Analysis of embedded options in individual pension schemes in Germany

Abstract

Newly introduced government-subsidized pension products in Germany are required to contain a promise by the seller to provide a "money-back guarantee" at the end of the term. The client is also given the right to stop paying premiums at any time (paid-up option). In this case, the amount of all premiums paid must also be guaranteed by the seller at maturity, no matter when the client stopped paying the premiums. Previous analyses of guarantees in such government-subsidized pension products have ignored this additional option. Within a generalized Black/Scholes framework, we analyze the value of the paid-up option for different products, market scenarios, and client behavior. Our results indicate that the paid-up option significantly increases the value of the money-back guarantee. Furthermore, we find that reducing volatility by shifting the client's assets from stocks to bonds as maturity approaches is a suitable means of reducing the risk arising from the "pure" money-back guarantee but much less effective in reducing the risk arising from the paid-up option. © Springer Science + Business Media, LLC 2006.