Vasicek model

Quantitative Finance Glossary

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.

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