Analysis of Embedded Options in Individual Pension Schemes in Germany

Newly introduced Government-subsidized pension products in Germany are requiredto contain a promise by the seller to provide a “money-back guarantee” atthe end of the term. The client is also given the right to stop paying premiums atany time (paid-up option). In this case, the amount of all premiums paid must alsobe guaranteed by the seller at maturity, no matter when the client stopped payingthe premiums. Previous analyses of guarantees in such government-subsidized pensionproducts have ignored this additional option. Within a generalizedBlack/Scholes framework, we analyze the value of the paid-up option for differentproducts, market scenarios, and client behavior. Our results indicate that the paidupoption significantly increases the value of the money-back guarantee. Furthermore,we find that reducing volatility by shifting the client’s assets from stocks tobonds as maturity approaches is a suitable means of reducing the risk resultingfrom the “pure” money-back guarantee but much less effective in reducing the riskresulting from the paid-up option.