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

Zhenyu Cui, Runhuan Feng, Anne MacKay

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)458-483
Number of pages26
JournalNorth American Actuarial Journal
Volume21
Issue number3
DOIs
StatePublished - Jul 3 2017

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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