VIX-linked fees for GMWBs via Explicit Solution Simulation Methods

TL;DR

This paper introduces a VIX-linked fee structure for GMWBs in variable annuities, using explicit solution simulation methods to evaluate its effectiveness in reducing volatility risk sensitivity.

Contribution

It presents an explicit weak solution for GMWB valuation and applies Monte Carlo simulations to analyze the impact of VIX-linked fees on liability sensitivity.

Findings

VIX-linked fees reduce liability sensitivity to volatility changes

Explicit weak solution improves GMWB valuation accuracy

Numerical results demonstrate effectiveness of the fee structure

Abstract

In a market with stochastic volatility and jumps, we consider a VIX-linked fee structure 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, 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.