Bayesian Parameter Uncertainty in Long-Term Interest Rate Extrapolation

Summary

This document examines how uncertainty in interest-rate model parameters affects projections far beyond the maturities of liquid instruments. It focuses on pricing very long-dated liabilities and quantifying rate uncertainty across horizons extending to a century. The proposed framework uses the mean-reverting affine Vasicek model and represents uncertainty about its parameters with Bayesian distributions.

The model’s cross-sectional and time-series parameters are estimated through a restricted bivariate VAR(1) specification. In the empirical example, long-horizon projections have very low confidence. The stated explanation is that parameter uncertainty compounds when mean reversion behaves close to a unit root. The excerpt does not provide the dataset, posterior details, numerical confidence intervals, or comparisons with alternative models, so it conveys the method and headline finding without enough information to assess calibration or robustness.

Key ideas

• Bayesian distributions are used to represent uncertainty in the parameters of a Vasicek interest-rate model.
• A restricted bivariate VAR(1) supplies cross-sectional and time-series parameter estimates.
• The analysis targets rate uncertainty at maturities where liquid market instruments are scarce.
• Long-horizon confidence is reported to be very low when mean reversion is near a unit root.

Tags

# Extrapolating the term structure of interest rates with parameter uncertainty


# Extrapolating the term structure of interest rates with parameter uncertainty









Pricing extremely long-dated liabilities market consistently deals with the decline in liquidity of financial instruments on long maturities. The aim is to quantify the uncertainty of rates up to maturities of a century. We assume that the interest rates follow the affine mean-reverting Vasicek model. We model parameter uncertainty by Bayesian distributions over the parameters. The cross-sectional and time series parameters are obtained via the restricted bivariate VAR(1) model. The empirical example shows extremely low confidence in long term extrapolations due to the accumulated effect of the mean-reversion`s behaviour close to the unit root.

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