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An improved approach for estimating large losses in insurance analytics and operational risk using the g-and-h distribution

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Listed:
  • Marco Bee
  • Julien Hambuckers
  • Luca Trapin

Abstract

In this paper, we study the estimation of parameters for g-and-h distributions. These distributions find applications in modeling highly skewed and fat-tailed data, like extreme losses in the banking and insurance sector. We first introduce two estimation methods: a numerical maximum likelihood technique, and an indirect inference approach with a bootstrap weighting scheme. In a realistic simulation study, we show that indirect inference is computationally more efficient and provides better estimates in case of extreme features of the data. Empirical illustrations on insurance and operational losses illustrate these findings.

Suggested Citation

  • Marco Bee & Julien Hambuckers & Luca Trapin, 2019. "An improved approach for estimating large losses in insurance analytics and operational risk using the g-and-h distribution," DEM Working Papers 2019/11, Department of Economics and Management.
    • Handle: RePEc:trn:utwprg:2019/11
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    References listed on IDEAS

    as
    1. Bill Ding & Hany A. Shawky, 2007. "The Performance of Hedge Fund Strategies and the Asymmetry of Return Distributions," European Financial Management, European Financial Management Association, vol. 13(2), pages 309-331, March.
    2. Degen, Matthias & Embrechts, Paul & Lambrigger, Dominik D., 2007. "The Quantitative Modeling of Operational Risk: Between G-and-H and EVT," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 265-291, November.
    3. M. Bee & J. Hambuckers & L. Trapin, 2019. "Estimating Value-at-Risk for the g-and-h distribution: an indirect inference approach," Quantitative Finance, Taylor & Francis Journals, vol. 19(8), pages 1255-1266, August.
    4. Julien Hambuckers & Andreas Groll & Thomas Kneib, 2018. "Understanding the economic determinants of the severity of operational losses: A regularized generalized Pareto regression approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(6), pages 898-935, September.
    5. Gareth W. Peters & Wilson Y. Chen & Richard H. Gerlach, 2016. "Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-moments," Papers 1603.01041, arXiv.org.
    6. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    7. Gareth W. Peters & Wilson Ye Chen & Richard H. Gerlach, 2016. "Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-Moments," Risks, MDPI, vol. 4(2), pages 1-41, May.
    8. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    9. Kabir Dutta & Jason Perry, 2006. "A tale of tails: an empirical analysis of loss distribution models for estimating operational risk capital," Working Papers 06-13, Federal Reserve Bank of Boston.
    10. Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004. "Constrained Indirect Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(4), pages 945-973.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Intractable likelihood; indirect inference; skewed distribution; tail modeling; bootstrap;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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