Instantaneous caps and floors on the short rate

In this paper we propose new types of caps and floors. The derivatives are written on the instantaneous short rate. The cap (floor) accumulates interest only when the short rate is above the cap rate (below the floor rate). The accumulation factors are the difference between the short rate and the cap rate and the difference between the floor rate and the short rate. The floor can also be used to construct a contract with an instantaneous minimum guaranteed rate of return. We propose a way to approximate the market values of these derivatives. To this end, we use derivatives for which the market values can be easily evaluated in closed from and combine the different values in a given way. Numerical investigations indicate that our approximations give highly reliable price estimates.