Interest Rate Derivatives: Bond Options, LIBOR and Swap Products

Abstract

The last chapter provides an exposition on the pricing models of several commonly traded interest rate derivatives, like the bond options, range notes, interest rate caps and swaptions. To facilitate the pricing of equity derivatives under stochastic interest rates, the technique of the forward measure is introduced. Under the forward measure, the bond price is used as the numeraire. In the pricing of the class of LIBOR derivative products, it is more effective to use the LIBORs as the underlying state variables in the pricing models. To each forward LIBOR process, the Lognormal LIBOR model assigns a forward measure defined with respect to the settlement date of the forward rate. Unlike the HJM approach which is based on the non-observable instantaneous forward rates, the Lognormal LIBOR models are based on the observable market interest rates. Similarly, the pricing of a swaption can be effectively performed under the Lognormal Swap Rate model, where an annuity (sum of bond prices) is used as the numeraire in the appropriate swap measure. Lastly, we consider the hedging and pricing of cross-currency interest rate swaps under an appropriate two-currency LIBOR model.