Vasicek model
Quantitative Finance glossary · Stochastic Calculus & Continuous Time Finance
Definition
Single-factor mean-reverting short-rate model: dr_t = κ(θ - r_t),dt + σ,dW_t — an Ornstein-Uhlenbeck process. Gaussian rates (permits negatives, an early objection that became a feature post-2014 ECB deposit-rate cuts). Affine term structure: P(t,T) = A(t,T)e^-B(t,T),r_t with closed-form bond prices and European options on bonds (Jamshidian decomposition extends to coupon bonds). The simplest model to derive analytically — a teaching benchmark and the platform on which Hull-White, G2++, and CIR build.
Vasicek model in plain English
The Vasicek model is a simple math story for how a short-term interest rate wanders over time. Its key idea is mean reversion: rates get pulled back toward a long-run 'normal' level θ, gently if they're close and harder if they've strayed far, while random shocks keep nudging them around. Picture a rubber band tied to a fixed post — the further the rate stretches away, the stronger the tug home, but a breeze (randomness) keeps it fidgeting. Because the math is so clean, it gives tidy formulas for bond prices and is the classic teaching starting point that fancier models (Hull-White, CIR) build on; its quirk is that it can let rates go negative, once seen as a flaw but oddly realistic after real-world negative rates appeared around 2014.
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