A Reserve Basis for Maturity Guarantees in Unit-Linked Life Assurance

Abstract

SynopsisThe main purpose of this paper is the determination of a basis for the calculation of “prudent” reserves for maturity guarantees in annual and single premium unit-linked life assurance policies, particularly those in which the investment medium is a broad range of U.K. equities. Estimates of the proceeds of equity investments required, and theories of stock market movements are discussed; it is concluded that yearly growth rates, including reinvested net income, may be represented approximately by the lognormal distribution and that yearly growth rates are not random, but negatively correlated. A mathematical model is then developed; the evaluation of the resulting distributions, which is a problem of some interest in its own right in the annual premium case, is discussed in the Appendix. There is a general discussion of certain valuation principles, and we give tables showing the level of reserves suggested by our methods. Various practical questions, such as the treatment of the assets and the effects on reserves of mortality, withdrawals, capital gains tax, policies with different terms and existing business, are also considered.