Updating the Ultimate Forward Rate over Time: A Possible Approach
|Author(s):|| doc. PhDr. Ing. Ing. Petr Jakubík Ph.D. Ph.D., |
Mgr. Diana Žigraiová ,
|ISSN / ISBN:|
|Published in:||Czech National Bank WP 03/2017|
|Keywords:||Extrapolation, Nelson-Siegel, Svensson, term structure of interest rates, Ultimate Forward Rate|
|JEL codes:||E43, G22, L51, M2|
|Grants:||The Impact of Low Interest Rate Environment on the European Insurance Sector|
|Abstract:||This study proposes a potential methodological approach to be used by regulators when updating the Ultimate Forward Rate (UFR) for the evaluation of insurers’ liabilities beyond the last liquid point observable in the market. Our approach is based on the optimisation of two contradictory aspects – stability and accuracy implied by economic fundamentals. We use U.S. Treasury term structure data over the period 1985-2015 to calibrate an algorithm that dynamically revises the UFR based on the distance between the value implied by the long-term growth of economic fundamentals in a given year and the regulatory value of the UFR valid in the prior year. We employ both the Nelson-Siegel and Svensson models to extrapolate yields over maturities of 21-30 years employing the selected value of the UFR and compare them with the observed yields using the mean square error statistic.
Furthermore, we optimise the parameters of the proposed UFR formula by minimising the defined loss function capturing both mentioned factors.