Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit (1411.5062v3)

Abstract: 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.

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

The paper, titled "Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit," investigates the challenges of optimal timing for trading a mean-reverting price spread under the constraint of transaction costs, emphasizing the importance of entry and exit strategy decisions in pairs trading.

Key Contributions

The authors address the double formulation problem of deciding optimal times to enter and exit the market. As an extension of existing studies, they integrate a stop-loss constraint to limit maximum losses. This research is motivated by industry practices where asset price reversion to the mean is exploited. Using an Ornstein-Uhlenbeck (OU) process to model price spreads, the authors rigorously derive the optimal price intervals for market entry and exit. The paper is notable for proposing a probabilistic methodology different from conventional variational inequalities, forming analytical expressions for contrived optimal strategies.

Analytical and Numerical Results

The research derives the optimal levels at which trading strategies should be executed. The bounded entry region is strictly set above the stop-loss level, indicating that it is not optimal to enter the market when prices are too low or close to this boundary, given the risk of an unfavorable exit. Furthermore, the research illustrates that a higher stop-loss level correlates with a lower take-profit threshold. The paper provides both analytical solutions and numerical illustrations, highlighting the dependencies of trading decisions on model parameters such as transaction costs and stop-loss levels.

Implications and Future Developments

The findings offer practical implications for traders and financial analysts, presenting a methodology to optimize trading strategies when dealing with mean-reverting assets. The paper challenges existing approaches by focusing on the probabilistic nature of price movements, proposing a potentially more effective means of structuring trading strategies that consider transaction costs and stop-loss constraints.

Theoretically, these results lend themselves to broader applications, such as adapting the method for different underlying asset models beyond OU, like exponential OU, CIR, or GARCH processes. Future developments might include testing this framework’s efficacy with more elaborate financial products or in different market conditions.

Conclusion

In conclusion, this research extends the literature on optimal stopping problems by incorporating transaction costs into the mean reversion trading strategy under the OU process. Its analytical derivations, presence of the stop-loss feature, and probabilistic focus provide valuable insights for practitioners looking to optimize trading strategies within pairs trading and related contexts. The anticipation of future studies adapting these methodologies to other trading models and contexts indicates the robustness and potential versatility of the work presented.