Ornstein-Uhlenbeck Mean-Reversion Process (Model 04) | KoshX Learning
Continuous stochastic calculus model estimating mean reversion speed theta, half-life decay, and stationary variance for swing trading.
Empirical Quantitative Methodology
The Ornstein-Uhlenbeck stochastic process models continuous mean reversion with drift and variance. Estimating theta yields the exact statistical half-life (decay time back to fair value), enabling traders to target oversold 2-sigma dislocations with predictable holding durations.
dX_t = \theta (\mu - X_t) dt + \sigma dW_t, \quad t_{1/2} = \frac{\ln 2}{\theta}
Frequently Asked Questions
What is the Ornstein-Uhlenbeck (OU) process in finance?
The OU process is a stationary, mean-reverting stochastic differential equation: dX_t = theta * (mu - X_t)dt + sigma * dW_t. Unlike Brownian motion (random walk), the OU process exerts an elastic drift pulling the stock price back toward its long-term statistical equilibrium mu whenever it stretches too far.
What is the mean reversion half-life (t½)?
Half-life is calculated as t½ = ln(2) / theta, representing the expected number of trading days required for a price dislocation to decay by 50% back toward equilibrium. In MTF swing trading, ideal half-lives range from 3 to 12 days, perfectly matching optimal margin holding periods.
How does KoshX trigger statistical snapback trades?
When a stock dislocates more than 2.0 standard deviations (2σ) below its estimated OU equilibrium mu, and the half-life confirms swift mean-reverting properties, the model flags an Elastic Snap buy signal with asymmetric upside potential.