Equilibrium Prices of Guarantees under Equity-Linked Contracts

TLDR

Equity‑linked contracts have become a prominent life‑insurance product, raising new pricing and reserving challenges for minimum death and maturity benefit guarantees that remain unsolved by traditional actuarial methods. The authors develop a theoretical model to price these guarantees and to prescribe an optimal investment policy for insurers. They derive equilibrium prices for death‑benefit and maturity‑benefit guarantees using recent results from financial‑theory equilibrium analysis. The resulting investment policy is optimal, providing insurers with a hedge against the investment risk inherent in issuing the guarantees.

Abstract

The prices of death benefit guarantees and maturity benefit guarantees under equity-linked contracts are obtained under conditions of market equilibrium using some recent results from the theory of finance. The model provides a theoretical basis for pricing these guarantees and some numerical results are given. In addition the model can be used to prescribe an optimal investment policy for the insurer selling these contracts. The investment policy is optimal in that it provides the insurer with a hedge against the investment risk associated with the granting of these guarantees. One of the most interesting life insurance products to have emerged in recent years has been the equity-linked contract. This product has given rise to a host of new problems some of which are not solvable by traditional actuarial methods. Perhaps the most intriguing of these problems concerns the pricing of minimum death benefit and maturity benefit guarantees and the establishing of proper reserves for these guarantees. Although there have been a number of papers in both the British and North American actuarial literature dealing with this subject the consensus seems to be that no completely satisfactory solution has yet been found. In the discussion on R. J. Squires' paper [1] presented to the Institute of Actuaries (London, England) in 1973 N. D. Freethy prophesied that the subject of maturity guarantees would continue to occupy the attention of the Institute for some time to come. S. Benjamin, in the same discussion, submitted that the problem of valuing maturity guarantees still was unsolved in general