The valuation of American options on bonds

Abstract

We value American options on bonds using a generalization of the Geske±Johnson (Geske, R., Johnson, H., 1984. Journal of Finance 39, 1151±1542) (GJ) technique. The method requires the valuation of European options, and options with multiple exercise dates. It is shown that a risk-neutral valuation relationship (RNVR) along the lines of Black±Scholes (Black, F., Scholes, M., 1973. Journal of Political Economy 81, 637±659) model holds for options exercisable on multiple dates, even under stochastic interest rates, when the price of the underlying asset is lognormally distributed. The proposed computational procedure uses the maximized value of these options, where the maximization is over all possible exercise dates. The value of the American option is then computed by Richardson extrapolation. The volatility of the underlying defaultfree bond is modeled using a two-factor model, with a short-term and a long-term interest rate factor. We report the results of simulations of American option values using 0378-4266/97/$17.00 Ó 1997 Elsevier Science B.V. All rights reserved. PII S 0 3 7 8 -4 2 6 6 ( 9 7 ) 0 0 0 3 4 -4 our method and show how they vary with the key parameter inputs, such as the maturity of the bond, its volatility, and the option strike price. Ó 1997 Elsevier Science B.V. All rights reserved.JEL classi®cation: G11

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