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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.

Suggested Citation

  • Jørgensen, Peter Løchte, 2006. "Lognormal Approximation of Complex Path-dependent Pension Scheme Payoffs," Finance Research Group Working Papers F-2006-09, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    • Handle: RePEc:hhb:aarbfi:2006-09
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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. Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, vol. 46(8), pages 1116-1136, August.
    3. 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.
    4. 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.
    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. Grosen, Anders & Jørgensen, Peter Løchte, 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(3), pages 249-268, November.
    7. Steven Vanduffel & Tom Hoedemakers & Jan Dhaene, 2005. "Comparing Approximations for Risk Measures of Sums of Nonindependent Lognormal Random Variables," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(4), pages 71-82.
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    More about this item

    Keywords

    Account-based pension schemes; return smoothing; payoff distributions; density approximation; Monte Carlo simulation; Asian options;
    All these keywords.

    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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