We estimate a term structure model on interest rate data with maturities up to 20 years and then extrapolate the yield curve to maturities up to 100 years. Such model based extrapolation is motivated by limited liquidity of very long-dated fixed income instruments. The extrapolated curves are always above observed swap rates at maturities in the 20-50 years range. The extrapolationappears mainly driven by the near unit root of the level factor underthe risk neutral measure. In a no-arbitrage term structure model this leads to a strong convexity effect, which implies that extrapolated yield curves are generally upward sloping for maturities longer than 20 years before eventually bending steeply downwards. Our estimates use Bayesian methods. The prior is informative on mean reversion parameters and imposes a zero lower bound on the unconditional means.