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A double-exponential GARCH model for stochastic mortality

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Abstract

In this paper, a generalized GARCH-based stochastic mortality model is developed, which incorporates conditional heteroskedasticity and conditional non-normality. First, a detailed empirical analysis of the UK mortality rates from 1922 to 2009 is provided, where it was found that both the conditional heteroskedasticity and conditional non-normality are important empirical long-term structures of mortality. To describe conditional non-normality, a double-exponential distribution that allows conditional skewness and the heavy-tailed features found in the datasets was selected. For the practical implementation of the proposed model, a two-stage scheme was introduced to estimate the unknown parameters. First, the Quasi-Maximum Likelihood Estimation (QMLE) method was employed to estimate the GARCH structure. Next, the MLE was adopted to estimate the unknown parameters of the double-exponential distribution using residuals as input data. The model was then back-tested against the previous 10 years of mortality data to assess its forecasting ability, before Monte Carlo simulation was carried out to simulate and produce a table of forecast mortality rates from the optimal distribution.

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Authors and Affiliations

  1. Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, North Ryde, NSW, 2109, Australia

    Celeste M. H. Chai, Tak Kuen Siu & Xian Zhou

Authors
  1. Celeste M. H. Chai
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  2. Tak Kuen Siu
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  3. Xian Zhou
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Corresponding author

Correspondence to Celeste M. H. Chai.

Appendix: Forecasts of mortality rates

Appendix: Forecasts of mortality rates

See Tables 7, 8, 9

Table 7 Selected AR-GARCH and double-exponential parameters (age process)
Full size table
Table 8 Selected AR-GARCH and double-exponential parameters (time process)
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Table 9 Selected simulated death rates (age process) for years 2010–2014
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Chai, C.M.H., Siu, T.K. & Zhou, X. A double-exponential GARCH model for stochastic mortality. Eur. Actuar. J. 3, 385–406 (2013). https://doi.org/10.1007/s13385-013-0077-5

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  • DOI: https://doi.org/10.1007/s13385-013-0077-5

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