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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.

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  • 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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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp102.pdf
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    1. Brennan, Michael J & Schwartz, Eduardo S, 1979. "Alternative Investment Strategies for the Issuers of Equity Linked Life Insurance Policies with an Asset Value Guarantee," The Journal of Business, University of Chicago Press, vol. 52(1), pages 63-93, January.
    2. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    3. Bacinello, Anna Rita, 2001. "Fair Pricing of Life Insurance Participating Policies with a Minimum Interest Rate Guaranteed," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 31(02), pages 275-297, November.
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    5. Aase Nielsen, J. & Sandmann, Klaus, 1995. "Equity-linked life insurance: A model with stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 16(3), pages 225-253, July.
    6. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 12(3), pages 245-257, June.
    7. Nicole El Karoui & Monique Jeanblanc-Picquè & Steven E. Shreve, 1998. "Robustness of the Black and Scholes Formula," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 93-126.
    8. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    9. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
    10. 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.
    11. 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.
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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. Antje B. Mahayni & Klaus Sandmann, 2008. "Return Guarantees with Delayed Payment," German Economic Review, Verein für Socialpolitik, vol. 9, pages 207-231, May.
    3. 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.
    4. 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.
    5. repec:fau:fauart:v:67:y:2017:i:4:p:342-369 is not listed on IDEAS

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