Interest rate caps and floors are, essentially, collections of interest rate options: each option has a positive payoff when it expires in the money and a zero payoff when it expires out of the money. The individual options are called, respectively, caplets and floorlets.
Note that caps and floors are commonly based on LIBOR or similar floating interest rates; as such, they are governed by the usual LIBOR characteristics:
They are based on a 360-day year, with 30-day months
The interest rates are quoted as nominal, annual rates…
To create a binomial interest rate tree, you need to start with:
A yield curve
An interest rate volatility
The yield curve can be a par curve, a spot curve, or a forward curve. (If you’re a bit fuzzy on the differences among these curves, look here.) For the remainder of this article, we’ll assume that we’re given a par curve; as we could generate the other curves given any one of them, it doesn’t really matter which one we get.
When you hear someone talk about “the yield curve”, they usually mean the par yield curve (and, more specifically, the par yield curve for risk-free bonds (e.g., the U.S. Treasury par curve)), but there are occasions when they might mean the spot yield curve or the forward yield curve.
In computing modified (or effective) duration for a portfolio of securities, we change the par interest rate (the yield to maturity) at every maturity by some small amount up and down (±Δy), and determine the percentage price change in the portfolio for 1% change in yield. In essence, we add ±Δy to the entire par curve. (Look here for a refresher on the par curve, and for a refresher on bootstrapping the spot curve from the par curve, which we shall be doing a bit later.)