Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging

J. Lars Kirkby and Duy Nguyen

Insurance: Mathematics and Economics, 2021, vol. 100, issue C, 408-428

Abstract: In this paper, we analyze a form of equity-linked Guaranteed Minimum Death Benefit (GMDB), whose payoff depends on a dollar cost averaging (DCA) style periodic investment in the risky index, with rider premiums paid at regular intervals. This rider is a very natural insurance vehicle for equity-linked variable annuities, and the DCA feature has a tendency to reduce the uncertainty associated with the final payoff, beyond the minimum benefit guaranteed to the beneficiary upon death of the insured. This makes the insurer risk easier to manage as the contract ages. From the policyholder's perspective, the protection is cheaper than a standard GMDB whose payoff depends solely on the risky index value upon death, but still offers the upside potential from an investment made at regular intervals. We derive closed-form valuation formulas under the fairly broad class of exponential Lévy models for the risky index, which includes Black-Scholes as a special case. Closed-form valuation is provided by a fundamental link between this contract and a series of Asian options, for which valuation is well established. We provide several valuation strategies, and demonstrate the soundness of the framework.

Keywords: GMDB; Guaranteed Minimum Death Benefit; Equity-linked; GMxB; Annuity; Dollar cost averaging; Lévy; Variable annuity (search for similar items in EconPapers)
JEL-codes: C15 G13 G22 G23 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167668721000834
Full text for ScienceDirect subscribers only

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:eee:insuma:v:100:y:2021:i:c:p:408-428

DOI: 10.1016/j.insmatheco.2021.04.012

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

More articles in Insurance: Mathematics and Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().