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

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.