The impact of policyholder behavior on pricing, hedging, and hedge efficiency of withdrawal benefit guarantees in variable annuities

Abstract

We analyze the impact of policyholder behavior on pricing, hedging and hedge efficiency of variable annuities with guaranteed lifetime withdrawal benefits. We consider different product designs, market models and approaches for modeling policyholder behavior in our analyses, covering deterministic behavior, behavior depending on the ‘moneyness’ of the guarantee, and optimal (value maximizing) behavior. First, we assess the risk of mispricing the guarantee due to inaccurate assumptions regarding future policyholder behavior. Comparing products with different ratchet mechanisms, we find that this potential for mispricing is the smallest for the product design with the most valuable ratchet mechanism. We further quantify the impact of different behavior models on the efficiency of the insurer’s hedging strategy and the risk that results if the insurer’s assumption for policyholder behavior deviates from actual behavior. Our analyses indicate significant differences between the considered products in terms of hedgeability and the sensitivity of the guarantee’s value towards policyholder behavior and towards changes in the underlying asset’s volatility. Also, we show that a simple path-dependent behavior model may not be suitable to fully assess the risk arising from policyholder behavior.