Optimizing Pairs-Trading Thresholds with Ornstein–Uhlenbeck Models

Summary

The document presents an analytical approach to choosing entry and exit thresholds for mean-reversion trading. It models a tradable process with an Ornstein–Uhlenbeck dynamic and uses first-passage-time calculations to derive the expected duration and variability of a trading cycle. Those quantities support estimates of return and risk per unit of time, allowing thresholds to be optimized for expected return or, in one formulation, Sharpe ratio while accounting for transaction costs and a risk-free rate.

It compares a one-sided, long-only formulation with an extension that allows both long and short positions through two-sided boundaries. A reported example replicates a published trading case, and a separate backtest is described as having lower returns but lower risk than buy-and-hold of either paired stock. These outcomes are specific to the example and do not establish general profitability. The article also highlights practical limits: the process may not fit real spreads well, structural breaks can prevent convergence, and a stop-loss policy is needed but not fully developed.

Key ideas

• First-passage-time formulas connect Ornstein–Uhlenbeck trade duration to return and risk per unit of time.
• Entry and exit thresholds can be selected by optimizing expected return or Sharpe ratio under trading costs.
• A two-sided boundary formulation extends threshold selection to long and short trades.
• The described backtest reports lower returns and lower risk than holding either paired asset.
• Poor process fit and structural breaks remain practical hazards, and the article calls for stop-loss rules.

Tags

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