Variable Annuities with VIX-Linked Fee Structure under a Heston-Type Stochastic Volatility Model. Issue 3 (3rd July 2017)

• Record Type: Journal Article
• Authors: Cui, Zhenyu; Feng, Runhuan; MacKay, Anne
• Is Part Of: North American actuarial journal. Volume 21:Issue 3(2017)
• Page Start: 458
• Page End: 483
• Publication Date: 2017-07-03
• Subjects: Life insurance -- Research -- North America -- Periodicals; Actuarial science -- North America -- Periodicals; Web sites; Electronic journals; 368.010973
• DOI: 10.1080/10920277.2017.1307765
• Languages: English
• ISSNs: 2325-0453

Abstract

Abstract : The Chicago Board of Options Exchange (CBOE) advocates linking variable annuity (VA) fees to its trademark VIX index in a recent white paper. It claims that the VIX-linked fee structure has several advantages over the traditional fixed percentage fee structure. However, the evidence presented is largely based on nonparametric 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 to verify some claims from the CBOE. In a Heston-type stochastic volatility setting, we jointly model the dynamics of an equity index (underlying the value of VA policyholders' accounts) and the VIX index. In this framework, we price a guaranteed minimum maturity benefit 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.