Selected Topics in Variable Annuities
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Date
2021-06-22
Authors
Wang, Yumin
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Variable annuities are long-term insurance products. They have become one of the most popular savings/investment vehicles over the past two decades due to their flexible investment options, stable long-term guarantees, and favorable tax-deferral treatment. The popularity of variable annuities has catalyzed an extensive amount of research papers looking into pricing and hedging of embedded guarantees and attempting to better understand policyholder behavior. This thesis aims to contribute to these two strands of research.
While an ample amount of literature has covered various topics in variable annuities, two important market trends/phenomena need further investigation: 1). the variable annuity market has seen decreasing sales ever since the year 2013; 2). there is evident discordance between the theoretical and empirical insurance fees and policyholder behavior. The theme of this thesis is to address these two market phenomena by offering potential remedy or reasonable explanation.
Chapter 3 aims to offer an appropriate potential remedy to the declining demand of the variable annuity market. In this chapter, we propose a novel high-water mark fee structure and examine its impact on variable annuity marketability. We apply a mean-variance preference model to evaluate policyholder welfare from holding a variable annuity. By also evaluating policyholder welfare from holding two alternative investments, we introduce a quantitative measure, namely a compatible set of risk aversions, to assess the marketability of the variable annuity under a certain fee structure. We find that the high-water mark fee structure improves the variable annuity’s marketability compared to a constant and a state-dependent fee structure.
Chapters 4 and 5 aim to address the aforementioned discordance by investigating the impact of policyholders' uncertainty in discount rates on their welfare and behavior from holding variable annuities. In Chapter 4, we consider policyholders of a variable annuity with guaranteed minimum death and maturity benefits whose subjective discount rates follow a Gamma distribution. We use a constant relative risk aversion utility model to evaluate policyholder welfare and surrender behavior from holding the variable annuity. We also compute an insurer's profit under given insurance fees and policyholder surrender behavior. We find that when sharing the same expected discount rate, Gamma discounting policyholders delay surrender behavior and value the variable annuity more than than exponential discounting policyholders. Moreover, the insurer makes higher profit when policyholders are Gamma discounting than when they are exponential discounting.
Chapter 5 considers policyholders of a variable annuity with guaranteed minimum withdrawal benefit whose subjective discount rates follow a Gamma distribution. Policyholder welfare and withdrawal behavior are quantified by the expected present value of variable annuity payouts. Different from the last two chapters, we deal with stochastic optimal control problems in this chapter due to the withdrawal type guarantees. Consistent with Chapter 4, we find that when having the same expected discount rate, Gamma discounting policyholders withdraw less and value the variable annuity more than exponential discounting policyholders.
To keep a smooth flow of the thesis, Chapter 1 presents the existing strands of literature and introduces the main motivation of this thesis. Chapter \ref{chapter:mp} presents the core mathematical preliminaries for the latter chapters. Chapter 6 concludes this thesis and proposes potential future research avenues.
Description
Keywords
variable annuity, policyholder behavior, marketability, time preferences, time inconsistency