Extrapolating Long-Maturity Bond Yields for Financial Risk Measurement

Abstract

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 longlived 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.JEL Classification: E43, E47, G12, G22, G28

Much Ado About Nothing: A Study of Differential Pricing and Liquidity of Short and Long Term Bonds

“…They find that the largest distortions are for Scandinavian countries, while we study the very liquid German market. Nevertheless the argument on the LLP is similar to our discussion in Section 6.3., as well as to the results of Christensen et al (2018). They show that extrapolating long-maturity bond yields by means of a dynamic Nelson-Siegel method produces reasonable discount rates, which are in line with predictions of professional forecasters, therefore fit for regulatory valuation.…”

“…Beber et al (2009) disentangle the effects of liquidity and credit quality in 10 Eurozone countries. Similarly, Schwarz (2015) Christensen et al (2018). Greenwood and Vissing-Jorgensen (2018) study the effect of the pension and insurance industries (P&I) on the yield curve, more specifically the yield spread between 10 and 30-year bonds.…”

Comparative analysis of interest rate term structures in the Solvency II environment

“…Christensen et al (2019) analyze the adequacy of the SW method and although their work is based on observable data, it does not incorporate market expectations of the future yield curve dynamics as reflected in the traded prices of government bonds.…”

A Note of Caution on Shadow Rate Estimates

“…Using the longer‐horizon data is consistent with the principle that UMP is intended to influence the entire yield curve and, related, the composition of the Federal Reserve's asset holdings; that is, $0.6 trillion of Treasury securities and $1.8 trillion of mortgage‐backed securities have maturities beyond 10 years (out of total holdings of $2.5 and $1.8 trillion in those respective securities, within total assets of $4.5 trillion). Christensen and Rudebusch (), Krippner (), and Christensen, Lopez, and Mussche () are examples that use GSW data out to 30 years to estimate shadow/LB models.…”

“…Mainly for completeness, because closer model fits do not necessarily correspond to superior model information (e.g., in forecasting), I also report two summary statistics of the model fit to the data. Hence, following Christensen, Lopez, and Mussche (), I take the mean of the root‐mean‐squared errors (RMSEs) between the model and the data. “Fit 2” provides the closest like‐with‐like comparison, because it uses a common data set to assess the fit, that is, the 30‐year data set plus the 15‐, 20‐, 25‐year data that are not used in any of the shadow/LB model estimations .…”