Statistical Arbitrage with Pairs Trading

We analyze statistical arbitrage with pairs trading assuming that the spread of two assets follows a mean‐reverting Ornstein–Uhlenbeck process around a long‐term equilibrium level. Within this framework, we prove the existence of statistical arbitrage and derive optimality conditions for trading the spread portfolio. In the existence of uncertainty in the long‐term mean and the volatility of the spread, statistical arbitrage is no longer guaranteed. However, the asymptotic probability of loss can be bounded as a function of the standard error of the model parameters. The proposed framework provides a new filtering technique for identifying best pairs in the market. Backtesting results are given for some of the pairs of stocks that are studied in the literature.