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Regret aversion and annuity risk in defined contribution pension plans
Authors:Rik GP Frehen  Roy PMM Hoevenaars  Franz C Palm  Peter C Schotman  
Institution:a Maastricht University, Limburg Institute of Financial Economics (LIFE), P.O. Box 616, 6200 MD, Maastricht, Netherlands
b Netspar P.O. Box 90153, Tilburg 5000 LE, Netherlands
c Maastricht University - Department of Quantitative Economics, P.O. Box 616, Maastricht NL 6200 MD, Netherlands
d ABP Investments - Research Department WTC Schiphol Airport, Tower G P.O. Box 75753, Schiphol 1118 ZX, Netherlands
e Centre for Economic Policy Research (CEPR), 90-98 Goswell Road, London EC1V 7RR, United Kingdom
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
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