International comparison of interest rate guarantees in life insurance

Interest rate guarantees seem to be included in life insurance and pension products in most countries. The exact implementations of these guarantees vary from country to country and are often linked to different distribution of investment surplus mechanisms. In this paper we first attempt to model practice in Germany, the UK, Norway, and Denmark by constructing contracts intended to capture practice in each country. All these contracts include rather sophisticated investment surplus distribution mechanisms, although they exhibit subtle differences. Common for all countries except the UK is the existence of a bonus account, an account where investment surplus is set aside in years with good investment returns to be used to cover the annual guarantee in years when the investment return is lower than the guarantee. These contracts are then compared with universal life insurance, a popular life product in the US market, which also include investment surplus distribution, but no bonus account. The contract parameters are calibrated for each contract so that all contracts have ’fair’ prices, i.e., the theoretical market price of the contract equals the theoretical market price of all benefits at the inception of the contract.

For simplicity mortality factors are ignored and the benefit is assumed to be paid out as a lump sum in 30 years. By comparing the probability distribution of the future benefit for the contracts with the market index, our preliminary results indicate that for low levels of the financial risk premium the Danish, German and UK contracts behave just like the market index, i.e., the guaranteed rate and the investment surplus distribution have virtually no impact on the probability distribution of the benefit. The Norwegian benefit has a lower standard deviation than the mentioned contracts, whereas the benefit of the universal life contract offers the lowest standard deviation. Our preliminary numerical analysis therefore indicates that the relative simple US contract outperforms the more complex European counterparts if the objective is to provide the insurance customer a future benefit with low risk.