Optimizing Ornstein–Uhlenbeck Trading Thresholds for Pairs Trading

Summary

The document explains a threshold-selection method for pairs trading when the modeled log price follows an Ornstein–Uhlenbeck process. It builds on earlier work by deriving expressions for the expected first-passage time with two-sided boundaries, then uses expected return per unit time to choose entry and exit thresholds while accounting for transaction costs. The strategy opens short and long positions at symmetric dimensionless boundaries and closes them at corresponding exit levels.

Two cases yield boundary choices that simplify the optimization: in the conventional rule, the exit threshold is zero; in the alternative rule, it is the negative of the entry threshold. The resulting equations can be solved for the optimal entry threshold, then mapped back to price units using the process mean, reversion speed, and volatility. The document also gives formulas for trade-length and return moments, and describes model fitting and performance metrics. These are theoretical results under the assumed OU model; the page provides no empirical profitability evidence. Real performance depends on model fit, transaction costs, and implementation assumptions.

Key ideas

• The method models log price as an Ornstein–Uhlenbeck process around a long-run mean.
• Expected return per unit of time is optimized after accounting for transaction costs.
• The conventional and alternative rules impose different optimal exit-boundary relationships.
• Dimensionless thresholds must be transformed using the OU process parameters before trading.
• The formulas rely on an OU model and do not establish live profitability.

Tags

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