OF INTEREST RATE GUARANTEES
IN LIFE INSURANCE
J. DAVID CUMMINS, KRISTIAN R. MILTERSEN, AND SVEIN-ARNE
Date: This version: January 31, 2004.
The authors thank Thorleif Borge, Andrew Cairns, Marc de Ceuster, Christian
Fotland, Stein Rytter and David Wilkie for valuable suggestions and discussions.
Parts of this article have previously been distributed as Miltersen and Persson
(2000). Earlier versions of this paper have been presented at the FIBE confer-
ence, NHH, Bergen, January 2003, Workshop on Financial Methods in Insurance,
Copenhagen, February 2003, 7th Congress on Insurance: Mathematics and Eco-
nomics, Lyon, June 2003, and 13th Annual International AFIR Colloquium 2003,
Maastricht, September 2003.
Abstract. Interest rate guarantees seem to be included in life
insurance and pension products in most countries. The exact im-
plementations of these guarantees vary from country to country
and are often linked to different distribution of investment sur-
plus mechanisms. In this paper we first attempt to model practice
in Germany, the UK, Norway, and Denmark by constructing con-
tracts intended to capture practice in each country. All these con-
tracts 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 invest-
ment 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 i