Valuation of long-term liabilities under solvency II – Extrapolation methods for the European interest rate market

For the upcoming Solvency II framework, the Smith-Wilson method constitutes the extrapolation technique for valuing long-term liabilities. Next to the Smith-Wilson method this paper considersthree other methods to extrapolate the long end of the Euro yield curve. Two of them belong to the popular Nelson-Siegel family and the other represents the equilibrium class of interest rate termstructure models. Evaluated by the models’ ability to reduce volatility for long-term yields and by their extrapolation errors, the Smith-Wilson method performs best. Unlike the other methods, it does not require parameter estimations. Only since mid-2011, when yields have shifted to unprecedentedly low levels, the Smith-Wilson method deteriorates and the Nelson-Siegel model exhibits substantiallybetter tted extrapolations.