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

## TL;DR

This paper develops a numerical framework to evaluate GMWB variable annuities considering both stochastic interest rates and taxation, revealing their significant impact on policy valuation and withdrawal strategies.

## Contribution

It introduces a novel numerical method to jointly model taxation and stochastic interest rates in GMWB valuation, enhancing accuracy over previous models.

## Key findings

- Taxation and stochastic interest rates significantly influence GMWB valuation.
- Accounting for these factors alters optimal withdrawal strategies.
- The model explains the popularity of GMWB products for retirement planning.

## 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 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 policy holder behavior, as observed by Gouden\`ege 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.