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 of 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.

Interest rate modeling is considered a fairly complex topic since interest rates are affected by a multitude of factors...