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Modeling and pricing longevity derivatives using Skellam distribution

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  • Kung, Ko-Lun
  • Liu, I-Chien
  • Wang, Chou-Wen

Abstract

We propose a novel mortality improvement model with the difference of death counts follows the Skellam distribution. We extend Mitchell et al. (2013) by considering the difference in Poisson death counts instead of the ratio of subsequent mortality rate, which does not have a known distribution. We derive the iterative estimators of the model from the Skellam distribution. Our model can employ maximum likelihood estimation for estimation issues such as missing data and provides a better fit than Mitchell et al. (2013). Using English and Wales mortality rate age 0-89 data during 1950-2016, the model estimate suggests that the age-dependent mortality improvement is slower than the benchmark, which coincides with a recent observation by Office for National Statistics (2018). The forecasting performance outperforms the Poisson and M10 model. We make inferences on the price of longevity swaps and analyze how the volatility shock of mortality improvement affects the premium of longevity swaps.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:insuma:v:99:y:2021:i:c:p:341-354
    DOI: 10.1016/j.insmatheco.2021.04.002
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    References listed on IDEAS

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    More about this item

    Keywords

    Mortality modeling; Skellam distribution; Mortality forecasting; Longevity swaps; Heavy tail;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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