Modeling Life Insurance Guarantees

Abstract: Insurance contracts with guarantees have been issued by insurance companies for a long time. For example, in the 1970s and the 1980s, when the interest rate in the UK was as high as 15-20%, these contracts were issued with guaranteed rates of as high as 10%, thinking the interest rate levels would stay around the same. However, the interest rate decreased and, as of today, interest rate levels are around and even below zero, which has led to insolvency problems for many insurance companies. Currently, with the low interest rate environment, guaranteed rates are mostly oered at a zero guaranteed rate, but with a rising interest level in sight, these rates are likely to come back into the market because of competitiveness reasons. To avoid such insolvency issues again, every risk in the contracts has to be identied, and we have focused on the risk in the interest rate process. This thesis highlights the risk involving the parameter estimation of the interest rate process. It also demonstrates the large price uctuations that occur from dierent types of yield curves and how it diers for dierent maturities. In these contracts, put options are embedded and a Fourier-Gauss-Laguerre model is used to price the options and we include both stochastic volatility and stochastic interest rate. Previous studies have shown that the parameter risk involving the mortality estimation cannot be ignored and the results in this thesis concludes that the uncertainty involved in the parameter estimation of the interest rate process canont be ignored either.