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

Abstract

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 effective 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.

Statistical Arbitrage Pairs Trading Strategies: Review and Outlook

“…() and Puspaningrum et al . () develop improved trading rules specifically designed for cointegrated securities. Their concepts have the potential to improve trading results and yet need to be tested on a large data set.…”

“…The latter point is addressed in a subsequent paper by Puspaningrum et al . (). They fit an AR(1)‐process to the spread of two cointegrated stocks and use an integral equation approach to numerically evaluate the estimated number of trades for any given trading threshold or minimum profit per trade.…”

“…Optimizing profit per trade usually does not optimize total profit over the trading horizon, since a higher minimum profit per trade leads to a lower number of trades and vice versa. The latter point is addressed in a subsequent paper by Puspaningrum et al (2010). They fit an AR(1)-process to the spread ε i j,t of two cointegrated stocks and use an integral equation approach to numerically evaluate the estimated number of trades for any given trading threshold or minimum profit per trade.…”

“…Rad et al (2015) provide the first largescale empirical application, albeit with a strong bias induced by preselecting pairs via SSD. Lin et al (2006) and Puspaningrum et al (2010) develop improved trading rules specifically designed for cointegrated securities. Their concepts have the potential to improve trading results and yet need to be tested on a large data set.…”

Optimizing the Pairs‐Trading Strategy Using Deep Reinforcement Learning with Trading and Stop‐Loss Boundaries

“…The results showed that, as the open condition value decreases, the number of trades and profits increases. Also [19] suggested optimal preset boundaries calculated from estimated parameters for the average trade duration, intertrade interval, and number of trades and used them to maximize the minimum total profit. They used the daily closing price data from January 2, 2004, to June 30, 2005, of seven pairs of stocks on the Australian Stock Exchange.…”