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Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps

Zhenyu Cui, J. Lars Kirkby and Duy Nguyen

Insurance: Mathematics and Economics, 2017, vol. 74, issue C, 46-62

Abstract: In this paper, we develop a novel and efficient transform-based method to price equity-linked annuities (ELAs), including equity-indexed annuities (EIAs) and cliquet-style payoff structures popular in the insurance market under a general class of stochastic volatility models with jumps. We utilize frame duality and density projection combined with a continuous-time Markov chain (CTMC) weak approximation scheme and spectral filtering. Contracts considered include EIAs with return guarantees of a cliquet style. Models considered include exponential Lévy processes, regime-switching Lévy processes, and stochastic volatility models with a general jump size distribution including Heston, Scott’s, Hull–White, Schöbel–Zhu, and the 3/2 models. We also consider some recently proposed stochastic volatility models in the literature such as the α-Hypergeometric model, and the 4/2 model. Our framework encompasses and extends the current literature on EIAs with highly efficient and accurate valuation methods. Numerical experiments confirm our findings.

Keywords: Life insurance; Equity-linked annuity; Cliquet-style guarantee; Stochastic volatility; Jump diffusion; Regime-switching (search for similar items in EconPapers)
JEL-codes: G13 G22 (search for similar items in EconPapers)
Date: 2017
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Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

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