Optimal pair-trading strategy over long/short/square positions-empirical study

Suzuki [Automatica, 2016, 67, 33-45] solves the optimal, finitely iterative, three-regime switching problem for investing in a mean-reverting asset that follows an Ornstein-Uhlenbeck price process and find explicit solutions. The remarkable feature of this model is that the investor can explicitly take either a long, short or square position and can switch the position, with transaction costs, during the investment period. We run empirical simulations of such multiple-regime switching models. There are very few such attempts in the existing literature because it is difficult to find, first, an explicit solution to the problem and second, appropriate financial assets that follow the artificial stochastic process required by the mathematical model. According to the Monte Carlo simulations of the optimal pair-trading strategy, the mean daily Sharp ratio is more than 2.3, whereas the mean Sharp ratio for the historical simulation of the 'stub' pairs (combinations of parent/subsidiary companies) is 0.6886. We believe that the results obtained from performing the empirical simulations are remarkable and consider that the optimal switching strategy of the rigorous mathematical model is applicable to businesses in the real world. For the reference many pseudo-program codes are added, which can help to replicate the optimal trading strategies.