Ornstein-Uhlenbeck process

Quantitative Finance Glossary

Mean-reverting Gaussian process: dX_t = κ(θ - X_t),dt + σ,dW_t, with closed-form solution X_t = θ + (X_0 - θ)e^-κ t + σint_0^t e^-κ(t-s)dW_s. Stationary distribution mathcalN(θ, σ^2/(2κ)); half-life t_1/2 = ln 2 / κ. Foundation of the Vasicek short-rate model, equity-pairs-trade spread dynamics, and the variance process in normal stochastic-vol models.

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