Working Papers

2018-09 | May 2019


Extrapolating Long-Maturity Bond Yields for Financial Risk Measurement


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. 2018. "Extrapolating Long-Maturity Bond Yields for Financial Risk Measurement," Federal Reserve Bank of San Francisco Working Paper 2018-09. Available at