Ornstein-Uhlenbeck Process in Pairs Trading: Calculating Reversion Half-Life [2026]
Date Published
1. The Stochastic Mathematics of Mean Reversion
The Ornstein-Uhlenbeck Differential Equation
The Ornstein-Uhlenbeck process is defined by the stochastic differential equation: dX_t = theta * (mu - X_t) dt + sigma * dW_t, where theta is the speed of mean reversion, mu is the long-term equilibrium mean, sigma is volatility, and W_t is a standard Brownian motion.
In statistical arbitrage, knowing theta allows quantitative portfolio managers to estimate how long capital will be tied up in a pair trade before reverting.
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