Interest rate derivatives are financial derivative products whose payoff is dependent on the interest rates.

There is a wide range of such products; the basic types include interest rate swaps, forward rate agreements, callable and puttable bonds, bond options, caps and floors, and so on.

In this chapter, we will start with the Black model (also referred to as the Black-76 model), which is a generalized version of the Black-Scholes model, and is often used to price interest rate derivatives. Then, we will show how to apply the Black model to price an interest rate cap.

A shortcoming of the Black model is that it assumes lognormal distribution for some underlying asset (for example, bond price or interest rate), and it neglects how interest rate changes across time. Consequently, Black's formula cannot be used for all kinds of interest rate derivatives. Sometimes, it is necessary to model the term structure of interest rate models...