Academic journal article Journal of Risk and Insurance

Creating Customer Value in Participating Life Insurance

Academic journal article Journal of Risk and Insurance

Creating Customer Value in Participating Life Insurance

Article excerpt

ABSTRACT

The value of a life insurance contract may differ depending on whether it is looked at from the customer's point of view or that of the insurance company. We assume that the insurer is able to replicate the life insurance contract's cash flows via assets traded on the capital market and can hence apply risk-neutral valuation techniques. The policyholder, on the other hand, will take risk preferences and diversification opportunities into account when placing a value on that same contract. Customer value is represented by policyholder willingness to pay and depends on the contract parameters, that is, the guaranteed interest rate and the annual and terminal surplus participation rate. The aim of this article is to analyze and compare these two perspectives. In particular, we identify contract parameter combinations that--while keeping the contract value fixed for the insurer--maximize customer value. In addition, we derive explicit expressions for a selection of specific cases. Our results suggest that a customer segmentation in this sense, that is, based on the different ways customers evaluate life insurance contracts and embedded investment guarantees while ensuring fair values, is worthwhile for insurance companies as doing so can result in substantial increases in policyholder willingness to pay.

INTRODUCTION

Participating life insurance contracts generally feature a minimum interest rate guarantee, guaranteed participation in the annual return of the insurer's asset portfolio, and a terminal bonus payment. Appropriate pricing of these features is crucial to an insurance company's financial stability. Risk-neutral valuation and other premium principles based on the duplication of cash flow serve well to evaluate contracts from the insurer's perspective. However, these techniques are only relevant if insurance policies priced according to them actually meet customer demand. Since policyholders may not be able to duplicate their claims via capital market instruments for valuation purposes, they will often judge its value based on individual preferences. Thus, their willingness to pay--referred to here as "customer value" of the contract--may be quite different from the fair premium calculated by the insurance company. (1) The aim of this article is to combine the insurer's perspective with that of the policyholders, which is done by identifying those fair contract parameters (guaranteed interest rate and annual and terminal surplus participation rate) that, while keeping the fair value fixed for the insurer, maximize customer value.

We extend the previous literature by combining these two approaches; however, there is a fair amount of previous research on each individual perspective. From the insurer perspective, the relevant area is option pricing theory and its application to participating life insurance contracts. Among this literature, we find in particular Briys and de Varenne (1997), Grosen and Jorgensen (2002), Bacinello (2003), Ballotta, Haberman, and Wang (2006), and Gatzert (2008). All these studies use option pricing models to determine the price of life insurance policies, but their objectives are various. Briys and de Varenne, for example, use a contingent claims approach to derive prices for life insurance liabilities and to compare the durations of equity and liabilities in the insurance and banking industries, respectively. In contrast, Gatzert analyzes the influence of asset management and surplus distribution strategies on the fair value of participating life insurance contracts.

From the policyholder perspective, the literature on utility theory and, in particular, on the demand for insurance, is relevant. In our article, the demand for insurance is derived by assuming that the policyholders follow mean-variance preferences, a common assumption in the literature. For example, Berketi (1999) assumes mean-variance preferences in an analysis of insurers' risk management activity, finding that although such activity does reduce the risk of insolvency, it also reduces the expected payments to the policyholders when considering participating life insurance contracts. …

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