Solvency II: QIS5 for Norwegian life and pension insurance

Abstract

This thesis describes, analyzes and applies the Solvency II on life and pension insurance by using the standard formulas in the Quantitative Impact Study 5 (QIS5) to calculate the Solvency Capital Requirement (SCR). We specifically examine the consequences for the Norwegian occupational defined benefit schemes, primarily for the private sector. The standard formulas in QIS5 to some extent specify stress scenarios without giving explicit formulas as they should be exact for the application. We therefore outline exact formulas for the Norwegian occupational defined benefit schemes. We do this both for the net expected cash flows and for the stressed cash flow. The latter we do by giving a method for calculating the stressed survival and hazard rate functions. We also price the embedded interest rate guarantee using market consistent prices from the Norwegian swaption market. We discuss bonds specifically and redistribution of cash flows generally to improve the precision. Using the contract boundary principle in Solvency II we base our calculations on that all policies are converted to paid up policies. This may primarily be relevant for pension schemes in the private sector. However, formulas for active policies are also given. Additionally one would only need the future risk premiums for market risk. At the end we perform a full QIS5 consequence study for a Norwegian pension fund, using the outlined formulas and discussing all relevant steps. To support this part we have developed algorithms in Mathematica to perform the necessary calculations.