A NOTE ON PRICING OF INTEREST RATE OPTIONS

Abstract

Interest rate options are options on underlying assets such as bonds the value of which depends on interest rates. For these options it is generally not possible to use Black and Scholes option pricing model for their valuation. The reason for this is that three critical assumptions of Black-Scholes stock option model do not fit in the case of bond options. For interest rate options the practice is to assume an evolution process for the interest rates instead of the prices. The problem with this procedure is in deciding which interest rate evolution to assume. For example, if we are valuing an option on a three-year bond should we look at the evolution of three-year rates. But a three year bond becomes a 2½ year bond in six months, so we need to know how the 2½ year rate is evolving, and so on. Thus, unless we assume the expectations hypothesis of the term structure (in which case knowing the evolution of short- term rates is enough to determine the evolution of the entire term structure), we will have to model the evolution of the entire term structure itself.