IDEAS home Printed from https://ideas.repec.org/p/uts/rpaper/102.html

The Risk Management of Minimum Return Guarantees

Author

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
    as

    Download full text from publisher

    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp102.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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, April.
    2. 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.
    3. Peter G Zhang, 1998. "Exotic Options:A Guide to Second Generation Options," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 3800, October.
    4. Bacinello, Anna Rita, 2001. "Fair Pricing of Life Insurance Participating Policies with a Minimum Interest Rate Guaranteed," ASTIN Bulletin, Cambridge University Press, vol. 31(2), pages 275-297, November.
    5. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees : A corrigendum," Insurance: Mathematics and Economics, Elsevier, vol. 13(3), pages 303-304, December.
    6. 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.
    7. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    8. 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.
    9. 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.
    10. Pelsser, Antoon, 2003. "Pricing and hedging guaranteed annuity options via static option replication," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 283-296, October.
    11. 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..
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Antje B. Mahayni & Klaus Sandmann, 2008. "Return Guarantees with Delayed Payment," German Economic Review, Verein für Socialpolitik, vol. 9(2), pages 207-231, May.
    4. repec:bla:germec:v:9:y:2008:i::p:207-231 is not listed on IDEAS
    5. 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.
    6. 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).
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Antje B. Mahayni & Klaus Sandmann, 2008. "Return Guarantees with Delayed Payment," German Economic Review, Verein für Socialpolitik, vol. 9(2), pages 207-231, May.
    3. 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.
    4. Kevin Fergusson & Eckhard Platen, 2013. "Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees," Research Paper Series 338, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. 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.
    6. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    7. repec:dau:papers:123456789/5374 is not listed on IDEAS
    8. Møller, T., 2002. "On Valuation and Risk Management at the Interface of Insurance and Finance," British Actuarial Journal, Cambridge University Press, vol. 8(4), pages 787-827, October.
    9. Miltersen, Kristian R. & Persson, Svein-Arne, 1999. "Pricing rate of return guarantees in a Heath-Jarrow-Morton framework," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 307-325, December.
    10. 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.
    11. Tak Siu & John Lau & Hailiang Yang, 2007. "On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(3), pages 255-275, September.
    12. David R. Ba~nos & Salvador Ortiz-Latorre & Oriol Zamora Font, 2023. "Thiele's PIDE for unit-linked policies in the Heston-Hawkes stochastic volatility model," Papers 2309.03541, arXiv.org, revised Feb 2024.
    13. repec:bla:germec:v:9:y:2008:i::p:207-231 is not listed on IDEAS
    14. Mykland, Per Aslak, 2019. "Combining statistical intervals and market prices: The worst case state price distribution," Journal of Econometrics, Elsevier, vol. 212(1), pages 272-285.
    15. repec:abd:kauiea:v:30:y:2017:i:2:no:12:p:135-157 is not listed on IDEAS
    16. Barbarin, Jerome & Devolder, Pierre, 2005. "Risk measure and fair valuation of an investment guarantee in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 297-323, October.
    17. Thomas Poufinas, 2015. "On the pricing of regular premium variable annuities using options," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 4(1), pages 54-77.
    18. Consiglio, Andrea & Cocco, Flavio & Zenios, Stavros A., 2008. "Asset and liability modelling for participating policies with guarantees," European Journal of Operational Research, Elsevier, vol. 186(1), pages 380-404, April.
    19. 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.
    20. Pelsser, Antoon, 2003. "Pricing and hedging guaranteed annuity options via static option replication," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 283-296, October.
    21. Bernard, Carole & Boyle, Phelim P., 2011. "A Natural Hedge for Equity Indexed Annuities," Annals of Actuarial Science, Cambridge University Press, vol. 5(2), pages 211-230, September.
    22. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    23. Alexander Melnikov & Shuo Tong, 2014. "Valuation of finance/insurance contracts: Efficient hedging and stochastic interest rates modeling," Risk and Decision Analysis, IOS Press, issue 5, pages 23-41.

    More about this item

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:uts:rpaper:102. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Duncan Ford (email available below). General contact details of provider: https://edirc.repec.org/data/qfutsau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.