Valuation of a Mixture of GMIB and GMDB Variable Annuity

Yichen Han, Dongchen Li, Kun Fan, Jiaxin Wan and Luyan Li ()
Additional contact information
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

Mathematics, 2024, vol. 12, issue 3, 1-22

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.

Keywords: variable annuity; Guaranteed Minimum Income–Death Benefit (GMIDB); mortality; dichotomy algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/3/441/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/3/441/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:3:p:441-:d:1329602

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().