Evaluating the solvency capital requirement of interest rate risk in Solvency II

In this paper, the question addressed is as to whether the Solvency II standard formula provides a good measure for the interest rate risk an insurer is facing. In order to answer this question, several simplifications of the standard formula are considered and an alternative method is proposed to simulate the future term structures of interest rates to provide a better insight in the interest rate risk of an insurer. This method makes use of cubic Hermite spline interpolation up to the last liquid point of the term structure and the Smith-Wilson extrapolation for interest rates beyond this point. The method is able to produce a wide range of term structure shapes, and provides a good fit with the yield curve and one year stress scenarios from the standard formula. By means of a case study, three illustrative liability portfolios are considered and the Solvency Capital Requirement (SCR) of interest rate risk is calculated based on the standard formula and the alternative method. From the case study it is concluded that the simplifications in the standard formula can lead to serious drawbacks in the management of interest rate risk, especially with respect of liabilities with high expected premium income, long term guarantees and/or a material risk margin.