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Valuation of a Mixture of GMIB and GMDB Variable Annuity

Author

Listed:
  • Yichen Han

    (School of Statistics, East China Normal University, Shanghai 200241, China)

  • Dongchen Li

    (School of Statistics, East China Normal University, Shanghai 200241, China)

  • Kun Fan

    (School of Statistics, East China Normal University, Shanghai 200241, China)

  • Jiaxin Wan

    (School of Statistics, East China Normal University, Shanghai 200241, China)

  • Luyan Li

    (Department of Social Security, Kunming Medical University, Kunming 650500, China)

Abstract

The Guaranteed Minimum Income Benefit (GMIB) and Guaranteed Minimum Death Benefit (GMDB) are options that may be included at the inception of a variable annuity (VA) contract. In exchange for small fees charged by the insurer, they give the policyholder a right to receive a guaranteed minimum level of annuity payment (GMIB) and a guaranteed minimum level of payment when the policyholder dies (GMDB), respectively. A combination of these two options may be attractive since it protects the policyholder’s investment from potential poor market behavior as well as mortality risk during the accumulation phase. This study examined the pricing of a composite variable annuity incorporating both the GMIB and GMDB options (a Guaranteed Minimum Income–Death Benefit, notated GMIDB). We used a non-arbitrage valuation method, decomposed the GMIDB value into two parts, and derived an analytical pricing formula based on a constant fee structure. The formula can be used to determine the fair fee to be charged. We conducted comprehensive sensitivity analyses on critical parameters to determine what drives the value of a GMIDB option. Our approach offers a simple and deterministic way to price a VA embedded with the GMIDB option. Our numerical findings suggested that the annuity conversion rate, age of the policyholder, and volatility of risky investments are significant in the valuation of a GMIDB option.

Suggested Citation

  • Yichen Han & Dongchen Li & Kun Fan & Jiaxin Wan & Luyan Li, 2024. "Valuation of a Mixture of GMIB and GMDB Variable Annuity," Mathematics, MDPI, vol. 12(3), pages 1-22, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:441-:d:1329602
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    References listed on IDEAS

    as
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