Random step functions model for interest rates

We propose a new model for pricing of bonds and their options based on the short rate when the latter exhibits a step function like behaviour. The model produces realistic looking spot rate curves, and allows one to derive explicit formulae for the yield curve and put and cap options. This model is appropriate for markets with pegged rates, such as the Australian market. We also give a general result on bond prices when the short rate is a sum of independent processes.