Arithmetic averaging equity-linked life insurance policies in Germany

This paper discusses two guaranteed arithmetic averaging equity-linked life-insurance products linked to the DAX30. According to German legislation, so called additional policy reserves might be required for such policies. As no pricing formulas are available, we use Monte Carlo simulation techniques to calculate the fair rate of index participation, as well as the reduced rate of index participation that results from subtracting the costs for hedging against the financial risk associated with additional policy reserves and negative market values of the policy from the first net premium. The risk emerging from additional policy reserves in case the insurance company does not use this hedging strategy is then analyzed in more detail by quantifying the corresponding distribution under different market scenarios.