  In a market with stochastic volatility and jumps, we consider a VIX-linked
fee structure for variable annuity contracts with guaranteed minimum withdrawal
benefits (GMWB). Our goal is to assess the effectiveness of the VIX-linked fee
structure in decreasing the sensitivity of the insurer's liability to
volatility risk. Since the GMWB payoff is highly path-dependent, it is
particularly sensitive to volatility risk, and can also be challenging to
price, especially in the presence of the VIX-linked fee. In this paper, we
present an explicit weak solution for the value of the VA account and use it in
Monte Carlo simulations to value the GMWB guarantee. Numerical examples are
provided to analyze the impact of the VIX-linked fee on the sensitivity of the
liability to changes in market volatility.
