Explain term structure models and the uses they are put to

Term structure models describe how the short rate evolves. Equilibrium models such as Cox–Ingersoll–Ross and Vasicek derive the curve from assumed dynamics, both with mean reversion toward a long-run level. In Cox–Ingersoll–Ross volatility is proportional to the square root of the rate, so rates cannot go negative, while in Vasicek volatility is constant and negative rates are possible. Arbitrage-free models such as Ho–Lee and Kalotay–Williams–Fabozzi take today's curve as given and use a time-dependent drift to match it exactly, which suits pricing derivatives consistently with market bond prices. Ho–Lee has constant volatility and can produce negative rates; Kalotay–Williams–Fabozzi models the log of the rate, keeping it positive.