In short-rate modeling, the short-rate, r(t), is the spot rate at a particular time. It is described as a continuously-compounded, annualized interest rate term for an infinitesimally short period of time on the yield curve. The short-rate takes on the form of a stochastic variable in interest-rate models, where the interest rates may change by small amounts at every point in time. Short-rate models attempt to model the evolution of interest rates over time, and hopefully describe the economic conditions at certain periods.
Short-rate models are frequently used in the evaluation of interest-rate derivatives. Bonds, credit instruments, mortgages, and loan products are sensitive to interest-rate changes. Short-rate models are used as interest rate components in conjunction with pricing implementations, such as numerical methods, to help price such derivatives...