Pairs trading with a mean-reverting jump–diffusion model on high-frequency data

Abstract

This paper develops a pairs trading framework based on a mean-reverting jump–diffusion model and applies it to minute-by-minute data of the S&P 500 oil companies from 1998 to 2015. The established statistical arbitrage strategy enables us to perform intraday and overnight trading. Essentially, we conduct a three-step calibration procedure to the spreads of all pair combinations in a formation period. Top pairs are selected based on their spreads’ mean-reversion speed and jump behaviour. Afterwards, we trade the top pairs in an out-of-sample trading period with individualized entry and exit thresholds. In the back-testing study, the strategy produces statistically and economically significant returns of 60.61% p.a. and an annualized Sharpe ratio of 5.30, after transaction costs. We benchmark our pairs trading strategy against variants based on traditional distance and time-series approaches and find its performance to be superior relating to risk–return characteristics. The mean-reversion speed is a main driver of successful and fast termination of the pairs trading strategy.

Keywords:

• Finance
• Statistical arbitrage
• Pairs trading
• High-frequency data
• Jump–diffusion model
• Mean-reversion

JEL Classification:

• C1
• C2
• C22
• C5
• C6

Acknowledgements

We are grateful to Ingo Klein, Christopher Krauß, Jonas Rende, and two anonymous referees for many helpful discussions and suggestions on this topic.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

† We sort the data set in decreasing order and remove the largest 10% of the observations.

† Calculating the standard deviation of the JDM analytically would require estimating the parameters of the jump size distribution. Dealing with a data base of only 30 days does not allow reasonable estimates since jumps are rather sparse compared to the total length of the data-set (Cartea and Figueroa 2005, Benth et al. 2012).

† We thank Kenneth R. French for providing all relevant data for these models on his website.