Call and put options embedded in bonds are of American-style, and cannot be priced in a closed-form. In this paper, we formulate the problem of pricing these options in a stochastic Dynamic Programming (DP) framework. We let the short-term risk-free interest rate move as in Vasicek (1977). We approximate the bond value by a piecewise linear interpolation at each step of the DP procedure, and solve the DP equation in closed-form. Then, we use the DP formulation to establish the basic properties of bonds, price their embedded call and put options, and determine their optimal exercise strategies. Numerical investigations show stability, consistency, and efficiency.
Published February 2002 , 21 pages