Taxation of a GMWB Variable Annuity in a Stochastic Interest Rate Model

Abstract

Modeling taxation of Variable Annuities has been frequently neglected, but accounting for it can significantly improve the explanation of the withdrawal dynamics and lead to a better modeling of the financial cost of these insurance products. The importance of including a model for taxation has first been observed by Moenig and Bauer (2016) while considering a Guaranteed Minimum Withdrawal Benefit (GMWB) Variable Annuity. In particular, they consider the simple Black–Scholes dynamics to describe the underlying security. Nevertheless, GMWB are long-term products, and thus accounting for stochastic interest rate has relevant effects on both the financial evaluation and the policyholder behavior, as observed by Goudenège et al. (2018). In this paper, we investigate the outcomes of these two elements together on GMWB evaluation. To this aim, we develop a numerical framework which allows one to efficiently compute the fair value of a policy. Numerical results show that accounting for both taxation and stochastic interest rate has a determinant impact on the withdrawal strategy and on the cost of GMWB contracts. In addition, it can explain why these products are so popular with people looking for a protected form of investment for retirement.

International Financial Activities: Accounting, Taxation and Insurance

“…General variations in financial and economic behavior and generalized global factors influencing it have been studied in detail by scholars, linking them to tax burdens (Molent, 2020). However, Lois P., Drogalas G., Karagiorgos A. and Karasteriou E. note the emergence of the phenomenon of unpredictable financial behavior, which is expressed in tax evasion due to undeclared employment (Lois, Drogalas, Karagiorgos, Karasteriou, 2020).…”

A semi‐Lagrangian ε$$ \varepsilon $$‐monotone Fourier method for continuous withdrawal GMWBs under jump‐diffusion with stochastic interest rate

“…To attract investors, variable annuities are often incorporated with additional features, among which Guaranteed Minimum Withdrawal Benefits (GMWBs) are popular. Since first introduced in the early 2000's, GBMWs have captured great attention from both industry and academia alike, as evidenced by a substantial and growing body of literature; see [61,17,19,22,6,42,44,45,29,37,40,62,4,83,1,65,43,57], among many other publications.…”

“…Under a discrete withdrawal scenario, fair prices and insurance fees are found to be remarkably sensitive to interest rates, in particular, in the case of (instantaneous) short-rate dynamics, such as the Vasicek model [66,75], the Hull-White [30,37,38,55], and the the Cox-Ingersoll-Ross model [6,40]. Substantial impact of short-rate dynamics on the holder's optimal withdrawal behavior is recently reported in [62]. We highlight that the combined effects of jumps and stochastic interest rate in the context of GMWBs have not been previously studied in the literature.…”