Working Papers

2018-09 | May 2019


Extrapolating Long-Maturity Bond Yields for Financial Risk Measurement

Author(s): Jens H. E. Christensen, Jose A. Lopez, and Paul L. Mussche

Insurance companies and pension funds have liabilities far into the future and typically well beyond the longest maturity bonds trading in fixed-income markets. Such long-lived liabilities still need to be discounted, and yield curve extrapolations based on the information in observed yields can be used. We use dynamic Nelson-Siegel (DNS) yield curve models for extrapolating risk-free yield curves for Switzerland, Canada, France, and the U.S. We find slight biases in extrapolated long bond yields of a few basis points. In addition, the DNS model allows the generation of useful financial risk metrics, such as ranges of possible yield outcomes over projection horizons commonly used for stress-testing purposes. Therefore, we recommend using DNS models as a simple tool for generating extrapolated yields for long-term interest rate risk management.

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Article Citation

Christensen, Jens H. E, Jose A. Lopez, and Paul L. Mussche. 2019. "Extrapolating Long-Maturity Bond Yields for Financial Risk Measurement," Federal Reserve Bank of San Francisco Working Paper 2018-09. Available at