TY - JOUR
T1 - Analysis of VIX-linked fee incentives in variable annuities via continuous-time Markov chain approximation
AU - MacKay, Anne
AU - Vachon, Marie Claude
AU - Cui, Zhenyu
N1 - Publisher Copyright:
© 2023 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2023
Y1 - 2023
N2 - We consider the pricing of variable annuities (VAs) with general fee structures under a class of stochastic volatility models which includes the Heston, Hull-White, Scott, α-Hypergeometric, 3/2, and 4/2 models. In particular, we analyze the impact of different VIX-linked fee structures on the optimal surrender strategy of a VA contract with guaranteed minimum maturity benefit (GMMB). Under the assumption that the VA contract can be surrendered before maturity, the pricing of a VA contract corresponds to an optimal stopping problem with an unbounded, time-dependent, and discontinuous payoff function. We develop efficient algorithms for the pricing of VA contracts using a two-layer continuous-time Markov chain approximation for the fund value process. When the contract is kept until maturity and under a general fee structure, we show that the value of the contract can be approximated by a closed-form matrix expression. We also provide a quick and simple way to determine the value of early surrenders via a recursive algorithm and give an easy procedure to approximate the optimal surrender surface. We show numerically that the optimal surrender strategy is more robust to changes in the volatility of the account value when the fee is linked to the VIX index.
AB - We consider the pricing of variable annuities (VAs) with general fee structures under a class of stochastic volatility models which includes the Heston, Hull-White, Scott, α-Hypergeometric, 3/2, and 4/2 models. In particular, we analyze the impact of different VIX-linked fee structures on the optimal surrender strategy of a VA contract with guaranteed minimum maturity benefit (GMMB). Under the assumption that the VA contract can be surrendered before maturity, the pricing of a VA contract corresponds to an optimal stopping problem with an unbounded, time-dependent, and discontinuous payoff function. We develop efficient algorithms for the pricing of VA contracts using a two-layer continuous-time Markov chain approximation for the fund value process. When the contract is kept until maturity and under a general fee structure, we show that the value of the contract can be approximated by a closed-form matrix expression. We also provide a quick and simple way to determine the value of early surrenders via a recursive algorithm and give an easy procedure to approximate the optimal surrender surface. We show numerically that the optimal surrender strategy is more robust to changes in the volatility of the account value when the fee is linked to the VIX index.
KW - American options
KW - Continuous-time Markov chain
KW - Heston model
KW - Optimal stopping
KW - Stochastic volatility
KW - Variable annuities
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U2 - 10.1080/14697688.2023.2215278
DO - 10.1080/14697688.2023.2215278
M3 - Article
AN - SCOPUS:85166346716
SN - 1469-7688
VL - 23
SP - 1055
EP - 1078
JO - Quantitative Finance
JF - Quantitative Finance
IS - 7-8
ER -