Model 04 • Stochastic Calculus

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.