IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v43y2008i1p41-55.html
   My bibliography  Save this article

Heath-Jarrow-Morton modelling of longevity bonds and the risk minimization of life insurance portfolios

Author

Listed:
  • Barbarin, Jérôme

Abstract

This paper has two parts. In the first, we apply the Heath-Jarrow-Morton (HJM) methodology to the modelling of longevity bond prices. The idea of using the HJM methodology is not new. We can cite Cairns et al. [Cairns A.J., Blake D., Dowd K, 2006. Pricing death: framework for the valuation and the securitization of mortality risk. Astin Bull., 36 (1), 79-120], Miltersen and Persson [Miltersen K.R., Persson S.A., 2005. Is mortality dead? Stochastic force of mortality determined by arbitrage? Working Paper, University of Bergen] and Bauer [Bauer D., 2006. An arbitrage-free family of longevity bonds. Working Paper, Ulm University]. Unfortunately, none of these papers properly defines the prices of the longevity bonds they are supposed to be studying. Accordingly, the main contribution of this section is to describe a coherent theoretical setting in which we can properly define these longevity bond prices. A second objective of this section is to describe a more realistic longevity bonds market model than in previous papers. In particular, we introduce an additional effect of the actual mortality on the longevity bond prices, that does not appear in the literature. We also study multiple term structures of longevity bonds instead of the usual single term structure. In this framework, we derive a no-arbitrage condition for the longevity bond financial market. We also discuss the links between such HJM based models and the intensity models for longevity bonds such as those of Dahl [Dahl M., 2004. Stochastic mortality in life insurance: Market reserves and mortality-linked insurance contracts, Insurance: Math. Econom. 35 (1) 113-136], Biffis [Biffis E., 2005. Affine processes for dynamic mortality and actuarial valuations. Insurance: Math. Econom. 37, 443-468], Luciano and Vigna [Luciano E. and Vigna E., 2005. Non mean reverting affine processes for stochastic mortality. ICER working paper], Schrager [Schrager D.F., 2006. Affine stochastic mortality. Insurance: Math. Econom. 38, 81-97] and Hainaut and Devolder [Hainaut D., Devolder P., 2007. Mortality modelling with Lévy processes. Insurance: Math. Econom. (in press)], and suggest the standard pricing formula of these intensity models could be extended to more general settings. In the second part of this paper, we study the asset allocation problem of pure endowment and annuity portfolios. In order to solve this problem, we study the "risk-minimizing" strategies of such portfolios, when some but not all longevity bonds are available for trading. In this way, we introduce different basis risks.

Suggested Citation

  • Barbarin, Jérôme, 2008. "Heath-Jarrow-Morton modelling of longevity bonds and the risk minimization of life insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 41-55, August.
    • Handle: RePEc:eee:insuma:v:43:y:2008:i:1:p:41-55
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(07)00105-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dahl, Mikkel & Moller, Thomas, 2006. "Valuation and hedging of life insurance liabilities with systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 193-217, October.
    2. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
    3. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 79-120, May.
    4. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    5. Aase, Knut K., 1988. "Contingent claims valuation when the security price is a combination of an Ito process and a random point process," Stochastic Processes and their Applications, Elsevier, vol. 28(2), pages 185-220, June.
    6. Thomas Møller, 2001. "Risk-minimizing hedging strategies for insurance payment processes," Finance and Stochastics, Springer, vol. 5(4), pages 419-446.
    7. Elisa Luciano & Elena Vigna, 2005. "Non mean reverting affine processes for stochastic mortality," ICER Working Papers - Applied Mathematics Series 4-2005, ICER - International Centre for Economic Research.
    8. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
    9. 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..
    10. Riesner, Martin, 2006. "Hedging life insurance contracts in a Lévy process financial market," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 599-608, June.
    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. Debonneuil, Edouard & Loisel, Stéphane & Planchet, Frédéric, 2018. "Do actuaries believe in longevity deceleration?," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 325-338.
    2. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    3. Li, Jackie & Haberman, Steven, 2015. "On the effectiveness of natural hedging for insurance companies and pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 286-297.
    4. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    5. David Blake & Andrew Cairns & Guy Coughlan & Kevin Dowd & Richard MacMinn, 2013. "The New Life Market," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 501-558, September.
    6. Elisa Luciano & Luca Regis & Elena Vigna, 2011. "Delta and Gamma hedging of mortality and interest rate risk," ICER Working Papers - Applied Mathematics Series 01-2011, ICER - International Centre for Economic Research.
    7. Zeddouk, Fadoua & Devolder, Pierre, 2022. "Pricing and hedging of longevity basis risk through securitization," LIDAM Discussion Papers ISBA 2022038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Tahir Choulli & Catherine Daveloose & Mich`ele Vanmaele, 2018. "Mortality/longevity Risk-Minimization with or without securitization," Papers 1805.11844, arXiv.org.
    9. Tahir Choulli & Catherine Daveloose & Michèle Vanmaele, 2021. "Mortality/Longevity Risk-Minimization with or without Securitization," Mathematics, MDPI, vol. 9(14), pages 1-27, July.
    10. Rihab Bedoui & Islem Kedidi, 2018. "Modeling Longevity Risk using Consistent Dynamics Affine Mortality Models," Working Papers hal-01678050, HAL.
    11. Blackburn, Craig & Sherris, Michael, 2013. "Consistent dynamic affine mortality models for longevity risk applications," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 64-73.
    12. Francesca Biagini & Andreas Groll & Jan Widenmann, 2016. "Risk Minimization for Insurance Products via F-Doubly Stochastic Markov Chains," Risks, MDPI, vol. 4(3), pages 1-26, July.
    13. Shen, Yang & Siu, Tak Kuen, 2013. "Longevity bond pricing under stochastic interest rate and mortality with regime-switching," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 114-123.
    14. Stefan Tappe & Stefan Weber, 2014. "Stochastic mortality models: an infinite-dimensional approach," Finance and Stochastics, Springer, vol. 18(1), pages 209-248, January.
    15. Luciano, Elisa & Regis, Luca & Vigna, Elena, 2012. "Delta–Gamma hedging of mortality and interest rate risk," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 402-412.

