One can value a bond by discounting each cash flows at its own zero-coupon(“spot”) rate. This procedure is equivalent to discounting the cash flows at a series of one-period forward rates. When a bond has one or more embedded options, however, its cash flow is uncertain. If a callable bond is called by the issuer, its cash flow will be truncated.
To value such a bond, one must consider the volatility of interest rates, as their volatility will affect the possibility of the call option being exercised. One can do so by constructing a binomial interest rate tree that models the random evolution of future interest rates. The volatility-dependent one-period forward rates produced by this tree can be used to discount the cash flows of any bond in order to arrive at bond value.
