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Measuring Tail Thickness under GARCH and an Application to Extreme Exchange Rate Changes


  • Niklas Wagner
  • Terry A. Marsh


Accurate modeling of extreme price changes is vital to financial risk management. We examine the small sample properties of adaptive tail index estimators under the class of student-t marginal distribution functions including GARCH and propose a model-based bias-corrected estimation approach. Our simulation results indicate that bias strongly relates to the underlying model and may be positively as well as negatively signed. The empirical study of daily exchange rate changes reveals substantial differences in measured tail-thickness due to small sample bias. As a consequence, high quantile estimation may lead to a substantial underestimation of tail risk.

Suggested Citation

  • Niklas Wagner & Terry A. Marsh, 2004. "Measuring Tail Thickness under GARCH and an Application to Extreme Exchange Rate Changes," Econometrics 0401008, EconWPA.
  • Handle: RePEc:wpa:wuwpem:0401008
    Note: Type of Document - pdf; prepared on win00; to print on laserjet; pages: 40

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    References listed on IDEAS

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    Cited by:

    1. Alex Yi-Hou Huang & Tsung-Wei Tseng, 2009. "Forecast of value at risk for equity indices: an analysis from developed and emerging markets," Journal of Risk Finance, Emerald Group Publishing, vol. 10(4), pages 393-409, August.
    2. Iglesias, Emma M. & Linton, Oliver, 2009. "Estimation of tail thickness parameters from GJR-GARCH models," UC3M Working papers. Economics we094726, Universidad Carlos III de Madrid. Departamento de Economía.
    3. Bollerslev, Tim & Todorov, Viktor & Li, Sophia Zhengzi, 2013. "Jump tails, extreme dependencies, and the distribution of stock returns," Journal of Econometrics, Elsevier, vol. 172(2), pages 307-324.
    4. Mohammad Karimi & Marcel Voia, 2015. "Identifying extreme values of exchange market pressure," Empirical Economics, Springer, vol. 48(3), pages 1055-1078, May.
    5. Vêlayoudom Marimoutou & Bechir Raggad & Abdelwahed Trabelsi, 2006. "Extreme Value Theory and Value at Risk : Application to Oil Market," Working Papers halshs-00410746, HAL.
    6. Wagner, Niklas, 2005. "Autoregressive conditional tail behavior and results on Government bond yield spreads," International Review of Financial Analysis, Elsevier, vol. 14(2), pages 247-261.
    7. Marimoutou, Velayoudoum & Raggad, Bechir & Trabelsi, Abdelwahed, 2009. "Extreme Value Theory and Value at Risk: Application to oil market," Energy Economics, Elsevier, vol. 31(4), pages 519-530, July.
    8. Beran, Jan & Schell, Dieter, 2012. "On robust tail index estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3430-3443.

    More about this item


    fat tails; tail index; stationary marginal distribution; GARCH; Hill estimator; foreign exchange;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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