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Nonparametric Risk Management with Generalized Hyperbolic Distributions

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  • Ying Chen
  • Wolfgang Härdle
  • Seok-Oh Jeong

Abstract

In this paper we propose the GHADA risk management model that is based on the gener- alized hyperbolic (GH) distribution and on a nonparametric adaptive methodology. Com- pared to the normal distribution, the GH distribution possesses semi-heavy tails and repre- sents the financial risk factors more appropriately. The nonparametric adaptive methodol- ogy 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

  • Ying Chen & Wolfgang Härdle & Seok-Oh Jeong, 2004. "Nonparametric Risk Management with Generalized Hyperbolic Distributions," SFB 649 Discussion Papers SFB649DP2005-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2005-001
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    References listed on IDEAS

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    1. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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    Cited by:

    1. Pavel Cizek & Karel Komorad, 2005. "Implied Trinomial Trees," SFB 649 Discussion Papers SFB649DP2005-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Ying Chen & Wolfgang Härdle & Vladimir Spokoiny, 2006. "GHICA - Risk Analysis with GH Distributions and Independent Components," SFB 649 Discussion Papers SFB649DP2006-078, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Ying Chen & Wolfgang Härdle & Vladimir Spokoiny, 2005. "Portfolio Value at Risk Based on Independent Components Analysis," SFB 649 Discussion Papers SFB649DP2005-060, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Stefan Kassberger & Rüdiger Kiesel, 2006. "A fully parametric approach to return modelling and risk management of hedge funds," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 20(4), pages 472-491, December.
    5. Yu, Yaming, 2017. "On normal variance–mean mixtures," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 45-50.

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    Keywords

    adaptive volatility estimation; generalized hyperbolic distribution; value at risk; risk management;
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