The Impact of Stochastic Volatility on Pricing, Hedging, and Hedge Efficiency of Withdrawal Benefit Guarantees in Variable Annuities

We analyze different types of guaranteed withdrawal benefits for life, the latest guarantee feature within variable annuities. Besides an analysis of the impact of different product features on the clients’ payoff profile, we focus on pricing and hedging of the guarantees. In particular, we investigate the impact of stochastic equity volatility on pricing and hedging. We consider different dynamic hedging strategies for delta and vega risks and compare their performance. We also examine the effects if the hedging model (with deterministic volatility) differs from the data-generating model (with stochastic volatility). This is an indication for the model risk an insurer takes by assuming constant equity volatilities for risk management purposes, whereas in the real world volatilities are stochastic.

Keywords: Variable Annuities, Guaranteed Minimum Benefits, Pricing, Hedging, Hedge Performance, Stochastic Volatility, Model Risk