# A note on the impact of management fees on the pricing of variable annuity guarantees

## TL;DR

This paper examines how management fees influence the pricing of variable annuity guarantees by modeling optimal withdrawal strategies from both policyholder and insurer perspectives, revealing significant deviations and explaining market fee differences.

## Contribution

It introduces a dynamic programming approach to compare optimal strategies and quantify the impact of management fees on guarantee pricing in variable annuities.

## Key findings

- Management fees cause notable differences between policyholder and insurer strategies.
- These differences lead to lower guarantee insurance fees in the market.
- Numerical experiments support the theoretical results.

## Abstract

Variable annuities, as a class of retirement income products, allow equity market exposure for a policyholder's retirement fund with electable additional guarantees to limit the downside risk of the market. Management fees and guarantee insurance fees are charged respectively for the market exposure and for the protection from the downside risk. We investigate the impact of management fees on the pricing of variable annuity guarantees under optimal withdrawal strategies. Two optimal strategies, from policyholder's and from insurer's perspectives, are respectively formulated and the corresponding pricing problems are solved using dynamic programming. Our results show that when management fees are present, the two strategies can deviate significantly from each other, leading to a substantial difference of the guarantee insurance fees. This provides a possible explanation of lower guarantee insurance fees observed in the market. Numerical experiments are conducted to illustrate our results.