    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. Shen, Yang & Siu, Tak Kuen, 2013. "Longevity bond pricing under stochastic interest rate and mortality with regime-switching," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 114-123.
    2. Marcus C. Christiansen, 2013. "Gaussian and Affine Approximation of Stochastic Diffusion Models for Interest and Mortality Rates," Risks, MDPI, vol. 1(3), pages 1-20, October.
    3. Chen, Bingzheng & Zhang, Lihong & Zhao, Lin, 2010. "On the robustness of longevity risk pricing," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 358-373, December.
    4. Date, P. & Mamon, R. & Jalen, L. & Wang, I.C., 2010. "A linear algebraic method for pricing temporary life annuities and insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 98-104, August.
    5. Luciano, Elisa & Spreeuw, Jaap & Vigna, Elena, 2008. "Modelling stochastic mortality for dependent lives," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 234-244, October.
    6. Qian, Linyi & Wang, Wei & Wang, Rongming & Tang, Yincai, 2010. "Valuation of equity-indexed annuity under stochastic mortality and interest rate," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 123-129, October.
    7. Jevtić, Petar & Regis, Luca, 2019. "A continuous-time stochastic model for the mortality surface of multiple populations," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 181-195.
    8. Kira Henshaw & Corina Constantinescu & Olivier Menoukeu Pamen, 2020. "Stochastic Mortality Modelling for Dependent Coupled Lives," Risks, MDPI, vol. 8(1), pages 1-28, February.
    9. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. Chou-Wen Wang & Sharon S. Yang, 2013. "Pricing Survivor Derivatives With Cohort Mortality Dependence Under the Lee–Carter Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 1027-1056, December.
    11. Tsai, Jeffrey T. & Wang, Jennifer L. & Tzeng, Larry Y., 2010. "On the optimal product mix in life insurance companies using conditional value at risk," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 235-241, February.
    12. Hainaut, Donatien & Devolder, Pierre, 2008. "Mortality modelling with Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 409-418, February.
    13. Stefan Tappe & Stefan Weber, 2014. "Stochastic mortality models: an infinite-dimensional approach," Finance and Stochastics, Springer, vol. 18(1), pages 209-248, January.
    14. Apicella, Giovanna & Dacorogna, Michel M, 2016. "A General framework for modelling mortality to better estimate its relationship with interest rate risks," MPRA Paper 75788, University Library of Munich, Germany.
    15. Stefan Tappe & Stefan Weber, 2019. "Stochastic mortality models: An infinite dimensional approach," Papers 1907.05157, arXiv.org.
    16. LUCIANO, Elisa & VIGNA, Elena, 2008. "Mortality risk via affine stochastic intensities: calibration and empirical relevance," MPRA Paper 59627, University Library of Munich, Germany.
    17. Wang, Ting & Young, Virginia R., 2016. "Hedging pure endowments with mortality derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 238-255.
    18. Blackburn, Craig & Sherris, Michael, 2013. "Consistent dynamic affine mortality models for longevity risk applications," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 64-73.
    19. Luciano, Elisa & Regis, Luca & Vigna, Elena, 2012. "Delta–Gamma hedging of mortality and interest rate risk," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 402-412.
    20. Russo, Vincenzo & Giacometti, Rosella & Ortobelli, Sergio & Rachev, Svetlozar & Fabozzi, Frank J., 2011. "Calibrating affine stochastic mortality models using term assurance premiums," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 53-60, July.

    More about this item

    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:eee:insuma:v:43:y:2008:i:1:p:41-55. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.