Pricing Path-Dependent Equity-Indexed Annuities

Sales of equity-indexed annuities (EIAs) have rapidly increased, but the growth rates in sales have recently shown signs of slowing down because the current volatile equity market increases the costs of guarantees in EIAs. New EIAs need to be designed that are similar to existing EIAs but have a cheaper guarantee and a higher participation rate. This paper proposes three types of EIAs with higher participation rates: up-and-in barrier EIA, aulual reset EIA with up-and-in barriers, and partial-time lookbackEIA. It also presents a probability distribution and the method of Esscher transforms, with which explicit pricing formulas for these EIAs are derived.