Taxation and Policyholder Behavior: The Case of Guaranteed Minimum Accumulation Benefits

Abstract

This paper considers variable annuity contracts embedded with guaranteed minimum accumulation benefit (GMAB) riders when policyholder's proceeds are taxed. These contracts promise the return of the premium paid by the policyholder, or a higher stepped up value, at the end of the investment period. A partial differential valuation framework, which exploits the numerical method of lines, is used to determine fair fees that render the policyholder and insurer profits neutral. Two taxation regimes are considered; one where capital gains are allowed to offset losses and a second where gains do not offset losses, reflecting stylized institutional arrangements in Australia and the US respectively. Most insurance providers highlight the tax-deferred feature of a variable annuity. We show that the regime under which the insurance provider is taxed significantly impacts supply and demand prices. If losses are allowed to offset gains then this enhances the market, narrowing the gap between fees, and even producing higher demand than supply fees. On the other hand, when losses are not allowed to offset gains, then the demand-supply gap increases. When charging the demand price, we show that insurance companies would be profitable on average. Low (high) Sharpe ratios are not as profitable as policyholders are more likely to stay long (surrender).

Cheaper by the bundle: The interaction of frictions and option exercise in variable annuities

“…On the demand side, Moenig & Bauer (2016) demonstrate that the preferential taxation of VAs will affect the policyholder's product valuation—determined by replicating the posttax VA cash flows using conventional mutual funds investments (also on a posttax basis)—and particularly yield it to deviate from the frictionless production value. More recent contributions in this field are building on this study to gain a more precise understanding of the role that taxation rules play on policyholder behavior and on the value of the VA guarantees (Alonso‐Garcia et al, 2019; Goudenège et al, 2019; Moenig & Zhu, 2018; Ulm, 2020).…”

“…The conventional analysis of VAs relies on the application of familiar option pricing techniques (Bauer et al, 2008; Dai et al, 2008; Milevsky & Posner, 2001; Milevsky & Salisbury, 2006; Moenig, 2021, among many others). More recent contributions acknowledge and accommodate the relevance of taxation rules in modeling VA cash flows when viewed from the policyholder perspective (Alonso‐Garcia et al, 2019; Goudenège et al, 2019; Moenig & Bauer, 2016; Moenig & Zhu, 2018; Ulm, 2020), which is natural since preferential tax treatment is a key aspect in explaining VA popularity (Brown & Poterba, 2006). Our approach is related to these contributions as we rely on a similar approach for determining optimal policyholder behavior.…”

Optimal Surrender Policy of Guaranteed Minimum Maturity Benefits in Variable Annuities with Regime-Switching Volatility

“…Bernard et al [1] split the value of VA contract into a European part and an early exercise premium and derived a Volterra-type integral equation with respect to the optimal surrender boundary under the assumption that the underlying risky asset follows the geometric Brownian motion (GBM) model. Alonso-Garcia et al [6] considered VA contract with GMAB rider when policyholder's proceeds are taxed. Shen et al [4] considered a VA contract with a GMMB rider and proposed a numerical approach to the value function of the VA contract and the optimal surrender boundary.…”