Updating the long term rate in time : a possible approach

This study proposes the potential methodological approach to be utilized by regulators when setting up a Long-Term Rate (LTR) for the evaluation of insurers' liabilities beyond the last liquid point observable in the market. Our approach is based on the optimization 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 LTR based on the distance between the value implied by long-term growth of economic fundamentals in a given year and the regulatory value of LTR valid in a year prior. We employ both Nelson-Siegel and Svensson models to extrapolate yields over maturities of 21-30 years employing the selected value of the LTR and compare them to the observed yields using mean square error statistic. Furthermore, we optimise the parameter of the proposed LTR formula by minimising the defined loss function capturing both mentioned factors.