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Estimating Value-at-Risk for the g-and-h distribution: an indirect inference approach

Author

Listed:
  • Marco Bee
  • Julien Hambuckers
  • Luca Trapin

Abstract

TThe g-and-h distribution is a flexible model with desirable theoretical properties. Especially, it is able to handle well the complex behavior of loss data and it is suitable for VaR estimation when large skewness and kurtosis are at stake. However, parameter estimation is di cult, because the density cannot be written in closed form. In this paper we develop an indirect inference method using the skewed- t distribution as instrumental model. We show that the skewed-t is a well suited auxiliary model and study the numerical issues related to its implementation. A Monte Carlo analysis and an application to operational losses suggest that the indirect inference estimators of the parameters and of the VaR outperform the quantile-based estimators.

Suggested Citation

  • Marco Bee & Julien Hambuckers & Luca Trapin, 2018. "Estimating Value-at-Risk for the g-and-h distribution: an indirect inference approach," DEM Working Papers 2018/08, Department of Economics and Management.
    • Handle: RePEc:trn:utwprg:2018/08
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    References listed on IDEAS

    as
    1. Andreas Jobst, 2007. "Consistent Quantitative Operational Risk Measurement and Regulation: Challenges of Model Specification, Data Collection and Loss Reporting," IMF Working Papers 2007/254, International Monetary Fund.
    2. repec:ulb:ulbeco:2013/136280 is not listed on IDEAS
    3. Dominicy, Yves & Veredas, David, 2013. "The method of simulated quantiles," Journal of Econometrics, Elsevier, vol. 172(2), pages 235-247.
    4. 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.
    5. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    6. Garcia, René & Renault, Eric & Veredas, David, 2011. "Estimation of stable distributions by indirect inference," Journal of Econometrics, Elsevier, vol. 161(2), pages 325-337, April.
    7. Giuseppe Galloppo & Alessandro Rogora, 2011. "What Has Worked In Operational Risk?," Global Journal of Business Research, The Institute for Business and Finance Research, vol. 5(3), pages 1-17.
    8. 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.
    9. Rene Garcia & Eric Renault & David Veredas, 2011. "Estimation of stable distributions with indirect inference," ULB Institutional Repository 2013/136186, ULB -- Universite Libre de Bruxelles.
    10. Kabir K. Dutta & David F. Babbel, 2002. "On Measuring Skewness and Kurtosis in Short Rate Distributions: The Case of the US Dollar London Inter Bank Offer Rates," Center for Financial Institutions Working Papers 02-25, Wharton School Center for Financial Institutions, University of Pennsylvania.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. Marco Bee, 2022. "The truncated g-and-h distribution: estimation and application to loss modeling," Computational Statistics, Springer, vol. 37(4), pages 1771-1794, September.

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    More about this item

    Keywords

    Value-at-Risk; g-and-h distribution; loss model; indirect infer- ence; simulation; intractable likelihood;
    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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