Analytical valuation of periodical premiums for equity-linked policies with minimum guarantee

Abstract

We consider the problem of computing fair periodical premiums of equity-linked policies with a minimum guarantee. The policy payoff at maturity may be decomposed into two components: a fixed part representing the guaranteed payment and a European call option written on the equity reference fund. The deemed periodical contributions into the reference fund may be considered as negative dividends paid by the reference fund and the fair value of the policy may be derived through a closed-form formula by mimicking the valuation of an option written on an underlying security that pays fixed dividends. Numerical results show that the proposed model computes accurate values.