Once the movement of the short rate is set, the price of a zero-coupon bond at each point in time is fixed, and the prices of interest rate options can be calculated from those bond prices. A paper from the Institute for Monetary and Economic Studies of the Bank of Japan divides conventional interest rate models into market models, which model market rates such as LIBOR and swap rates, and short-rate models, which model the short rate.
An option with several exercise dates, such as a Bermudan swaption, can be valued by moving the short rate on a binomial tree and calculating backward through the tree.