IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v82y2018icp95-116.html
   My bibliography  Save this article

A comparative study of pricing approaches for longevity instruments

Author

Listed:
  • Leung, Melvern
  • Fung, Man Chung
  • O’Hare, Colin

Abstract

The presence of systematic risk in mortality forecasts, known as longevity risk, has called for the introduction of longevity instruments and their market development. Management of longevity risk has been an ongoing issue for insurance companies and pension funds who offer products with payout depending on the lifetime of policyholders. One of the major difficulties in pricing longevity instruments is the determination of a longevity risk-premium. This problem arises from the fact that the longevity market is illiquid and is considered to be incomplete. In this paper we provide an insight to the study of several pricing approaches for longevity instruments that have been proposed in the literature. To account for parameter uncertainty in mortality forecasts and longevity instruments pricing, our analysis hinges on a Bayesian state-space mortality model. The sampling-based Bayesian approach allows us to obtain a distribution of the longevity risk-premium, thus providing an alternative perspective in analyzing the pricing methods. We also discussed the advantages and disadvantages of the considered pricing approaches.

Suggested Citation

  • Leung, Melvern & Fung, Man Chung & O’Hare, Colin, 2018. "A comparative study of pricing approaches for longevity instruments," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 95-116.
    • Handle: RePEc:eee:insuma:v:82:y:2018:i:c:p:95-116
    DOI: 10.1016/j.insmatheco.2018.06.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668717303773
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2018.06.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Fung, Man Chung & Peters, Gareth W. & Shevchenko, Pavel V., 2017. "A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting," Annals of Actuarial Science, Cambridge University Press, vol. 11(2), pages 343-389, September.
    2. Enrico Biffis & David Blake & Lorenzo Pitotti & Ariel Sun, 2016. "The Cost of Counterparty Risk and Collateralization in Longevity Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(2), pages 387-419, June.
    3. Koissi, Marie-Claire & Shapiro, Arnold F. & Hognas, Goran, 2006. "Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 1-20, February.
    4. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    5. Ngai, Andrew & Sherris, Michael, 2011. "Longevity risk management for life and variable annuities: The effectiveness of static hedging using longevity bonds and derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 100-114, July.
    6. Olivieri, Annamaria & Pitacco, Ermanno, 2008. "Assessing the cost of capital for longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1013-1021, June.
    7. Geweke, John & Koop, Gary & van Dijk, Herman (ed.), 2011. "The Oxford Handbook of Bayesian Econometrics," OUP Catalogue, Oxford University Press, number 9780199559084.
    8. Andrew Cairns & David Blake & Kevin Dowd & Guy Coughlan & David Epstein & Alen Ong & Igor Balevich, 2009. "A Quantitative Comparison of Stochastic Mortality Models Using Data From England and Wales and the United States," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(1), pages 1-35.
    9. Hunt, Andrew & Blake, David, 2015. "Modelling longevity bonds: Analysing the Swiss Re Kortis bond," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 12-29.
    10. Alonso-García, Jennifer & Devolder, Pierre, 2016. "Guarantee Valuation In Notional Defined Contribution Pension Systems," ASTIN Bulletin, Cambridge University Press, vol. 46(3), pages 677-707, September.
    11. Boyer, M. Martin & Stentoft, Lars, 2013. "If we can simulate it, we can insure it: An application to longevity risk management," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 35-45.
    12. Michel Denuit & Pierre Devolder & Anne‐Cécile Goderniaux, 2007. "Securitization of Longevity Risk: Pricing Survivor Bonds With Wang Transform in the Lee‐Carter Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(1), pages 87-113, March.
    13. Wai-Sum Chan & Johnny S-H Li & Kenneth Q Zhou & Rui Zhou, 2016. "Towards a Large and Liquid Longevity Market: A Graphical Population Basis Risk Metric," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 41(1), pages 118-127, January.
    14. Li, Johnny Siu-Hang, 2010. "Pricing longevity risk with the parametric bootstrap: A maximum entropy approach," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 176-186, October.
    15. 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.
    16. Stutzer, Michael, 1996. "A Simple Nonparametric Approach to Derivative Security Valuation," Journal of Finance, American Finance Association, vol. 51(5), pages 1633-1652, December.
    17. Liu, Yanxin & Li, Johnny Siu-Hang, 2016. "It’s all in the hidden states: A longevity hedging strategy with an explicit measure of population basis risk," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 301-319.
    18. Yinglu Deng & Patrick L. Brockett & Richard D. MacMinn, 2012. "Longevity/Mortality Risk Modeling and Securities Pricing," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(3), pages 697-721, September.
    19. Bayraktar, Erhan & Milevsky, Moshe A. & David Promislow, S. & Young, Virginia R., 2009. "Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 676-691, March.
    20. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718, December.
    21. Fung, Man Chung & Ignatieva, Katja & Sherris, Michael, 2014. "Systematic mortality risk: An analysis of guaranteed lifetime withdrawal benefits in variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 103-115.
    22. Lin, Yijia & Cox, Samuel H., 2008. "Securitization of catastrophe mortality risks," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 628-637, April.
