We extrapolate interest rate yield curves for the purpose of discounting very long-dated pension liabilities and insurance contracts. The extrapolation uses a no-arbitrage term structure model estimated on liquid euro swap instruments with maturities between 5 and 20 years. The extrapolation...

We address two empirical issues related to the long end of the yield curve based on euro swap rates. First, for maturities longer than 20 years we find evidence for an `excess' downward slope that cannot be explained by convexity. Second, volatility at the very long end of the yield curve is...

The first three factors resulting from a principal components analysis of term structure data are in the literature typically interpreted as driving the level, slope and curvature of the term structure. Using slight generalisations of theorems from total positivity, we present sufficient...