Ornstein-Uhlenbeck Process

The Ornstein-Uhlenbeck process is a mathematical model used in quantitative finance to describe a stochastic process that tends to return to a long-term mean. Unlike a simple random walk, this process has a drift term that pulls the variable back toward the average, making it ideal for modeling asset prices that exhibit mean-reverting behavior.

In the context of derivatives, it is used to model the evolution of interest rates and volatility. For a trader, it provides a rigorous basis for identifying when a price is statistically significant in its distance from the mean.

This allows for the construction of systematic trading rules that enter positions when the deviation exceeds a certain threshold. It is a foundational concept for statistical arbitrage and pairs trading.