Optimal Stopping for Ornstein–Uhlenbeck Pairs Trading

Summary

This article applies optimal stopping theory to a mean-reverting spread formed from two co-moving assets. It models the spread with an Ornstein–Uhlenbeck process, estimates the process parameters and asset hedge ratio by maximizing average log-likelihood, then formulates separate decisions for entering and liquidating a position. The objective is to maximize expected discounted value after accounting for transaction costs.

The article also considers a stop-loss constraint and summarizes how the model’s optimal entry and exit thresholds vary with the long-term mean, reversion speed, volatility, transaction costs, and stop-loss level. Its discussion draws on analytical results from Leung and Li, rather than presenting an independent empirical backtest. The framework assumes a fitted OU process and focuses on a single entry and exit; parameter quality, model fit, and real-world trading frictions therefore limit how directly its thresholds can be applied. Repeated entry and exit decisions are identified as a broader extension.

Key ideas

• A spread can be modeled as an Ornstein–Uhlenbeck process to represent mean reversion.
• The hedge ratio and process parameters are selected by maximizing the spread’s average log-likelihood.
• Optimal stopping formulates entry and liquidation as separate expected discounted value problems.
• Transaction costs and a stop-loss constraint affect the optimal thresholds.
• The presented setup covers a single entry and exit and depends on the OU model’s suitability.

Tags

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