss. 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
stop-loss 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 cost and stop-loss
level.
