Academic journal article Journal of Risk and Insurance

Assessing the Risk Potential of Premium Payment Options in Participating Life Insurance Contracts

Academic journal article Journal of Risk and Insurance

Assessing the Risk Potential of Premium Payment Options in Participating Life Insurance Contracts

Article excerpt

ABSTRACT

Most life insurance contracts embed the right to stop premium payments during the term of the contract (paid-up option). Thereby, the contract is not terminated but continues with reduced benefits and often provides the right to resume premium payments later, thus increasing the previously reduced benefits (resumption option). In our analysis, we start with a basic contract with two standard options, namely, an interest rate guarantee and annual surplus participation. Next, in addition to the features of the basic contract, a paid-up and resumption option is included in the framework. The valuation process is not based on assumptions about a particular policyholders' exercise strategy but instead assesses the risk potential from the insurer's viewpoint by providing an upper bound for any possible exercise behavior. This approach provides important information to the insurer about the potential hazard of offering the paid-up and resumption option. Further, the approach allows an analysis of the impact of guaranteed interest rate, annual surplus participation, and investment volatility on the values of the premium payment options.

INTRODUCTION

In most life insurance contracts, the policyholder has the right to stop premium payments at any time during the term of the contract (paid-up option). This feature is contained, for example, in level premium whole life insurance contracts in the U.S. market or endowment policies in the European market. The paid-up option differs from a surrender option in that the contract is not terminated but continues with reduced benefits. Additionally, the contract can provide the right to resume premium payments later and thus to increase the previously reduced benefits (resumption option). Flexible premium payments are offered in universal life insurance contracts sold in the United States and can also be found in European insurance markets. The aim of this article is to study the risk potential of premium payment options within participating life insurance contracts that include two standard options--an interest rate guarantee and a guaranteed annual surplus participation.

Life insurance contracts often embed various types of implicit options. Concern over embedded options was intensified in 2000 when the British life insurer Equitable Life had to stop taking new business due to an improper hedging of provided options. The growing interest in the field of valuation and risk management of embedded options in life insurance contracts is also demonstrated by the increasing number of scientific contributions to this field: Briys and de Varenne (1994) treat the bonus option and the insolvency option in a contingent claim framework. Hansen and Miltersen (2002) and Tanskanen and Lukkarinen (2003) conduct a fair pricing of contracts with a guaranteed interest rate and different annual surplus participation schemes. Ballotta, Haberman, and Wang (2006) consider guarantees in participating life insurance contracts commonly offered in the United Kingdom while studying the effect of the default option on fair pricing. Grosen and Jorgensen (2000) add to the analysis of guaranteed interest rate and surplus participation by also taking the surrender option into account. In Grosen and Jorgensen (2002), the insurer's insolvency option and regulatory intervention are considered. Bacinello (2003a,b) analyzes the surrender option in an Italian life insurance contract with single and periodic premiums, including mortality risk; Bacinello (2005) performs this analysis for unit-linked contracts; Albizzati and Geman (1994) analyze the value of a surrender option in French life insurance contracts while establishing the concept of exercise probabilities.

Among the literature on paid-up options, Herr and Kreer (1999) model a life insurance contract with surrender and paid-up options with underlying stochastic interest rates; however, the surplus participation rate of the contract is assumed to be deterministic. …

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