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Nonparametric risk management with generalized hyperbolic distributions

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  • Chen, Ying
  • Härdle, Wolfgang Karl
  • Jeong, Seok-Oh

Abstract

In this paper we propose the GHADA risk management model that is based on the generalized hyperbolic (GH) distribution and on a nonparametric adaptive methodology. Compared to the normal distribution, the GH distribution possesses semi-heavy tails and represents the financial risk factors more appropriately. The nonparametric adaptive methodology has the desirable property of estimating homogeneous volatility in a short time interval. For DEM/USD exchange rate data and a German bank portfolio data the proposed GHADA model provides more accurate value at risk calculation than the traditional model based on the normal distribution. All calculations and simulations are done with XploRe.

Suggested Citation

  • Chen, Ying & Härdle, Wolfgang Karl & Jeong, Seok-Oh, 2005. "Nonparametric risk management with generalized hyperbolic distributions," SFB 649 Discussion Papers 2005-001, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2005-001
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    References listed on IDEAS

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    1. Wolfgang Hardle & Helmut Herwartz & Vladimir Spokoiny, 2003. "Time Inhomogeneous Multiple Volatility Modeling," Journal of Financial Econometrics, Oxford University Press, vol. 1(1), pages 55-95.
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    Cited by:

    1. Fengler, Matthias & Okhrin, Ostap, 2012. "Realized Copula," Economics Working Paper Series 1214, University of St. Gallen, School of Economics and Political Science.
    2. Willmot, Gordon E. & Woo, Jae-Kyung, 2022. "Remarks on a generalized inverse Gaussian type integral with applications," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    3. J. Hambuckers & C. Heuchenne, 2017. "A robust statistical approach to select adequate error distributions for financial returns," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(1), pages 137-161, January.
    4. Michal Skorepa, 2014. "Concurrent Capital Buffers in a Banking Group," Occasional Publications - Chapters in Edited Volumes, in: CNB Financial Stability Report 2013/2014, chapter 0, pages 128-136, Czech National Bank, Research and Statistics Department.
    5. Mencía, Javier & Sentana, Enrique, 2009. "Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation," Journal of Econometrics, Elsevier, vol. 153(2), pages 105-121, December.
    6. Fengler, Matthias R. & Okhrin, Ostap, 2016. "Managing risk with a realized copula parameter," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 131-152.
    7. Chen, Ying & Härdle, Wolfgang Karl & Spokoiny, Vladimir, 2005. "Portfolio value at risk based on independent components analysis," SFB 649 Discussion Papers 2005-060, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. Saralees Nadarajah & Bo Zhang & Stephen Chan, 2014. "Estimation methods for expected shortfall," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 271-291, February.
    9. Adam Misiorek & Rafal Weron, 2010. "Heavy-tailed distributions in VaR calculations," HSC Research Reports HSC/10/05, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    10. Beatrice Foroni & Luca Merlo & Lea Petrella, 2024. "Hidden Markov graphical models with state-dependent generalized hyperbolic distributions," Papers 2412.03668, arXiv.org.
    11. Borak, Szymon & Misiorek, Adam & Weron, Rafał, 2010. "Models for heavy-tailed asset returns," SFB 649 Discussion Papers 2010-049, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    12. Julien Chevallier & Stéphane Goutte, 2017. "Estimation of Lévy-driven Ornstein–Uhlenbeck processes: application to modeling of $$\hbox {CO}_2$$ CO 2 and fuel-switching," Annals of Operations Research, Springer, vol. 255(1), pages 169-197, August.
    13. d’Addona, Stefano & Khanom, Najrin, 2022. "Estimating tail-risk using semiparametric conditional variance with an application to meme stocks," International Review of Economics & Finance, Elsevier, vol. 82(C), pages 241-260.
    14. Härdle Wolfgang Karl & Okhrin Ostap & Okhrin Yarema, 2013. "Dynamic structured copula models," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 361-388, December.
    15. Seok-Oh Jeong & Kee-Hoon Kang, 2009. "Nonparametric estimation of value-at-risk," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(11), pages 1225-1238.
    16. Alexios Ghalanos & Eduardo Rossi & Giovanni Urga, 2015. "Independent Factor Autoregressive Conditional Density Model," Econometric Reviews, Taylor & Francis Journals, vol. 34(5), pages 594-616, May.
    17. Yuru Sun & Worapree Maneesoonthorn & Ruben Loaiza-Maya & Gael M. Martin, 2023. "Optimal probabilistic forecasts for risk management," Papers 2303.01651, arXiv.org.
    18. repec:hum:wpaper:sfb649dp2012-034 is not listed on IDEAS
    19. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    20. Härdle, Wolfgang Karl & Okhrin, Ostap & Okhrin, Yarema, 2010. "Time varying hierarchical archimedean copulae," SFB 649 Discussion Papers 2010-018, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    21. Chen, Ying & Härdle, Wolfgang & Spokoiny, Vladimir, 2010. "GHICA -- Risk analysis with GH distributions and independent components," Journal of Empirical Finance, Elsevier, vol. 17(2), pages 255-269, March.

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