Minimum Rate of Return Guarantees: The Danish Case

Abstract

Hansen M, Miltersen KR. Minimum rate of return guarantees: the Danish case. Scand. Actuarial J. 2002; 4: 280 -318. We analyze minimum rate of return guarantees for life-insurance (investment) contracts and pension plans with a smooth surplus distribution mechanism. We speci cally model the smoothing mechanism used by most Danish life-insurance companies and pension funds. The annual distribution of bonus will be based on this smoothing mechanism after taking the minimum rate of return guarantee into account. In addition, based on the contribution method the customer will receive a nal (non-negative) undistributed surplus when the contract matures.We consider two different methods that the company can use to collect payment for issuing these minimum rate of return guarantee contracts: the direct method where the company gets a xed (percentage) fee of the customer's savings each year, e.g. 0.5% in Denmark, and the indirect method where the company gets a share of the distributed surplus. In both cases we analyze how to set the terms of the contract in order to have a fair contract between an individual customer and the company.Having analyzed the one-customer case, we turn to analyzing the case with two customers. We consider the consequences of pooling the undistributed surplus over two inhomogeneous customers. This implies setting up different mechanisms for distributing nal bonus (undistributed surplus) between the customers.

Guaranteed Investment Contracts: Distributed and Undistributed Excess Return

“…In many real-life life-insurance contracts the undistributed surplus mechanism pools the bonus accounts for a large group of customers, cf. Hansen and Miltersen (2000). The introduction of for three different levels of the minimum rate of return guarantee (g = 3%, g = 4%, g = 5%), two different volatilities (σ = 10%, σ = 20%), r = 10%, and T = 30. a pooled undistributed surplus mechanism opens up a number of new and interesting issues including game theoretical considerations for the individual customers of when to enter into these life-insurance contracts and when to surrender if the contract includes a surrender option.…”

“…More detailed descriptions for the situations in Denmark, Germany, Japan, and the Netherlands may be found in Hansen and Miltersen (2000), Mertens (1999), Matsuyama (1999), and Donselaar (1999), respectively. Historically, the initial level of these guarantees was low and, furthermore, fixed throughout the contract period.…”

A general asset–liability management model for the efficient simulation of portfolios of life insurance policies

“…Each model point corresponds to an individual policyholder account or to a pool of similar policyholder accounts which can be used to reduce the computational complexity, in particular in the case of very large insurance portfolios. We thus can also investigate effects which arise from the pooling of non-homogeneous policyholders like, e.g., in [17] where the pooling of two policyholders is considered.…”

A Two-Account Life Insurance Model for Scenario-Based Valuation Including Event Risk

“…An important goal of this paper is to formalize exactly how these bonus schemes work and interact. Other papers with a similar focus on bonus include [17][18][19][20], but again, none of them include event risk. In our treatment of unit-linked insurance, we have special focus on the implementation of guarantees and on the similarities and differences in relation to participating life insurance.…”