Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-13T09:21:27.702Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

Abel, A.B. (1990) Asset prices under habit formation and catching up with the Joneses. American Economic Review, 80(2), 38–42.Google Scholar
Bacinello, A.R., Millossovich, P., Olivieri, A. and Pitacco, E. (2011) Variable annuities: A unifying valuation approach. Insurance: Mathematics and Economics, 49(3), 285–297.Google Scholar
Balter, A.G., Rangvid, J. and Kallestrup-Lamb, M. (2019) The move towards riskier pensions: The importance of mortality. Working Paper.Google Scholar
Bauer, D., Kling, A. and Russ, J. (2008) A universal pricing framework for guaranteed minimum benefits in variable annuities. ASTIN Bulletin: The Journal of the IAA, 38(2), 621–651.CrossRefGoogle Scholar
Bernard, C., Hardy, M. and MacKay, A. (2014) State-dependent fees for variable annuity guarantees. ASTIN Bulletin: The Journal of the IAA, 44(3), 559–585.CrossRefGoogle Scholar
Blake, D., Wright, D. and Zhang, Y. (2014) Age-dependent investing: Optimal funding and investment strategies in defined contribution pension plans when members are rational life cycle financial planners. Journal of Economic Dynamics and Control, 38, 105–124.CrossRefGoogle Scholar
Bovenberg, A., Nijman, T.E. and Werker, B. (2012) Voorwaardelijke pensioenaanspraken: Over waarderen, beschermen, communiceren en beleggen. Netspar Occasional Paper.Google Scholar
Bruhn, K. and Steffensen, M. (2013) Optimal smooth consumption and annuity design. Journal of Banking & Finance, 37(8), 2693–2701.CrossRefGoogle Scholar
Carroll, C.D. (2000). Solving consumption models with multiplicative habits. Economics Letters, 68(1), 67–77.CrossRefGoogle Scholar
Chen, A., Hentschel, F. and Klein, J.K. (2015) A utility-and CPT-based comparison of life insurance contracts with guarantees. Journal of Banking & Finance, 61, 327–339.CrossRefGoogle Scholar
Coleman, T.F., Li, Y. and Patron, M.-C. (2006) Hedging guarantees in variable annuities under both equity and interest rate risks. Insurance: Mathematics and Economics, 38(2), 215–228.Google Scholar
Constantinides, G.M. (1990) Habit formation: A resolution of the equity premium puzzle. Journal of Political Economy, 98(3), 519–543.CrossRefGoogle Scholar
Cox, J.C. and Huang, C.-f. (1989) Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory, 49(1), 33–83.CrossRefGoogle Scholar
Crawford, I. (2010) Habits revealed. The Review of Economic Studies, 77(4), 1382–1402.CrossRefGoogle Scholar
Davidoff, T., Brown, J.R. and Diamond, P.A. (2005). Annuities and individual welfare. American Economic Review, 95(5), 1573–1590.CrossRefGoogle Scholar
Dellinger, J.K. (2006). The Handbook of Variable Income Annuities. Hoboken: John Wiley & Sons.Google Scholar
Fuhrer, J.C. (2000). Habit formation in consumption and its implications for monetary-policy models. American Economic Review, 90(3), 367–390.CrossRefGoogle Scholar
Guillén, M., Jørgensen, P.L. and Nielsen, J.P. (2006). Return smoothing mechanisms in life and pension insurance: Path-dependent contingent claims. Insurance: Mathematics and Economics, 38(2), 229–252.Google Scholar
Horneff, W.J., Maurer, R.H., Mitchell, O.S. and Stamos, M.Z. (2009). Asset allocation and location over the life cycle with investment-linked survival-contingent payouts. Journal of Banking & Finance, 33(9), 1688–1699.CrossRefGoogle Scholar
Horneff, W.J., Maurer, R.H., Mitchell, O.S. and Stamos, M.Z. (2010). Variable payout annuities and dynamic portfolio choice in retirement. Journal of Pension Economics & Finance, 9(2), 163–183.CrossRefGoogle Scholar
Karatzas, I. and Shreve, S.E. (1998). Methods of Mathematical Finance. New York: Springer-Verlag.Google Scholar
Kling, A., Ruez, F. and Russ, J. (2011). The impact of stochastic volatility on pricing, hedging, and hedge efficiency of withdrawal benefit guarantees in variable annuities. ASTIN Bulletin: The Journal of the IAA, 41(2), 511–545.Google Scholar
Kling, A., Russ, J. and Schilling, K. (2014). Risk analysis of annuity conversion options in a stochastic mortality environment. ASTIN Bulletin: The Journal of the IAA, 44(2), 197–236.CrossRefGoogle Scholar
Koijen, R.S., Nijman, T.E. and Werker, B.J. (2011) Optimal annuity risk management. Review of Finance, 15(4), 799–833.CrossRefGoogle Scholar
Mahayni, A. and Schneider, J.C. (2012) Variable annuities and the option to seek risk: Why should you diversify? Journal of Banking & Finance, 36(9), 2417–2428.CrossRefGoogle Scholar
Maurer, R., Mitchell, O.S., Rogalla, R. and Siegelin, I. (2016) Accounting and actuarial smoothing of retirement payouts in participating life annuities. Insurance: Mathematics and Economics, 71, 268–283.Google Scholar
Merton, R.C. (1969) Lifetime portfolio selection under uncertainty: The continuous-time case. The Review of Economics and Statistics, 51(3), 247–257.CrossRefGoogle Scholar
Merton, R.C. (1971) Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3(4), 373–413.CrossRefGoogle Scholar
Munk, C. (2017) Dynamic Asset Allocation. Lecture Notes, Copenhagen Business School, February 2017.Google Scholar
Nirmalendran, M., Sherris, M. and Hanewald, K. (2014). Pricing and solvency of value-maximizing life annuity providers. ASTIN Bulletin: The Journal of the IAA, 44(1), 39–61.CrossRefGoogle Scholar
Peijnenburg, K., Nijman, T. and Werker, B.J. (2016). The annuity puzzle remains a puzzle. Journal of Economic Dynamics and Control, 70, 18–35.CrossRefGoogle Scholar
Trottier, D.-A., Godin, F. and Hamel, E. (2018). Local hedging of variable annuities in the presence of basis risk. ASTIN Bulletin: The Journal of the IAA, 48(2), 611–646.CrossRefGoogle Scholar