Question ID: 262
Regulation Reference: Risk-Free Interest Rate - Extrapolation
Article: 46
Status: Final
Date of submission: 30 Apr 2015
Question
Starting from the EUR zc spot rates without VA it is possible to derive the UFR @ 60yr that is 4.147% and so not in line with the target (4.19%-4.21%)
In addition the extrapolation lead to an unsmoothed path for the forward rates in the long term
Is it possible to have a confirmation that the yield curve provided @ End of February for the extrapolation are in line with the technical document regarding the risk free interes rate term structure (EIOPA-VoS-15/035)
EIOPA answer
According to the Annex of Subsection 6.A of the Technical Documentation, the criteria for the convergence speed to the ultimate forward rate is based on forward intensities. Hence, for the euro the forward intensity at the maturity of 60 years should be within a ±1 bps corridor around the ultimate forward intensity that corresponds to the ultimate forward rate of 4,2%. That ultimate forward intensity is log(1+ 4,2%) = 0.0411419433.
For the end 2014 euro term structure without VA, the forward intensity at the maturity of 60 years is 0.0410419447, being 0.9999987 bps below the ultimate forward intensity (rates rounded to 11 decimals).
The published spot rates are rounded to three decimal digits, and thus contain little rounding errors. When calculating a forward rates curve from those spot rates the rounding error may result in an unsmoothed path.