A dynamic programming approach for pricing options embedded in bonds

We propose a dynamic programming (DP) approach for pricing options embedded in bonds, the focus being on call and put options with advance notice. An efficient procedure is developed 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. We provide numerical illustrations, for the Vasicek and CIR models, comparing our DP method with finite-difference methods. Our procedure compares quite favorably in terms of both efficiency and accuracy. An important advantage of the our DP approach is that it can be applied to more general models calibrated to capture the term structure of interest rates (e.g., the generalized Vasicek model).