Valuation of Ratchet Equity-Indexed Annuities

Abstract

Ratchet equity-indexed annuities (EIAs) are the most popular EIAs. Most ratchet EIAs credit returns to policyholders annually based on the higher of the calculated index return during the year and the minimum guaranteed rate. This annual reset feature allows the credited return to be locked in and thus the value of the policy will never decrease. In this paper we derive the pricing formulas under the standard Black-Scholes framework for more ratchet EIA products than the literature. Via these pricing formulas and numerical demonstration, we are able to analyze the impacts of various contract features on the policy value. These results can be helpful guides to ratchet EIA design and valuation.