As explained in Section II, there are various models that have been developed to value a bond with embedded options. The one that we will use to illustrate the issues and assumptions associated with valuing bonds with embedded options is the binomial model. The interest rates that are used in the valuation process are obtained from a binomial interest rate tree. We’ll explain the general characteristics of this tree first. Then we see how to value a bond using the binomial interest rate tree. We will then see how to construct this tree from an on-the-run yield curve. Basically, the derivation of a binomial interest rate tree is the same in principle as deriving the spot rates using the bootstrapping method described in Chapter 6—that is, there is no arbitrage.