Regret Aversion and Annuity Risk in Defined Contribution Pension Plans

34 Pages Posted: 31 Jan 2008

See all articles by Roy P. M. M. Hoevenaars

Roy P. M. M. Hoevenaars

APG Asset Management

Franz C. Palm

University of Maastricht - Department of Economics; CESifo (Center for Economic Studies and Ifo Institute)

Rik Frehen

Tilburg University - Department of Finance

Peter C. Schotman

Maastricht University - Department of Finance

Abstract

The high value of the implicit option to choose a retirement date at which interest rates are particularly high and life annuities relatively cheap, leads to the possibility to introduce regret aversion in the retirement investment decision of defined contribution plan participants. As a remedy for regret aversion in retirement investment decisions, this paper develops and prices a lookback option on a life annuity contract. We determine a closed-form option value under the restriction that the option holder invests risklessly during the time to maturity of the option and without the guarantee that the exact amount of retirement wealth is converted into a life annuity at retirement. Thereafter the investment restriction is relaxed and the guarantee of exact conversion is imposed and the option is priced via Monte Carlo simulations in an economic environment with a stochastic discount factor. Option price sensitivities are determined via the pricing of alternative options. We find that the price of a lookback option, with a maturity of three years, amounts to 8-9\% of the wealth at the option issuance date. The option price is highly sensitive to the exercise price of the option, i.e. pricing alternative options (e.g. Asian) substantially lowers the price. Time to maturity and interest rate volatility are other important option price drivers. Asset allocation decisions and initial interest rates hardly affect the option price.

Keywords: Lookback Option, Life Annuity, Annuity Risk, Defined Contribution, Stochastic Discount Factor

JEL Classification: C15, G12, G13, G23

Suggested Citation

Hoevenaars, Roy P. M. M. and Palm, Franz C. and Frehen, Rik and Schotman, Peter C., Regret Aversion and Annuity Risk in Defined Contribution Pension Plans. Insurance: Mathematics and Economics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=1088070

Roy P. M. M. Hoevenaars

APG Asset Management ( email )

P.O. Box 75283
1070 AG
Amsterdam
Netherlands
+31206048313 (Phone)

Franz C. Palm

University of Maastricht - Department of Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands
+31-(0)43-3883833 (Phone)
+31-(0)43-3258535 (Fax)

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

HOME PAGE: http://www.cesifo.de

Rik Frehen (Contact Author)

Tilburg University - Department of Finance ( email )

P.O. Box 90153
Tilburg, DC Noord-Brabant 5000 LE
Netherlands

Peter C. Schotman

Maastricht University - Department of Finance ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands
+31 43 388 3862 (Phone)
+31 43 388 4875 (Fax)

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