Introduction to Option-Adjusted Spread Analysis: Revised and Expanded Third Edition of the OAS Classic by Tom Windas

CHAPTER 7

VOLATILITY AND THE BINOMIAL TREE

IN CHAPTER 5, a set of risk-free interest rates for a sequence of future semiannual periods were derived from the observed yields of benchmark bonds that make up the risk-free yield curve. Each implied forward rate quantifies the risk-free rate of return for the six-month period with which it is associated and forms the framework on which the binomial interest-rate tree is built. These implied forward rates, along with their associated periods, are shown in FIGURE 7.1.

If option models were simply to use implied forward rates to generate a price for an option’s underlying bond on a future date, their analyses would implicitly assume that interest rates implied by today’s market for future periods would ...