Simulating and Calibrating Ornstein–Uhlenbeck Mean-Reverting Spreads
Summary
This article applies the Ornstein–Uhlenbeck (OU) process to mean-reverting spreads, including those used in pairs trading. It contrasts Euler–Maruyama simulation, which introduces discretization error, with Doob’s exact simulation method, which uses the process’s conditional normal distribution to generate steps without that approximation. It then reviews parameter estimation through AR(1) regression, a known-mean variant, direct maximum likelihood, and moment adjustments.
The main caution is that mean-reversion speed can be difficult to estimate accurately, even with many observations. Finite samples can bias estimates upward, making a trading strategy appear to revert faster and seem more profitable than it may be. The article notes that estimates become especially unreliable when reversion is slow or samples are limited, and that noise or jumps add further complications. It presents indirect inference as a possible finite-sample improvement, with greater computational cost. The discussion describes estimation methods and cited statistical findings; it does not establish that any particular pairs-trading strategy will be profitable.
Key ideas
- Doob’s exact simulation method avoids the discretization error of a basic Euler scheme for the OU process.
- Mean-reversion speed is harder to estimate reliably than the long-run mean and process volatility.
- Finite-sample estimators can overstate reversion speed and create overly optimistic expectations for pairs trading.
- AR(1), likelihood, and moment-based estimators have different finite-sample behavior.
- Slow reversion, limited observations, noise, and jumps all weaken calibration reliability.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.