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The Risk Management of Minimum Return Guarantees

  • Antje Mahayni
  • Erik Schlögl

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 plan 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 the 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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Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse18_2003.

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Length: 32
Date of creation: Jul 2003
Date of revision:
Handle: RePEc:bon:bonedp:bgse18_2003
Contact details of provider: Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

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  1. Nielsen, J. Aase & Klaus Sandmann, 1995. "Equity-linked life insurance - a model with stochastic interest rates," Discussion Paper Serie B 291, University of Bonn, Germany, revised Mar 1995.
  2. 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.
  3. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
  4. Chen, An & Suchanecki, Michael, 2007. "Default risk, bankruptcy procedures and the market value of life insurance liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 231-255, March.
  5. 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.
  6. Grosen, Anders & Løchte Jørgensen, Peter, 2001. "Life Insurance Liabilities at Market Value," Finance Working Papers 01-4, University of Aarhus, Aarhus School of Business, Department of Business Studies.
  7. 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.
  8. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
  9. 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.
  10. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
  11. Schrager, David F. & Pelsser, Antoon A.J., 2004. "Pricing Rate of Return Guarantees in Regular Premium Unit Linked Insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 369-398, October.
  12. T. J. Lyons, 1995. "Uncertain volatility and the risk-free synthesis of derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 117-133.
  13. Grosen, Anders & Lochte Jorgensen, Peter, 2000. "Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 37-57, February.
  14. 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.
  15. 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.
  16. 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.
  17. Antje B. Mahayni & Klaus Sandmann, 2008. "Return Guarantees with Delayed Payment," German Economic Review, Verein für Socialpolitik, vol. 9, pages 207-231, 05.
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