Designing and Pricing Guarantee Options in Defined Contribution Pension Plans

30 Pages Posted: 12 Feb 2015 Last revised: 11 Dec 2015

See all articles by Andrea Consiglio

Andrea Consiglio

University of Palermo - d/SEAS

Michele Tumminello

University of Palermo; Carnegie Mellon University - Department of Social and Decision Sciences

Stavros A. Zenios

University of Cyprus; Bruegel; University of Pennsylvania - Wharton Financial Institutions Center

Date Written: September 28, 2015

Abstract

The shift from defined benefit (DB) to defined contribution (DC) is pervasive among pension funds, due to demographic changes and macroeconomic pressures. In DB all risks are borne by the provider, while in plain vanilla DC all risks are borne by the beneficiary. For DC to provide income security some kind of guarantee is required. A minimum guarantee clause can be modeled as a put option written on some underlying reference portfolio of assets and we develop a discrete model that optimally selects the reference portfolio to minimise the cost of a guarantee. While the relation DB-DC is typically viewed as a binary one, the model can be used to price a wide range of guarantees creating a continuum between DB and DC. Integrating guarantee pricing with asset allocation decision is useful to both pension fund managers and regulators. The former are given a yardstick to assess if a given asset portfolio is fit-for-purpose; the latter can assess differences of specific reference funds with respect to the optimal one, signalling possible cases of moral hazard. We develop the model and report numerical results to illustrate its uses.

Keywords: Pensions, minimum guarantee, defined benefits, defined contributions, embedded options, risk sharing, portfolio selection, stochastic programming

JEL Classification: G23, C61, G11, G22, G28

Suggested Citation

Consiglio, Andrea and Tumminello, Michele and Zenios, Stavros A., Designing and Pricing Guarantee Options in Defined Contribution Pension Plans (September 28, 2015). Insurance: Mathematics and Economics, Vol. 65, pp. 267–279, November 2015, . Available at SSRN: https://ssrn.com/abstract=2563087 or http://dx.doi.org/10.2139/ssrn.2563087

Andrea Consiglio

University of Palermo - d/SEAS ( email )

Viale delle Scienze, edificio 13
Palermo, 90124
Italy

HOME PAGE: http://portale.unipa.it/persone/docenti/c/andrea.consiglio

Michele Tumminello

University of Palermo ( email )

Viale delle Scienza
Palermo, Palermo 90128
Italy

Carnegie Mellon University - Department of Social and Decision Sciences ( email )

Pittsburgh, PA 15213-3890
United States

Stavros A. Zenios (Contact Author)

University of Cyprus ( email )

75 Kallipoleos Street
P.O. Box 20537
Nicosia CY-1678
Cyprus
+357 2 893605 (Phone)

HOME PAGE: http://https://www.researchgate.net/profile/Stavros_Zenios

Bruegel ( email )

Rue de la Charité 33
B-1210 Brussels Belgium
Belgium

University of Pennsylvania - Wharton Financial Institutions Center ( email )

3733 Spruce Street
Philadelphia, PA 19104-6374
United States

HOME PAGE: http://zenios.wordpress.com

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