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On the calibration of mortality forward curves

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  • Johnny Siu‐Hang Li
  • Andrew Cheuk‐Yin Ng
  • Wai‐Sum Chan

Abstract

In 2007, a major investment bank launched a product called “q‐forward,” which may be regarded as a forward contract on a mortality rate. The pricing of mortality forwards is similar to the pricing of other forward‐rate contracts, such as interest‐rate forwards or foreign exchange forwards. In particular, since investors require compensation to take on longevity risk, the forward mortality rate at which q‐forward contracts will trade will be smaller than the expected mortality rate. The relationship between the forward rate and the time to maturity is called a mortality forward curve. In this study, we contribute a method for calibrating mortality forward curves. This method consists of two parts, one of which is the generation of the distribution of future mortality rates, and the other of which is the transformation of the distribution into its risk‐neutral counterpart, using the idea of canonical valuation developed by Stutzer, M. ( 1996 ). To illustrate the method, mortality forward curves for English and Welsh males are calibrated. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark

Suggested Citation

  • Johnny Siu‐Hang Li & Andrew Cheuk‐Yin Ng & Wai‐Sum Chan, 2011. "On the calibration of mortality forward curves," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(10), pages 947-970, October.
    • Handle: RePEc:wly:jfutmk:v:31:y:2011:i:10:p:947-970
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    Cited by:

    1. 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.
    2. Zhou, Rui & Li, Johnny Siu-Hang & Tan, Ken Seng, 2015. "Modeling longevity risk transfers as Nash bargaining problems: Methodology and insights," Economic Modelling, Elsevier, vol. 51(C), pages 460-472.
    3. Xu, Wei & Šević, Aleksandar & Šević, Željko, 2022. "Implied volatility surface construction for commodity futures options traded in China," Research in International Business and Finance, Elsevier, vol. 61(C).
    4. Tzuling Lin & Cary Chi‐Liang Tsai, 2023. "A new option for mortality–interest rates," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(2), pages 273-293, February.

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