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

VIX-linked fees for GMWBs via Explicit Solution Simulation Methods