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Actuarial Applications and Estimation of Extended CreditRisk+

Author

Listed:
  • Jonas Hirz

    (BELTIOS GmbH, Lehargasse 1, Vienna 1060, Austria)

  • Uwe Schmock

    (Department of Financial and Actuarial Mathematics, TU Wien, Wiedner Hauptstr. 8–10, Vienna 1040, Austria)

  • Pavel V. Shevchenko

    (Department of Applied Finance and Actuarial Studies, Macquarie University, NSW 2109, Australia)

Abstract

We introduce an additive stochastic mortality model which allows joint modelling and forecasting of underlying death causes. Parameter families for mortality trends can be chosen freely. As model settings become high dimensional, Markov chain Monte Carlo (MCMC) is used for parameter estimation. We then link our proposed model to an extended version of the credit risk model CreditRisk+. This allows exact risk aggregation via an efficient numerically stable Panjer recursion algorithm and provides numerous applications in credit, life insurance and annuity portfolios to derive P&L distributions. Furthermore, the model allows exact (without Monte Carlo simulation error) calculation of risk measures and their sensitivities with respect to model parameters for P&L distributions such as value-at-risk and expected shortfall. Numerous examples, including an application to partial internal models under Solvency II, using Austrian and Australian data are shown.

Suggested Citation

  • Jonas Hirz & Uwe Schmock & Pavel V. Shevchenko, 2017. "Actuarial Applications and Estimation of Extended CreditRisk+," Risks, MDPI, vol. 5(2), pages 1-29, March.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:2:p:23-:d:94636
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    References listed on IDEAS

    as
    1. Fung, Man Chung & Peters, Gareth W. & Shevchenko, Pavel V., 2017. "A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting," Annals of Actuarial Science, Cambridge University Press, vol. 11(2), pages 343-389, September.
    2. Andrew Cairns & David Blake & Kevin Dowd & Guy Coughlan & David Epstein & Alen Ong & Igor Balevich, 2009. "A Quantitative Comparison of Stochastic Mortality Models Using Data From England and Wales and the United States," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(1), pages 1-35.
    3. Pavel V. Shevchenko & Jonas Hirz & Uwe Schmock, 2015. "Forecasting Leading Death Causes in Australia using Extended CreditRisk$+$," Papers 1507.07162, arXiv.org.
    4. Alai, Daniel H. & Arnold (-Gaille), Séverine & Sherris, Michael, 2015. "Modelling cause-of-death mortality and the impact of cause-elimination," Annals of Actuarial Science, Cambridge University Press, vol. 9(1), pages 167-186, March.
    5. Schmock, Uwe, 1999. "Estimating the Value of the Wincat Coupons of the Winterthur Insurance Convertible Bond: A Study of the Model Risk1," ASTIN Bulletin, Cambridge University Press, vol. 29(1), pages 101-163, May.
    6. Booth, H. & Tickle, L., 2008. "Mortality Modelling and Forecasting: a Review of Methods," Annals of Actuarial Science, Cambridge University Press, vol. 3(1-2), pages 3-43, September.
    7. Stefan Gerhold & Uwe Schmock & Richard Warnung, 2010. "A generalization of Panjer’s recursion and numerically stable risk aggregation," Finance and Stochastics, Springer, vol. 14(1), pages 81-128, January.
    8. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    9. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.
    10. Johnny Li & Mary Hardy, 2011. "Measuring Basis Risk in Longevity Hedges," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 177-200.
    11. Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272.
    12. Sundt, Bjørn, 1999. "On Multivariate Panjer Recursions," ASTIN Bulletin, Cambridge University Press, vol. 29(1), pages 29-45, May.
    13. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2015. "A State-Space Estimation of the Lee-Carter Mortality Model and Implications for Annuity Pricing," Papers 1508.00322, arXiv.org.
    14. Godfrey, Leslie G, 1978. "Testing against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1293-1301, November.
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    Cited by:

    1. Pavel V. Shevchenko, 2018. "Special Issue “Ageing Population Risks”," Risks, MDPI, vol. 6(1), pages 1-2, March.
    2. Søren Kjærgaard & Yunus Emre Ergemen & Malene Kallestrup-Lamb & Jim Oeppen & Rune Lindahl-Jacobsen, 2019. "Forecasting Causes of Death using Compositional Data Analysis: the Case of Cancer Deaths," CREATES Research Papers 2019-07, Department of Economics and Business Economics, Aarhus University.

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