In this paper we present a nonlinear dynamic programming algorithm for the computation of forward rates within the maximum smoothness framework. The algorithm implements the forward rate positivity constraint for a one-parametric family of smoothness measures and it handles price spreads in the constraining data set. We investigate the outcome of the algorithm using the Swedish Bond market showing examples where the absence of the positive constraint leads to negative interest rates. Furthermore we investigate the predictive accuracy of the algorithm as we move along the family of smoothness measures. Among other things we observe that the inclusion of spreads not only improves the smoothness of forward curves but also significantly reduces the predictive error.