What does a term structure model imply about very long-term interest rates?

Anne G. Balter*, Antoon Pelsser, Peter C. Schotman

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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.
Original languageEnglish
Pages (from-to)202-219
Number of pages18
JournalJournal of Empirical Finance
Publication statusPublished - Jun 2021

JEL classifications

  • g12 - "Asset Pricing; Trading volume; Bond Interest Rates"
  • e43 - Interest Rates: Determination, Term Structure, and Effects
  • c58 - Financial Econometrics


  • Term structure models
  • Parameter uncertainty
  • Extrapolation
  • Insurance supervision

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