The Valuation of American-Style Options on Bonds

Abstract

We value American options on bonds using the Geske-Johnsan (1992). The method requires the valuation of European options with two and three possible exercise dates.It is shown that a risk-neutral valuation relationship along the lines of Black-Scholes (1973) model holds for option exercisable on multiple date, even under stochastic interest rates, when the price of the underlying asset is longormally distributed. The proposed computational procdure uses the maxmized value of these options, where the maximization is over all prossible exercise dates. The value of American option is then computed by Richardson extrapolation. The volatility of the underlying default-free bond is modelled using a two-factor model, with a short-term and a long-term interest rate factor, where the short-term interest rate is mean-reverting. Simulations show that penny accuracy is achieved with this computationally efficient method.