    23. Kevin Dowd & Andrew Cairns & David Blake & Guy Coughlan & David Epstein & Marwa Khalaf-Allah, 2010. "Backtesting Stochastic Mortality Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(3), pages 281-298.
    24. Blake, D. & Cairns, A. J. G. & Dowd, K., 2006. "Living with Mortality: Longevity Bonds and Other Mortality-Linked Securities," British Actuarial Journal, Cambridge University Press, vol. 12(1), pages 153-197, March.
    25. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
    26. Wang, Shaun S., 2002. "A Universal Framework for Pricing Financial and Insurance Risks," ASTIN Bulletin, Cambridge University Press, vol. 32(2), pages 213-234, November.
    27. Andreas Eichler & Gunther Leobacher & Michaela Szolgyenyi, 2016. "Utility Indifference Pricing of Insurance Catastrophe Derivatives," Papers 1607.01110, arXiv.org, revised May 2017.
    28. Czado, Claudia & Delwarde, Antoine & Denuit, Michel, 2005. "Bayesian Poisson log-bilinear mortality projections," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 260-284, June.
    29. Samuel Bowles & Herbert Gintis, 2000. "Walrasian Economics in Retrospect," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 115(4), pages 1411-1439.
    30. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    31. 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.
    32. F. Douglas Foster & Charles H. Whiteman, 2006. "Bayesian Prediction, Entropy, and Option Pricingx," Australian Journal of Management, Australian School of Business, vol. 31(2), pages 181-205, December.
    33. Carlo Maccheroni & Samuel Nocito, 2017. "Backtesting the Lee–Carter and the Cairns–Blake–Dowd Stochastic Mortality Models on Italian Death Rates," Risks, MDPI, vol. 5(3), pages 1-23, July.
    34. Cox, Samuel H. & Lin, Yijia & Pedersen, Hal, 2010. "Mortality risk modeling: Applications to insurance securitization," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 242-253, February.
    35. Rajnish Kamat & Shmuel S. Oren, 2002. "Exotic Options for Interruptible Electricity Supply Contracts," Operations Research, INFORMS, vol. 50(5), pages 835-850, October.
    36. Blackburn, Craig & Hanewald, Katja & Olivieri, Annamaria & Sherris, Michael, 2017. "Longevity Risk Management And Shareholder Value For A Life Annuity Business," ASTIN Bulletin, Cambridge University Press, vol. 47(1), pages 43-77, January.
    37. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    38. 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.
    39. Rui Zhou & Johnny Siu-Hang Li & Ken Seng Tan, 2015. "Economic Pricing of Mortality-Linked Securities: A Tâtonnement Approach," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 82(1), pages 65-96, March.
    40. Bauer, Daniel & Börger, Matthias & Ruß, Jochen, 2010. "On the pricing of longevity-linked securities," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 139-149, February.
    41. Kogure, Atsuyuki & Kurachi, Yoshiyuki, 2010. "A Bayesian approach to pricing longevity risk based on risk-neutral predictive distributions," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 162-172, February.
    42. Erhan Bayraktar & Virginia Young, 2008. "Pricing options in incomplete equity markets via the instantaneous Sharpe ratio," Annals of Finance, Springer, vol. 4(4), pages 399-429, October.
    43. Pelsser, Antoon, 2008. "On the Applicability of the Wang Transform for Pricing Financial Risks," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 171-181, May.
    44. Dowd, Kevin & Cairns, Andrew J.G. & Blake, David & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2010. "Evaluating the goodness of fit of stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 255-265, December.
    45. Kogure Atsuyuki & Kitsukawa Kenji & Kurachi Yoshiyuki, 2009. "A Bayesian Comparison of Models for Changing Mortalities toward Evaluating Longevity Risk in Japan," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 3(2), pages 1-22, April.
    46. Xiaopeng Zou & Zihan Ye & Qiuzi Zhang, 2016. "Securitization of longevity risk – survivor swap perspective," China Finance Review International, Emerald Group Publishing Limited, vol. 6(4), pages 322-341, November.
    47. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin & Coughlan, Guy D. & Khalaf-Allah, Marwa, 2011. "Bayesian Stochastic Mortality Modelling for Two Populations," ASTIN Bulletin, Cambridge University Press, vol. 41(1), pages 29-59, May.
    48. Johnny Li & Mary Hardy, 2011. "Measuring Basis Risk in Longevity Hedges," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 177-200.
    49. Johnny Siu‐Hang Li & Andrew Cheuk‐Yin Ng, 2011. "Canonical Valuation of Mortality‐Linked Securities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(4), pages 853-884, December.
    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. 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.
    2. Xiaoyi Zhang & Yanan Li & Junyi Guo, 2024. "The Role of Longevity-Indexed Bond in Risk Management of Aggregated Defined Benefit Pension Scheme," Risks, MDPI, vol. 12(3), pages 1-17, March.
    3. Börger, Matthias & Freimann, Arne & Ruß, Jochen, 2021. "A combined analysis of hedge effectiveness and capital efficiency in longevity hedging," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 309-326.
    4. Yajing Xu & Michael Sherris & Jonathan Ziveyi, 2020. "Market Price of Longevity Risk for a Multi‐Cohort Mortality Model With Application to Longevity Bond Option Pricing," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 87(3), pages 571-595, September.
    5. Leung, Melvern & Li, Youwei & Pantelous, Athanasios A. & Vigne, Samuel A., 2021. "Bayesian Value-at-Risk backtesting: The case of annuity pricing," European Journal of Operational Research, Elsevier, vol. 293(2), pages 786-801.
    6. Fadoua Zeddouk & Pierre Devolder, 2019. "Pricing of Longevity Derivatives and Cost of Capital," Risks, MDPI, vol. 7(2), pages 1-29, April.
    7. Wang, Pengjie & Pantelous, Athanasios A. & Vahid, Farshid, 2023. "Multi-population mortality projection: The augmented common factor model with structural breaks," International Journal of Forecasting, Elsevier, vol. 39(1), pages 450-469.

