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From deterministic to stochastic surrender risk models: impact of correlation crises on economic capital

Author

Listed:
  • Stéphane Loisel

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

  • Xavier Milhaud

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

Abstract

In this paper we raise the matter of considering a stochastic modeling of the surrender rate instead of the classical S-shaped deterministic curve (in function of the spread), still used in almost all insurance companies. A stochastic model in which surrenders are conditionally independent with respect to a S-curve disturbance would be tempting in some extreme scenarii, especially to address the question of the lack of data. However, we explain why this conditional independence between policyholders, which has the advantage to be the simplest assumption, looks particularly maladaptive when the spread increases. Indeed the correlation between policyholders' decisions is most likely to increase in this situation. We suggest and develop a simple model which integrates those phenomena. With stochastic orders it is possible to compare it to the conditional independence approach qualitatively. In an partially internal Solvency II model, we quantify the impact of the correlation phenomenon on a real life portfolio for a global risk management strategy.

Suggested Citation

  • Stéphane Loisel & Xavier Milhaud, 2011. "From deterministic to stochastic surrender risk models: impact of correlation crises on economic capital," Post-Print hal-00502847, HAL.
  • Handle: RePEc:hal:journl:hal-00502847
    DOI: 10.1016/j.ejor.2011.04.038
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00502847
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    References listed on IDEAS

    as
    1. Laurent Devineau & Stéphane Loisel, 2009. "Risk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula?," Post-Print hal-00403662, HAL.
    2. Xavier Milhaud & Marie-Pierre Gonon & Stéphane Loisel, 2010. "Les comportements de rachat en Assurance Vie en régime de croisière et en période de crise," Post-Print hal-00502851, HAL.
    3. Biard, Romain & Lefèvre, Claude & Loisel, Stéphane, 2008. "Impact of correlation crises in risk theory: Asymptotics of finite-time ruin probabilities for heavy-tailed claim amounts when some independence and stationarity assumptions are relaxed," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 412-421, December.
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    Cited by:

    1. Barsotti, Flavia & Milhaud, Xavier & Salhi, Yahia, 2016. "Lapse risk in life insurance: Correlation and contagion effects among policyholders’ behaviors," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 317-331.
    2. Guillou, Armelle & Loisel, Stéphane & Stupfler, Gilles, 2013. "Estimation of the parameters of a Markov-modulated loss process in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 388-404.
    3. Christophe Dutang & Hansjoerg Albrecher & Stéphane Loisel, 2013. "Competition among non-life insurers under solvency constraints: A game-theoretic approach," Post-Print hal-01616156, HAL.
    4. Martin Eling & Michael Kochanski, 2013. "Research on lapse in life insurance: what has been done and what needs to be done?," Journal of Risk Finance, Emerald Group Publishing, vol. 14(4), pages 392-413, August.
    5. Fabrice Borel-Mathurin & Pierre-Emmanuel Darpeix & Quentin Guibert & Stéphane Loisel, 2015. "Main Determinants of Profit Sharing Policy in the French Life Insurance Industry," Working Papers halshs-01165475, HAL.
    6. Bensusan, Harry & El Karoui, Nicole & Loisel, Stéphane & Salhi, Yahia, 2016. "Partial splitting of longevity and financial risks: The longevity nominal choosing swaptions," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 61-72.
    7. Marcos Escobar & Mikhail Krayzler & Franz Ramsauer & David Saunders & Rudi Zagst, 2016. "Incorporation of Stochastic Policyholder Behavior in Analytical Pricing of GMABs and GMDBs," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-36, November.
    8. Dutang, Christophe & Albrecher, Hansjoerg & Loisel, Stéphane, 2013. "Competition among non-life insurers under solvency constraints: A game-theoretic approach," European Journal of Operational Research, Elsevier, vol. 231(3), pages 702-711.
    9. F. Borel-Mathurin & P.-E. Darpeix & Q. Guibert & S. Loisel, 2015. "Main determinants of profit sharing policy in the French life insurance industry," Débats économiques et financiers 17, Banque de France.
    10. Feodoria, Mark & Förstemann, Till, 2015. "Lethal lapses: How a positive interest rate shock might stress German life insurers," Discussion Papers 12/2015, Deutsche Bundesbank.
    11. Xavier Milhaud & Marie-Pierre Gonon & Stéphane Loisel, 2010. "Les comportements de rachat en Assurance Vie en régime de croisière et en période de crise," Post-Print hal-00502851, HAL.

    More about this item

    Keywords

    risk management; applied probability; life insurance; surrender risk; correlation risk;

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