Finding the Optimal Pre-set Boundaries for Pairs Trading Strategy Based on Cointegration Technique

Pairs trading is one of the arbitrage strategies that can be used in trading stocks on the stock market. It incorporates the use of a standard statistical model to exploit the stocks that are out of equilibrium for short-term time. In determining which two stocks can be a pair, Banerjee et al. (1993) shows that the cointegration technique is more ffective than correlation criterion for extracting profit potential in temporary pricing anomalies for share prices driven by common underlying factors. This paper explores the ways in which the pre-set boundaries chosen to open a trade can influence the minimum total profit over a specified trading horizon. The minimum total profit relates to the pre-set minimum profit per trade and the number of trades during the trading horizon. The higher the pre-set boundaries for opening trades, the higher the profit per trade but the lower the trade numbers. The opposite applies for lowering the boundary values. The number of trades over a specified trading horizon is determined jointly by the average trade duration and the average inter-trade interval. For any pre-set boundaries, both of these values are estimated by making an analogy to the mean first-passage time. The aims of this paper are to develop numerical algorithm to estimate the average trade duration, the average inter-trade interval, and the average number of trades and then use them to find the optimal pre-set boundaries that would maximize the minimum total profit for cointegration error following an AR(1) process.