What does a term structure model imply about very long-term interest rates?
基于欧元互换利率，研究发现20年以上期限的收益率曲线存在无法由凸性解释的过度下行斜率，且超长期波动率高于无套利模型预测，表明监管曲线采用的均值回归假设过强。
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 larger than predicted by no-arbitrage models. We construct a model-based arbitrage-free extrapolation of the yield-curve and compare it to the regulatory discount curve. Because of near-zero mean reversion, there is no convergence towards an ‘ultimate forward rate’ and convexity effects cause the arbitrage-free extrapolations to have slightly downward sloping curves. The low level of mean-reversion also implies that the volatility of long-term rates does not decline relative to the 20-year volatility. Therefore, we conclude that the mean-reversion and resulting smoothing adopted by the regulatory curve is much too strong.