Variable Annuities: Market Incompleteness and Policyholder Behavior

Abstract

Variable annuities (VAs) are popular personal savings and investment vehicles with long-term guarantees. They include various exercise-dependent features, and the pricing, valuation and hedging of the guarantees depend critically on the investors' decision making. I study whether the optimal exercise behavior of a VA investor is affected by market incompleteness, which arises since the VA generates payout profiles that intersect financial risk and idiosyncratic mortality risk and can thus not be (fully) replicated with traditional financial and insurance products. Implementing a generic VA policy with a withdrawal guarantee (GMWB) that reflects typical US product characteristics, I find that the optimal withdrawal behavior derived from a lifecycle utility model is closely approximated by the corresponding (after-tax) value maximization strategy. That is, from the perspective of the investor, the market around VA policies is sufficiently complete to justify the common approach of assessing optimal VA policyholder behavior with a risk-neutral valuation method.