Equity-linked endowment policies with or without embedded surrender options

This article proposes a model to compute the fair premium for equity-linked contracts that include a surrender option. In an equity linked policy, the premium can either be paid at inception in a unique solution or “divided ” in smaller amounts typically paid at the beginning of each year. The policy payoff is strictly dependent on the performance of the reference fund. The policy-holder bears the risk of a negative performance of the reference fund, hence, insurance companies generally include into the contract a minimum guarantee providing a lower bound for the policy payoff that protects the insured investment. In the case of equity-linked contracts that include a surrender option, the policy-holder can exercise the option and receive the pre-specified surrender value expiring the contract immediately while, if he decides to hold the contract until the maturity date, he receives the stated benefits. The problem of computing the premium values for equity-linked policies with minimum guarantee has been tackled for the first time by Brennan and Schwartz in 1976. They pointed out that the policy payoff may be decomposed in two parts, one of which representing the payoff of a European call or put option and the other representing the value of the minimum guarantee or the value of the reference fund, so that they could adapt th