We propose a Dynamic Programming (DP) approach combined with approximation for pricing options embedded in bonds, the focus being on call and put options with advance notice. An efficient approximation method is developed in detail for the cases where the interest rate process follows the Vasicek, Cox-Ingersoll-Ross (CIR), or generalized Vasicek models. Our DP methodology uses the exact joint distribution of the interest rate and integrated interest rate at a future date, conditional on the current value of the interest rate,for these models. We provide numerical illustrations, for the Vasicek and CIR models, comparing DP with finite difference methods. The results indicate that DP compares quite favorably in terms of both efficiency and accuracy. An important advantage of the DP approach is that it can be applied to more general models calibrated to capture the term structure of interest rates, such as the generalized Vacicek model, for example, where the only available methods are the (rather inaccurate)trinomial trees.
Published April 2004 , 24 pages