We propose a multifactor model in which the spot rate, LIBOR, follows a lognormal process, with a stochastic conditional mean, under the risk-neutral measure. In addition to the spot rate factor, the second factor is related to the premium of the first futures rate over the spot LIBOR. Similarly, the third factor is related to the premium of the second futures rate over the first futures rate. We calibrate the model to the initial term structure of futures rates and to the implied volatilities of interest rate caplets. We then apply the model to price interest rate derivatives such as European- and Bermudan-style swaptions, and yieldspread options. The model can be employed to price more complex interest rate derivatives such as path-dependent derivatives or multi-currency-dependent derivatives because of its Markovian property.

ABSTRACT The Geske–Johnson approach provides an efficient and intuitively appealing technique for the valuation and hedging of American‐style contingent claims. Here, we generalize their approach to a stochastic interest rate economy. The method is implemented using options exercisable on one of a finite number of dates. We illustrate how the value of an American‐style option increases with interest rate volatility. The magnitude of this effect depends on the extent to which the option is in the money, the volatilities of the underlying asset and the interest rates, as well as the correlation between them.