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Lognormal Approximation of Complex Path-dependent Pension Scheme Payoffs

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Abstract

This paper analyzes an explicit return smoothing mechanism which has recently been introduced as part of a new type of pension savings contract that has been offered by Danish life insurers. We establish the payoff function implied by the return smoothing mechanism and show that its probabilistic properties are accurately approximated by a suitably adapted lognormal distribution. The quality of the lognormal approximation is explored via a range of simulation based numerical experiments, and we point to several other potential practical applications of the paper’s theoretical results.

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Bibliographic Info

Paper provided by University of Aarhus, Aarhus School of Business, Department of Business Studies in its series Finance Research Group Working Papers with number F-2006-09.

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Length: 38 pages
Date of creation: 21 Nov 2006
Date of revision:
Handle: RePEc:hhb:aarbfi:2006-09

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Postal: The Aarhus School of Business, Fuglesangs Allé 4, DK-8210 Aarhus V, Denmark
Fax: + 45 86 15 19 43
Web page: http://www.asb.dk/about/departments/bs.aspx
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Related research

Keywords: Account-based pension schemes; return smoothing; payoff distributions; density approximation; Monte Carlo simulation; Asian options;

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  1. Guillen, Montserrat & Jorgensen, Peter Lochte & Nielsen, Jens Perch, 2006. "Return smoothing mechanisms in life and pension insurance: Path-dependent contingent claims," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 229-252, April.
  2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  3. Grosen, Anders & J Rgensen, Peter L Chte, 2002. "The bonus-crediting mechanism of Danish pension and life insurance companies: an empirical analysis," Journal of Pension Economics and Finance, Cambridge University Press, vol. 1(03), pages 249-268, November.
  4. Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, vol. 46(8), pages 1116-1136, August.
  5. Boyle, Phelim P. & Hardy, Mary R., 1997. "Reserving for maturity guarantees: Two approaches," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 113-127, November.
  6. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
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