An Analysis of the Guaranteed Withdrawal Benefits for Life Option

35 Pages Posted: 8 Dec 2008 Last revised: 29 Sep 2010

See all articles by Premal Shah

Premal Shah

Massachusetts Institute of Technology (MIT) - Operations Research Center

Dimitris Bertsimas

Massachusetts Institute of Technology (MIT) - Sloan School of Management

Date Written: December 7, 2008

Abstract

In this paper, we present an analysis of the "Guaranteed Withdrawal Benefits'' (GWB) for life option, a recent and popular product that many insurance companies are offering as a retirement planning solution. Under the GWB for life plan, the investor is promised increasing withdrawals during retirement for her lifetime, while still being invested in the markets. GWB for life thus transfers financial and longevity related risks from an individual investor to the insurance company underwriting the guarantee. We first analyze a continuous time version of this product in a Black Scholes economy with simplifying assumptions on population mortality and obtain an analytical solution for the product value. This analysis reveals the high sensitivity the product bears to several risk factors. We then price the GWB in a realistic setting using different asset pricing models, including those that allow the interest rates and the volatility of returns to be stochastic. Our analysis reveals that 1) GWB has insufficient price discrimination and is susceptible to adverse selection and 2) valuations can vary substantially depending on which class of models is used. We believe the ambiguity in value and the presence of significant risks, which can be challenging to hedge, should create concerns to the insurance companies offering the GWB, their investors and clients as well as the regulators.

Keywords: GWB for life, Variable Annuities, stochastic interest rate, stochastic volatility, pension, risk neutrl pricing, insurance

Suggested Citation

Shah, Premal and Bertsimas, Dimitris, An Analysis of the Guaranteed Withdrawal Benefits for Life Option (December 7, 2008). Available at SSRN: https://ssrn.com/abstract=1312727 or http://dx.doi.org/10.2139/ssrn.1312727

Premal Shah (Contact Author)

Massachusetts Institute of Technology (MIT) - Operations Research Center ( email )

77 Massachusetts Avenue
Bldg. E 40-149
Cambridge, MA 02139
United States

Dimitris Bertsimas

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

E53-359
Cambridge, MA 02142
United States
617-253-4223 (Phone)
617-258-7579 (Fax)

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