This article analyzes the numerical impact of different surplus distribution mechanisms on the risk exposure of a life insurance company selling with profit life insurance policies with a cliquet-style interest rate guarantee. Three representative companies are considered, each using a different type of surplus distribution: a mechanism, where the guaranteed interest rate also applies to surplus that has been credited in the past, a slightly less restrictive type in which a guaranteed rate of interest of O percent applies to past surplus, and a third mechanism that allows for the company to use former surplus in order to compensate for underperformance in "bad" years. Although at the outset all contracts offer the same guaranteed benefit at maturity, a distribution mechanism of the third type yields preferable results with respect to the considered risk measure. In particular, throughout the analysis, our representative company 3 faces ceteris paribus a significantly lower shortfall risk than the other two companies. Offering "strong" guarantees puts companies at a significant competitive disadvantage relative to insurers providing only the third type of surplus distribution mechanism.
Many with profit life insurance policies contain an interest rate guarantee. Often, this guarantee is given on a point-to-point basis; that is, the guarantee is only relevant at maturity of the contract. Other products (which are predominant, e.g., in the German market), however, offer a so-called cliquet-style (or year-by-year) guarantee. This means that the policyholders have an account to which every year a certain rate of return has to be credited. Typically, life insurance companies try to provide the guaranteed rate of interest plus some surplus on the policyholders' accounts.
There are different mechanisms defining how the annual surplus can be distributed to the insured. These mechanisms vary from country to country and sometimes from insurance company to insurance company. They can be divided into three different categories and combinations thereof:
1. Surplus may be credited to the policy reserves. In this case, it is guaranteed that this surplus will earn the guaranteed rate of interest in future years.
2. Surplus may be credited to a surplus account that is owned by the policyholder and may therefore not be reduced anymore. Thus, there is a guaranteed interest rate of O percent on money that is in this surplus account.
3. Surplus may be credited to a terminal bonus account. Money that has been credited to this account will only be distributed to the insured at maturity of their contracts but not (or only partially) if they cancel the contract. Furthermore, money may be taken from this account in order to pay interest rate guarantees (on the policy reserves) if in some year the return on assets is not sufficient to pay for these guarantees.
It is obvious that ceteris paribus, insurance companies using different surplus distribution mechanisms may have a significantly different risk profile. In the past, this may have been of minor importance since there was a comfortable margin between market interest rates and the guaranteed rates that were typically offered within life insurance policies. Recently, however, these margins have been significantly reduced, in particular for contracts that have been sold years ago with rather high guaranteed rates. This development illustrates that analyzing and managing an insurance company's financial risks should not only be restricted to management of the assets but also be concerned with reducing risks that result from the product design.
A number of papers have recently addressed interest rate guarantees, in particular Briys and de Varenne (1997), Grosen and Jorgensen (2000), Jensen, Jorgensen, and Grosen (2001), Hansen and Miltersen (2002), Grosen and Jorgensen (2002), Bacinello (2003), Miltersen and Persson (2003), Tanskanen and Lukkarinen (2003), Bauer et al. …