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THE EFFECT OF THE ASSUMED INTEREST RATE AND SMOOTHING ON VARIABLE ANNUITIES

Published online by Cambridge University Press:  31 October 2019

Anne G. Balter Open the ORCID record for Anne G. Balter [Opens in a new window]  and
Bas J. M. Werker
Anne G. Balter*
Affiliation:
Department of Econometrics and Operations ResearchTilburg University and Netspar Tilburg 5037AB, The Netherlands E-Mail: [email protected]
Bas J. M. Werker
Affiliation:
Department of Econometrics and Operations Research; Department of FinanceTilburg University and Netspar Tilburg 5037AB, The Netherlands E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

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In this paper, we consider the risk–return trade-off for variable annuities in a Black–Scholes setting. Our analysis is based on a novel explicit allocation of initial wealth over the payments at various horizons. We investigate the relationship between the optimal consumption problem and the design of variable annuities by deriving the optimal so-called assumed interest rate for an investor with constant relative risk aversion preferences. We investigate the utility loss due to deviations from this. Finally, we show analytically how habit-formation-type smoothing of financial market shocks over the remaining lifetime leads to smaller year-to-year volatility in pension payouts, but to increases in the longer-term volatility.

Keywords

Optimal consumptioncertainty equivalent lossvariable annuitiesassumed interest ratesconversion risksmoothing financial market shocksG22G23J26D81
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 1 , January 2020 , pp. 131 - 154
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© Astin Bulletin 2019

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