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Valuing inflation-linked death benefits under a stochastic volatility framework

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  • Liang, Zongxia
  • Sheng, Wenlong

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.

Suggested Citation

  • Liang, Zongxia & Sheng, Wenlong, 2016. "Valuing inflation-linked death benefits under a stochastic volatility framework," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 45-58.
    • Handle: RePEc:eee:insuma:v:69:y:2016:i:c:p:45-58
    DOI: 10.1016/j.insmatheco.2016.03.014
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    References listed on IDEAS

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    More about this item

    Keywords

    IE50; IB10; Guaranteed minimum death benefits; Variable annuities; Heath–Jarrow–Morton model; Schöbel and Zhu model; Stochastic volatility; Stochastic inflation; Stochastic interest rates;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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