## Binomial Pricing Trees (for Options)

In this article, we’ll be concerned with the application of binomial trees to the valuation of call and put options (on, for example, stocks or commodities).

## Interest Rate Caps and Floors

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…

## Creating a Binomial Interest Rate Tree

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.

## Valuing Derivatives

Valuing derivatives – forwards, futures, FRAs, and swaps – is much the same as pricing them. The value of a derivative is the amount that one party would have to pay the other if the derivative were to expire today; it depends on the price of the underlying today compared to the price at the inception of the derivative.

## Pricing Derivatives

Pricing derivatives – forwards, futures, FRAs, and swaps – is generally not difficult, and the principle that underlies all pricing relationships is quite easy: arbitrage.