Home Research Papers Trading Strategies Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit

# Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit

In this research, published in the International Journal of Theoretical and Applied Finance, Tim Leung from the University of Washington’s Department of Applied Math and Xin Li from Columbia University delve into the optimal timing strategies for trading a mean-reverting price spread, inspired by the industry practice of pairs trading.

Framed as an optimal double stopping problem, the study aims to analyze the timing of initiating and subsequently liquidating a position while considering transaction costs. The price spread is modeled using an Ornstein-Uhlenbeck process, and a probabilistic methodology is applied to rigorously derive optimal price intervals for market entry and exit.

In an innovative extension, the researchers incorporate a stop-loss constraint to limit the maximum loss, revealing that the entry region is characterized by a bounded price interval situated strictly above the stop-loss level. Regarding exit timing, a higher stop-loss level consistently implies a lower optimal take-profit level.

The paper provides both analytical and numerical results, offering a comprehensive understanding of how timing strategies depend on model parameters such as transaction cost and stop-loss level. This research contributes valuable insights into the nuanced dynamics of optimal mean reversion trading with transaction costs and stop-loss exit.

## Abstract Of Paper

Motivated by the industry practice of pairs trading, we study the optimal timing strategies for trading a mean-reverting price spread. An optimal double stopping problem is formulated to analyze the timing to start and subsequently liquidate the position subject to transaction costs. Modeling the price spread by an Ornstein-Uhlenbeck process, we apply a probabilistic methodology and rigorously derive the optimal price intervals for market entry and exit. As an extension, we incorporate a stop-loss constraint to limit the maximum loss. We show that the entry region is characterized by a bounded price interval that lies strictly above the stop-loss level. As for the exit timing, a higher stop-loss level always implies a lower optimal take-profit level. Both analytical and numerical results are provided to illustrate the dependence of timing strategies on model parameters such as transaction cost and stop-loss level.

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## Author

Tim Leung
University of Washington – Department of Applied Math

Xin Li
Columbia University

## Conclusion

In this study conducted by Tim Leung and Xin Li, inspired by pairs trading in financial markets, the primary focus is on optimal mean reversion trading strategies. These strategies are designed while considering transaction costs and incorporating a stop-loss exit constraint.

The investigation formulates the problem as an optimal double stopping scenario, exploring the most advantageous timing for entering and subsequently liquidating a position, all while taking into account the impact of transaction costs.

The price spread is modeled using an Ornstein-Uhlenbeck process, and a probabilistic methodology is employed to rigorously derive optimal price intervals for both market entry and exit.

As an extension to the study, a stop-loss constraint is introduced to limit potential maximum losses. Intriguingly, the entry region is characterized by a bounded price interval situated strictly above the stop-loss level, revealing a key feature of the optimal mean reversion trading strategy.

Regarding exit timing, the study uncovers a significant relationship – a higher stop-loss level consistently corresponds to a lower optimal take-profit level. This dynamic underscores the delicate balance involved in crafting effective mean reversion trading strategies, especially when considering risk management through stop-loss constraints.

The study provides both analytical and numerical results, offering valuable insights into the dependency of timing strategies on crucial model parameters such as transaction costs and stop-loss levels.

Overall, this research contributes to a nuanced understanding of optimal mean reversion trading, providing practical guidance for market participants navigating the complexities of financial markets with transaction costs and risk mitigation through stop-loss mechanisms.

## FAQ:

– What is the primary focus of the research paper “Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit” by Tim Leung and Xin Li?

The research paper examines optimal timing strategies for trading a mean-reverting price spread, particularly in the context of pairs trading. It formulates a double stopping problem to address the timing of market entry and exit while considering transaction costs.

– How does the paper model the price spread dynamics and derive optimal timing strategies for trading?

The research utilizes an Ornstein-Uhlenbeck process to model the price spread and employs a probabilistic methodology to rigorously derive optimal price intervals for both market entry and exit. The study also extends the analysis by introducing a stop-loss constraint to limit potential maximum losses in the trading strategy.

– What key insights are provided regarding optimal timing strategies, and how do they depend on model parameters?

The paper reveals that the entry region is characterized by a bounded price interval positioned strictly above the stop-loss level. Additionally, there is an inverse relationship between the stop-loss level and the optimal take-profit level for exit. The research discusses the dependence of these optimal timing strategies on model parameters, such as transaction costs and the stop-loss level, offering valuable guidance for traders and investors involved in mean-reversion trading.

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I’ve got an Msc from Heriot-Watt University, Edinburgh (1996), in addition a to a business administration degree the Norwegian School of Management (BI – 1994). Did my mandatory military service in between. After university, I worked two years as an auditor (1996-1998). I co-founded Aksjeforum.com in 1998/99 - one of the first websites about trading and investing in Norway. It was later acquired by Digi.no in 2001. From 2001 until 2018 I was a full-time independent and automated day trader, mainly via Echotrade LLC (USA), trading successfully to become a FIRE. I passed the Series 7 exam in 2001, but it has since lapsed. Since 2018 until today full-time investor.