Valuation of Ratchet Equity-Indexed Annuities

Ratchet EIAs are the most popular equity-indexed annuities (EIAs) because returns are credited periodically with a guaranteed minimum and the account value never decreases once the return is credited. Pricing ratchet EIAs, however, is challenging. This paper derives pricing formulas that cover more contract features of ratchet EIAs than any in the literature. We obtain closed-form solutions in the Black-Scholes framework for both compound and simple versions of annual-reset ratchet products that may have a return cap and employ two types of geometric return averaging. Our numerical results demonstrate the impacts of individual contract features on contract value and the interactions among these features.