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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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Suggested Citation

  • Løchte Jørgensen, Peter, 2006. "Lognormal Approximation of Complex Pathdependent Pension Scheme Payoffs," Working Papers 2006-9, Copenhagen Business School, Department of Finance.
  • Handle: RePEc:hhs:cbsfin:2006_009
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    File URL: http://openarchive.cbs.dk/cbsweb/handle/10398/7142
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    References listed on IDEAS

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    1. 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.
    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 637-654, May-June.
    3. 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.
    4. 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.
    5. Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, vol. 46(8), pages 1116-1136, August.
    6. 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.
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    Keywords

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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