An Analysis of the Ultra Long-Term Yields

The discounting of very long-term cash-flows is crucial for the valuation oflong-term investment projects. In this paper, we analyze the market prices ofUS government bonds with very long-term time-to-maturity, and emphasizesome statistical specificities of very long-term zero-coupon rates, that stan-dard Gaussian affine term structure models do not account for. In addition,we describe and estimate three Gaussian Nelson-Siegel affine term structuremodels, and highlight the model characteristics, which are necessary to matchthe dynamics of very long-term interest rates.