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Equity-Linked Pension Schemes with Guarantees

This paper analyses the relationship between the level of a return guarantee in an equity-linked pension scheme and the proportion of an investor's contribution needed to finance this guarantee. Three types of schemes are considered: investment guarantee, contribution guarantee and participation surplus. The evaluation of each scheme involves pricing an Asian option, for which relatively tight upper and lower bounds can be calculated in a numerically efficient manner. We find a negative (and for two contracts pecifications also concave) relationship between the participation in the surplus return of the investment strategy and the guarantee level in terms of a minimum rate of return. Furthermore, the introduction of a possibility of early termination of the contract (e.g. due to the death of the investor) has no qualitative and very little quantitative impact on this relationship.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp270.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 270.

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Length: 33
Date of creation: 01 Jan 2010
Date of revision:
Handle: RePEc:uts:rpaper:270
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Web page: http://www.qfrc.uts.edu.au/
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  1. Nielsen, J.A. & Sandmann, K., 1998. "Asian Exchange Rate Options under Stochastic Interest Rates: Pricing as a Sum of Delayed Payment Options," Discussion Paper Serie B 431, University of Bonn, Germany.
  2. J. Aase Nielsen & Klaus Sandmann, 1996. "Uniqueness of the Fair Premium for Equity-Linked Life Insurance Contracts," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 21(1), pages 65-102, June.
  3. Nielsen, J. Aase & Sandmann, Klaus, 2003. "Pricing Bounds on Asian Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(02), pages 449-473, June.
  4. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 12(3), pages 245-257, June.
  5. Steinar Ekern & Svein-Arne Persson, 1996. "Exotic Unit-Linked Life Insurance Contracts," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 21(1), pages 35-63, June.
  6. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
  7. Nielsen, J. Aase & Klaus Sandmann, 1995. "Equity-linked life insurance - a model with stochastic interest rates," Discussion Paper Serie B 291, University of Bonn, Germany, revised Mar 1995.
  8. Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, vol. 40(12), pages 1705-1711, December.
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