Skip to content
All library documents

Optimal Entry and Exit for Mean-Reverting Spreads with Stop-Losses

Article arXiv papers · Author: Tim Leung et al.
Read the original

Summary

This study develops a timing method for trading a mean-reverting price spread, motivated by pairs trading. It models the spread as an Ornstein–Uhlenbeck process and frames opening and closing a position as a double stopping problem, with transaction costs included. A probabilistic analysis derives optimal price intervals for entering and exiting trades.

The study extends the framework with a stop-loss constraint. It finds that the entry interval is bounded and lies above the stop-loss level, and that raising the stop-loss level lowers the optimal take-profit level. Analytical and numerical results illustrate how transaction costs and the stop-loss setting affect timing. The document does not provide the model equations, parameter values, or empirical market tests, so it offers a theoretical framework rather than evidence that the rules are profitable in live trading.

Key ideas

  • The spread is modeled as an Ornstein–Uhlenbeck process to represent mean reversion.
  • Entry and exit are treated as linked optimal stopping decisions with transaction costs.
  • The optimal entry region is bounded and sits above the stop-loss level.
  • A higher stop-loss level implies a lower optimal take-profit level.
  • Analytical and numerical illustrations show sensitivity to model parameters.

Tags

Mean reversionPairs tradingRisk managementStatistics

Cited by

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


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









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.