VIX-linked fees for GMWBs via explicit solution simulation methods

In a market with stochastic volatility and jumps, we consider a VIX-linked fee structure (see Cui et al. 2017) 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, following Kouritzin, 2018, 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.