Stochastic Interest Rates: A Generalization of the Geske-Johnson Technique

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.