Numerical pricing of American put options on zero-coupon bonds

In this paper we study finite volume methods and finite element methods for American put options on zero-coupon bonds. Stability and convergence are established for both methods. Numerical examples show that our methods converge and provide very accurate options prices and early exercise interest rates for all parameter combinations. We also present an error indicator by which one can examine the accuracy of the approximate option prices and early exercise interest rates actually obtained by a numerical method and determine how fine a grid should be used to achieve the desired accuracy.