IDEAS home Printed from https://ideas.repec.org/a/taf/uaajxx/v18y2014i1p22-37.html
   My bibliography  Save this article

Modeling and Pricing Longevity Derivatives Using Stochastic Mortality Rates and the Esscher Transform

Author

Listed:
  • Shuo-Li Chuang
  • Patrick Brockett

Abstract

The Lee-Carter mortality model provides a structure for stochastically modeling mortality rates incorporating both time (year) and age mortality dynamics. Their model is constructed by modeling the mortality rate as a function of both an age and a year effect. Recently the MBMM model (Mitchell et al. 2013) showed the Lee Carter model can be improved by fitting with the growth rates of mortality rates over time and age rather than the mortality rates themselves. The MBMM modification of the Lee-Carter model performs better than the original and many of the subsequent variants. In order to model the mortality rate under the martingale measure and to apply it for pricing the longevity derivatives, we adapt the MBMM structure and introduce a Lévy stochastic process with a normal inverse Gaussian (NIG) distribution in our model. The model has two advantages in addition to better fit: first, it can mimic the jumps in the mortality rates since the NIG distribution is fat-tailed with high kurtosis, and, second, this mortality model lends itself to pricing of longevity derivatives based on the assumed mortality model. Using the Esscher transformation we show how to find a related martingale measure, allowing martingale pricing for mortality/longevity risk–related derivatives. Finally, we apply our model to pricing a q-forward longevity derivative utilizing the structure proposed by Life and Longevity Markets Association.

Suggested Citation

  • Shuo-Li Chuang & Patrick Brockett, 2014. "Modeling and Pricing Longevity Derivatives Using Stochastic Mortality Rates and the Esscher Transform," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 22-37.
    • Handle: RePEc:taf:uaajxx:v:18:y:2014:i:1:p:22-37
    DOI: 10.1080/10920277.2013.873708
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10920277.2013.873708
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10920277.2013.873708?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.

    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. 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. 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.
    4. Wang, Ling & Chiu, Mei Choi & Wong, Hoi Ying, 2021. "Volterra mortality model: Actuarial valuation and risk management with long-range dependence," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 1-14.
    5. Liu, Yanxin & Li, Johnny Siu-Hang, 2018. "A strategy for hedging risks associated with period and cohort effects using q-forwards," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 267-285.
    6. Kung, Ko-Lun & Liu, I-Chien & Wang, Chou-Wen, 2021. "Modeling and pricing longevity derivatives using Skellam distribution," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 341-354.
    7. Ling Wang & Mei Choi Chiu & Hoi Ying Wong, 2020. "Volterra mortality model: Actuarial valuation and risk management with long-range dependence," Papers 2009.09572, arXiv.org.

    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:taf:uaajxx:v:18:y:2014:i:1:p:22-37. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/uaaj .

    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.