  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.
