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The Risk Management of Minimum Return Guarantees

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Abstract

We analyse contracts which pay out a guaranteed minimum rate of return and a fraction of a positive excess rate, which is specified on the basis of a benchmark portfolio. These contracts are closely related to unit-linked life-insurance/savings plans products and can be considered as alternatives to a direct investment in the underlying benchmark portfolio. The option embedded into the savings plan is in fact a power option, and thus the specification of the "fair" contract parameters is closely related to well known features of these financial derivatives. The key issue, both in order to rigorously justify valuation by arbitrage arguments and to prevent the guarantees from becoming uncontrollable liabilities to the issuer, is the risk management of the embedded options by a tractable and realistic hedging strategy. The long maturity of life-insurance products makes it necessary to lift Black/Scholes assumptions and consider an uncertain volatility scenario, thus explicitly taking into account "model risk". In this context, we show how to determine the contract parameters conservatively and implement robust risk management strategies. This highlights the necessity of a careful choice of guarantees which are granted to the insurance customer and suggests a new role for a type of "bonus account" customary in many life-insurance contracts.

Suggested Citation

  • Antje Mahayni & Erik Schlögl, 2003. "The Risk Management of Minimum Return Guarantees," Research Paper Series 102, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:102
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    Cited by:

    1. Nielsen, J. Aase & Sandmann, Klaus & Schlögl, Erik, 2011. "Equity-linked pension schemes with guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 547-564.
    2. Chen, An, 2008. "Loss analysis of a life insurance company applying discrete-time risk-minimizing hedging strategies," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1035-1049, June.
    3. Branger, Nicole & Mahayni, Antje & Schneider, Judith C., 2010. "On the optimal design of insurance contracts with guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 485-492, June.
    4. Chen, An, 2005. "Loss Analysis of a Life Insurance Company Applying Discrete-time Risk-minimizing Hedging Strategies," Bonn Econ Discussion Papers 19/2005, University of Bonn, Bonn Graduate School of Economics (BGSE).
    5. Antje B. Mahayni & Klaus Sandmann, 2008. "Return Guarantees with Delayed Payment," German Economic Review, Verein für Socialpolitik, vol. 9(2), pages 207-231, May.
    6. repec:bla:germec:v:9:y:2008:i::p:207-231 is not listed on IDEAS
    7. Petar Pierre Matek & Masa Galic, 2017. "The Impact of Minimum Return Guarantees on Management of Mandatory Pension Funds in Croatia," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 67(4), pages 342-369, August.

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    More about this item

    Keywords

    minimum return guarantee; defined-contribution pension plans; life-insurance; uncertain volatility; conservative pricing; robust hedging; model misspecification; model risk;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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