Overview of common short-rate interest rate models

Describe the principal short-rate models used for interest rates and explain how they differ from one another.

They split into equilibrium models (Vasicek, CIR) and no-arbitrage models (Ho-Lee, Hull-White, Black-Derman-Toy, Black-Karasinski). Vasicek has mean reversion with normal rates (can go negative); CIR scales volatility by $\sqrt r$ to keep rates positive. Ho-Lee and Hull-White add a time-dependent drift so the model fits today's yield curve exactly, Hull-White adding mean reversion; BDT and Black-Karasinski model $\ln r$ for lognormal rates. They trade off tractability, positivity and calibration fit.