Better late than never: The case of the rollover option

In addition to death and maturity guarantees on the mutual funds they sell, some insurance companies make it possible for the investor to extend the guarantees for a fixed number of years. In this paper, we consider the case when the option is of the European type; that is, the investor, at maturity, can either close out the contract or extend it for the stated fixed term. When extended, the guarantee is on the value of the fund at the original maturity date. The fund is assumed to be fully invested in common stock. lue of the option, called the rollover option, is derived in a risk-neutral environment. Mortality is also taken into account when calculating the value of the option. The formulae obtained are of the Black-Scholes type.