Valuing inflation-linked death benefits under a stochastic volatility framework

Zongxia Liang and Wenlong Sheng

Insurance: Mathematics and Economics, 2016, vol. 69, issue C, 45-58

Abstract: In this paper we construct a framework to price the inflation-linked derivatives with the stochastic inflation rate, the stochastic interest rate, and stochastic risky assets with stochastic volatility. Because of the popularity of the guaranteed minimum death benefit (GMDB) in insurance market, we mainly study two types of GMDBs: the inflation guarantee and the combination guarantee. We consider the guaranteed minimum death benefit as an European option with a random maturity date, the closed-form pricing formulas for the GMDBs are derived by Fourier-based method. Moreover, we give an elaborate sensitivity analysis to explain economical behaviors of our models. The numerical results show that the death benefit of inflation guarantee is slightly overpriced in constant volatility of stock situation.

Keywords: IE50; IB10; Guaranteed minimum death benefits; Variable annuities; Heath–Jarrow–Morton model; Schöbel and Zhu model; Stochastic volatility; Stochastic inflation; Stochastic interest rates (search for similar items in EconPapers)
JEL-codes: G13 G22 G23 (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:69:y:2016:i:c:p:45-58

DOI: 10.1016/j.insmatheco.2016.03.014

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