An Analysis of the Ultra Long-Term Yields

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