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Lognormal Approximation of Complex Pathdependent Pension Scheme Payoffs

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  • Løchte Jørgensen, Peter

    (Department of Finance, Copenhagen Business School)

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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File URL: http://openarchive.cbs.dk/cbsweb/handle/10398/7142
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Bibliographic Info

Paper provided by Copenhagen Business School, Department of Finance in its series Working Papers with number 2006-9.

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Length: 38 pages
Date of creation: 01 Jan 2006
Date of revision:
Handle: RePEc:hhs:cbsfin:2006_009

Contact details of provider:
Postal: Department of Finance, Copenhagen Business School, Solbjerg Plads 3, A5, DK-2000 Frederiksberg, Denmark
Phone: +45 3815 3815
Email:
Web page: http://www.cbs.dk/departments/finance/
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  1. 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.
  2. 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.
  3. 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.
  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. 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.
  6. 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.
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