Variable Annuities with VIX-Linked Fee Structure under a Heston-Type Stochastic Volatility Model

The Chicago Board of Options Exchange (CBOE) advocates linking variable annuity (VA) fees to its trademark VIX index in a white paper (CBOE, 2013a, b). It claims that the VIX-linked fee structure has several advantages over the traditional fixed percentage fee structure. However, the evidence presented in the white paper was largely based on non-parametric extrapolation of historical data on market prices. Our work lays out a theoretical basis with a parametric model to analyze the impact of the VIX-linked fee structure and put to test some claims from the CBOE white paper. In a Heston-type stochastic volatility setting, we jointly model the dynamics of an equity index underlying VA policyholders' accounts and the VIX index. In this framework, we price a guaranteed minimum maturity benefit (GMMB) with VIX-linked fees. Through numerical examples, we show that the VIX-linked fee reduces the sensitivity of the insurer's liability to market volatility, when compared to a VA with the traditional fixed fee rate