Advanced OU Mean Reversion: Strategy & Backtesting in Python

I remember spending countless hours searching for reliable trading edges. One concept that always intrigued me was mean reversion — the idea that prices tend to revert to an average level over time. While simple moving average crossovers felt intuitive, I wanted something more mathematically grounded. That’s when I dove into the Ornstein-Uhlenbeck (OU) process, a tool often used in physics but surprisingly applicable to financial markets, especially for modeling the fluctuating spread between related assets in pairs trading.

This tutorial stems from that exploration. We won’t just talk theory; we’ll get our hands dirty. I’ll guide you through building a trading strategy based on the OU process, estimating its parameters from real market data and, crucially, implementing a professional-grade vectorized backtest in Python. The goal is to move beyond simple strategy ideas and towards rigorous evaluation, tackling common pitfalls like lookahead bias and unrealistic assumptions head-on. We’ll focus specifically on applying this to pairs trading, a classic quantitative strategy.

Photo by m. on Unsplash

Table of Contents

• Mathematical Foundations of the Ornstein-Uhlenbeck Process: Understanding the OU stochastic differential equation, its parameters (θ, μ, σ) and the vital property of stationarity for trading.