In the theme of this release we address the subject of prepayment modelling for interest only bonds. Since a current assessment of the distribution of Danish mortgage bonds shows that approximately 47% of the bonds have delayed amortization, this is a highly relevant topic. We introduce and analyse a variety of models and examine their performance. Through the whole chapter performance is measured by the difference between the estimated and actual prepayment rates.
Our first analysis shows that the DMBS model performs equally well for bonds with and without interest only periods. The same conclusion is reached if we extend the estimation sample with 55 interest only bonds and re-estimate the DMBS model. In the next analysis we include a dummy variable for delayed amortization in the prepayment function. We term the resulting model DMBSext. Comparing this model to the DMBS model, we conclude that the DMBSext model performs marginally better than the DMBS model for the interest only bonds, while the two models perform equally well for the remaining bonds. A similar conclusion is reached if we replace the maturity variable with a non-callable duration instead of extending the prepayment function with an extra variable.
Even though our findings indicate that it is possible to handle interest only bonds properly in our current DMBS set-up making only a few corrections, a preliminary analysis of including interest only bonds in the estimation of the M1 model shows that this leads to significant changes in the parameters. Most likely this is due to a different gain level in this model compared to DMBS which occurs because the gains used in the M1 model are calculated directly on the swap curve, i.e. with no spread added. Consequently we have chosen not to make any changes to the estimation samples or the prepayment functions in this release. Instead we will strive to come up with a more solid solution before the next release.
Another interesting topic of this release is found in the ‘Results’ chapter, where a section concerning the preliminary redemption model has been added. We have added this section because the single parameter of the recommended model (1Y) has changed significantly in connection with this quarters re-estimation. Therefore, we give a short introduction to the model set-up and try to assess the effects from the parameter change by visual inspection of the old (09Q4_1Y) and new (10Q1_1Y) models. Moreover, to better illustrate the effect on the estimated prepayment rates and option adjusted key figures we perform calculations for a single bond.