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In the core of longevity risk: hidden dependence in stochastic mortality models and cut-offs in prices of longevity swaps

Author

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  • Stéphane Loisel

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Daniel Serant

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

In most stochastic mortality models, either one stochastic intensity process (for example a jump-diffusion process) or a collection of independent processes is used to model the stochastic evolution of survival probabilities. We propose and calibrate a new model that takes inter-age correlations into account. The so-called stochastic logit's Deltas model is based on the study of the multivariate time series of the differences of logits of yearly mortality rates. These correlations are important and we illustrate our study on a real-life portfolio. We determine their impact on the price of a longevity swap type reinsurance contract, in which most of the financial risk is taken by a third party. The hypotheses of our model are statistically tested and various measures of risk of the present value of liabilities are found to be significantly smaller in our model than in the case of one common underlying stochastic process.

Suggested Citation

  • Stéphane Loisel & Daniel Serant, 2007. "In the core of longevity risk: hidden dependence in stochastic mortality models and cut-offs in prices of longevity swaps," Working Papers hal-00201393, HAL.
    • Handle: RePEc:hal:wpaper:hal-00201393
    Note: View the original document on HAL open archive server: https://hal.science/hal-00201393
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    Cited by:

    1. Paul Doukhan & Joseph Rynkiewicz & Yahia Salhi, 2021. "Optimal Neighborhood Selection for AR-ARCH Random Fields with Application to Mortality," Stats, MDPI, vol. 5(1), pages 1-26, December.
    2. Chou-Wen Wang & Sharon S. Yang, 2013. "Pricing Survivor Derivatives With Cohort Mortality Dependence Under the Lee–Carter Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 1027-1056, December.
    3. 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.
    4. Apostolos Bozikas & Ioannis Badounas & Georgios Pitselis, 2022. "Pricing Longevity Bonds under a Credibility Framework with Limited Available Data," Risks, MDPI, vol. 10(5), pages 1-15, May.
    5. Rihab Bedoui & Islem Kedidi, 2018. "Modeling Longevity Risk using Consistent Dynamics Affine Mortality Models," Working Papers hal-01678050, HAL.

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