Options on Tontines: An Innovative Way of Combining Tontines and Annuities

29 Pages Posted: 14 Jun 2019 Last revised: 20 Oct 2019

See all articles by An Chen

An Chen

University of Ulm

Manuel Rach

University of Ulm - Institute of Insurance Science

Date Written: October 18, 2019

Abstract

Increases in the life expectancy, the low interest rate environment and the tightening solvency regulation have led to the rebirth of tontines. Compared to annuities, where insurers bear all the longevity risk, policyholders bear most of the longevity risk in a tontine. Following Donnelly and Young (2017), we come up with an innovative retirement product which contains the annuity and the tontine as special cases: a tontine with a minimum guaranteed payment. The payoff of this product consists of a guaranteed payoff and a call option written on a tontine. Extending Donnelly and Young (2017), we consider the tontine design described in Milevsky and Salisbury (2015) for designing the new product and find that it is able to achieve a better risk sharing between policyholders and insurers than annuities and tontines. For the majority of risk-averse policyholders, the new product can generate a higher expected lifetime utility than annuities and tontines. For the insurer, the new product is able to reduce the (conditional) expected loss drastically compared to an annuity, while the loss probability remains fairly the same. In addition, by varying the guaranteed payments, the insurer is able to provide a variety of products to policyholders with different degrees of risk aversion and liquidity needs.

Keywords: annuity, tontine, option pricing, optimal retirement products, net loss analysis

JEL Classification: G22, G13

Suggested Citation

Chen, An and Rach, Manuel, Options on Tontines: An Innovative Way of Combining Tontines and Annuities (October 18, 2019). Available at SSRN: https://ssrn.com/abstract=3398144 or http://dx.doi.org/10.2139/ssrn.3398144

An Chen

University of Ulm ( email )

Helmholtzstrasse 20
Ulm, D-89081
Germany

HOME PAGE: http://www.uni-ulm.de/mawi/ivw/team

Manuel Rach (Contact Author)

University of Ulm - Institute of Insurance Science ( email )

Ulm, 89081
Germany

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