Ekstrapolering af rentekurven med henblik på værdiansættelse af langsigtede forpligtelser

Nanna Maria Wieslander

Student thesis: Master thesis


Abstract: The upcoming Solvency II for the insurance and pension sector will change the current valuation of long-term liabilities, which is due to non-existing or illiquid long-term market interest rates. EIOPA has in this connection suggested to use an extrapolating technique developed by Smith and Wilson. The main purpose of this paper is to evaluate alternative extrapolating methods to the Smith-Wilson. Next to the Smith-Wilson will this thesis consider two term structure of interest rate from the Nelson-Siegel family namely the Nelson-Siegel model and the Svensson model. Besides these two this thesis will also consider the Vasicek interest rate model, which can be classified as an equilibrium model and the Hull-White model, a no-arbitrage model. These five term structure of interest rate models will be used to evaluate the fair value of an interest rate guarantee in order to determine the extrapolating techniques influence on the capital requirement. Evaluated by the models’ ability to reduce volatility in the extrapolated interest rates, I find Smith-Wilson to perform best, and the Nelson-Siegel models to perform worst. In contrast the Nelson-Siegel produces the extrapolated yield curve with the lowest spread to the observed swap rates, where Hull-White underperforms in that matter. The main argument for using the Vasicek model is its ability to incorporate the price of markets risk in its long-run equilibrium rate and also correct the extrapolated interest rate for the relative convexity effect. Even though the Smith-Wilson model produces the most stabil interest rate curve, I find overall the method, is the least attractive model due to the many disadvantages of the method. I find the valuation of long term-liabilities to be very sensitive to the different extrapolations. The Hull-White and Smith- Wilson will result in small valuation and in combination with the big spread to the market rates, these methods will result in a capital requirement which may not be appropriate regarding the true interest rate risk. Besides that the different extrapolations can result in different capital requirement, I find that other initiatives both on the asset side and the liability side can have an influence on the capital requirement. The biggest influence will be totally removing the interest rate guarantees from the firms product portfolio, which as a bonus will reduce the firms interest rate risk.

EducationsMSc in Mathematics , (Graduate Programme) Final Thesis
Publication date2015
Number of pages88