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Fitting an Ornstein–Uhlenbeck Model for Optimal Mean-Reversion Trading

Article Stratmill research code

Summary

The document presents a framework for trading a mean-reverting portfolio, often formed by holding one asset and shorting another. It models portfolio value with an Ornstein–Uhlenbeck process, estimates the long-run mean, reversion speed, and volatility by maximizing the likelihood of observed values, and selects the portfolio hedge ratio that best fits the model. The stated guidance favors data frequencies from yearly to daily; very small intraday time steps may cause optimization problems.

Given the fitted process, the method formulates optimal stopping rules for entering and liquidating positions while accounting for transaction costs and discount rates. It describes threshold solutions for the basic case and entry intervals and liquidation levels when a stop-loss is included. The document supplies equations and implementation guidance, but no empirical trading results. Its conclusions depend on the OU model and assumptions such as constant costs and discount rates, so fit quality and practical performance require separate assessment.

Key ideas

  • The OU process represents a portfolio that tends to return toward a long-run mean.
  • Maximum likelihood estimation is used to fit the process parameters to observed portfolio values.
  • A hedge ratio can be selected by comparing the fitted likelihood across portfolio constructions.
  • Optimal entry and liquidation rules are expressed as stopping thresholds that account for costs and discounting.
  • Adding a stop-loss changes the optimal liquidation solution and can create an entry interval.
  • The document cautions that very high-frequency data may destabilize optimization.

Tags

Mean reversionPairs tradingStatisticsRisk management

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