    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. 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.
    2. 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.
    3. Bahl, Raj Kumari & Sabanis, Sotirios, 2021. "Model-independent price bounds for Catastrophic Mortality Bonds," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 276-291.
    4. David Blake & Marco Morales & Enrico Biffis & Yijia Lin & Andreas Milidonis, 2017. "Special Edition: Longevity 10 – The Tenth International Longevity Risk and Capital Markets Solutions Conference," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(S1), pages 515-532, April.
    5. Min Zheng, 2015. "Heterogeneous Expectations and Speculative Behavior in Insurance-Linked Securities," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-12, March.
    6. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2017. "Cohort effects in mortality modelling: a Bayesian state-space approach," Papers 1703.08282, arXiv.org.
    7. Chen, Hua & MacMinn, Richard & Sun, Tao, 2015. "Multi-population mortality models: A factor copula approach," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 135-146.
    8. Johnny Siu‐Hang Li & Andrew Cheuk‐Yin Ng, 2011. "Canonical Valuation of Mortality‐Linked Securities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(4), pages 853-884, December.
    9. Huang, Yu-Lieh & Tsai, Jeffrey Tzuhao & Yang, Sharon S. & Cheng, Hung-Wen, 2014. "Price bounds of mortality-linked security in incomplete insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 30-39.
    10. 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.
    11. Hua Chen & Michael Sherris & Tao Sun & Wenge Zhu, 2013. "Living With Ambiguity: Pricing Mortality-Linked Securities With Smooth Ambiguity Preferences," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 705-732, September.
    12. Liu, Yanxin & Li, Johnny Siu-Hang, 2015. "The age pattern of transitory mortality jumps and its impact on the pricing of catastrophic mortality bonds," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 135-150.
    13. Raj Kumari Bahl & Sotirios Sabanis, 2016. "Model-Independent Price Bounds for Catastrophic Mortality Bonds," Papers 1607.07108, arXiv.org, revised Dec 2020.
    14. Li, Johnny Siu-Hang, 2010. "Pricing longevity risk with the parametric bootstrap: A maximum entropy approach," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 176-186, October.
    15. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2016. "A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting," Papers 1605.09484, arXiv.org.
    16. Man Chung Fung & Katja Ignatieva & Michael Sherris, 2019. "Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives," Risks, MDPI, vol. 7(1), pages 1-25, January.
    17. Susanna Levantesi & Massimiliano Menzietti, 2017. "Maximum Market Price of Longevity Risk under Solvency Regimes: The Case of Solvency II," Risks, MDPI, vol. 5(2), pages 1-21, May.
    18. Man Chung Fung & Katja Ignatieva & Michael Sherris, 2015. "Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives," Papers 1508.00090, arXiv.org.
    19. Bauer, Daniel & Börger, Matthias & Ruß, Jochen, 2010. "On the pricing of longevity-linked securities," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 139-149, February.
    20. Yang, Bowen & Li, Jackie & Balasooriya, Uditha, 2015. "Using bootstrapping to incorporate model error for risk-neutral pricing of longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 16-27.

    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:82:y:2018:i:c:p:95-116. 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.