Abstract
Variable annuities, as a class of retirement income products, allow equity market exposure for a policyholder’s retirement fund with optional guarantees to limit the downside risk of the market. Management fees andguarantee insurance fees are charged respectively for the market exposure and for the protection from the downside risk. We investigate the pricing of variable annuity guarantees under optimal withdrawal strategies when management fees are present. We consider from both policyholder’s and insurer’s perspectives optimal withdrawal strategies and calculate the respective fair insurance fees. We reveal a discrepancy where the fees from the insurer’s perspective can be significantly higher due to the management fees serving as a form of market friction. Our results provide a possible explanation of lower guarantee insurance fees observed in the market than those predicted from the insurer’s perspective. Numerical experiments are conducted to illustrate the results.
Highlights
Variable annuities (VA) with guarantees of living and death benefits are offered by wealth management and insurance companies worldwide to assist individuals in managing their pre-retirement and post-retirement financial plans
We begin with the setup of the framework for the pricing of guaranteed minimum withdrawal and death benefit (GMWDB) contract and describe the features of this type of guarantees. (In the sequel, we refer to the VA contract with GMWDB rider as the GMWDB contract, unless explicitly stated otherwise.) The pricing problem is formulated under a general setting so that the resulting pricing formulation can be applied to different contract specifications
Two policyholder’s withdrawal strategies were considered: total value maximization and guarantee value maximization, which differs from each other when management fees are present. We demonstrated that these two withdrawal strategies imply different fair insurance fee rates, where maximizing total value implies lower fair fees than those implied by maximizing guarantee value, which represents the maximal hedging costs from the insurer’s perspective
Summary
Variable annuities (VA) with guarantees of living and death benefits are offered by wealth management and insurance companies worldwide to assist individuals in managing their pre-retirement and post-retirement financial plans. Different models have been proposed to account for the real-world behaviors of policyholders, including the reduced-form exercise rules of Ho et al (2005), and the subjective risk neutral valuation approach taken by Moenig and Bauer (2015). When the management fee of the policyholder’s wealth account is zero, and deterministic withdrawal behavior is assumed, Hyndman and Wenger (2014) and Fung et al (2014) show that risk-neutral pricing of guaranteed withdrawal benefits in both a policyholder’s and an insurer’s perspectives will result in the same fair insurance fee. Despite a large range of papers mentioned above on VA guarantee pricing with management fees, the important question of how the management fees as a form of market friction will impact withdrawal behaviors of the policyholder, and the hedging cost for the insurer, is yet to be examined in a dynamic withdrawal setting.
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