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

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  • Niklas Wagner
  • Terry A. Marsh

Abstract

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, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0401008
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    Cited by:

    1. Iglesias, Emma M., 2015. "Value at Risk of the main stock market indexes in the European Union (2000–2012)," Journal of Policy Modeling, Elsevier, vol. 37(1), pages 1-13.
    2. 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.
    3. 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.
    4. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    5. Lu, Xinjie & Zeng, Qing & Zhong, Juandan & Zhu, Bo, 2024. "International stock market volatility: A global tail risk sight," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 91(C).
    6. Vêlayoudom Marimoutou & Bechir Raggad & Abdelwahed Trabelsi, 2006. "Extreme Value Theory and Value at Risk : Application to Oil Market," Working Papers halshs-00410746, HAL.
    7. Mohammad Karimi & Marcel Voia, 2015. "Identifying extreme values of exchange market pressure," Empirical Economics, Springer, vol. 48(3), pages 1055-1078, May.
    8. Emma M. Iglesias, 2012. "An analysis of extreme movements of exchange rates of the main currencies traded in the Foreign Exchange market," Applied Economics, Taylor & Francis Journals, vol. 44(35), pages 4631-4637, December.
    9. Dai, Yun-Shi & Dai, Peng-Fei & Zhou, Wei-Xing, 2023. "Tail dependence structure and extreme risk spillover effects between the international agricultural futures and spot markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 88(C).
    10. Raj Aggarwal & Min Qi, 2009. "Distribution of extreme changes in Asian currencies: tail index estimates and value-at-risk calculations," Applied Financial Economics, Taylor & Francis Journals, vol. 19(13), pages 1083-1102.
    11. 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.
    12. 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.
    13. Aboura, Sofiane & Wagner, Niklas, 2016. "Extreme asymmetric volatility: Stress and aggregate asset prices," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 41(C), pages 47-59.
    14. Horváth, Roman & Šopov, Boril, 2016. "GARCH models, tail indexes and error distributions: An empirical investigation," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 1-15.
    15. Iglesias, Emma M., 2015. "Value at Risk and expected shortfall of firms in the main European Union stock market indexes: A detailed analysis by economic sectors and geographical situation," Economic Modelling, Elsevier, vol. 50(C), pages 1-8.
    16. 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.
    17. Emma M. Iglesias & Mar�a Dolores Lagoa Varela, 2012. "Extreme movements of the main stocks traded in the Eurozone: an analysis by sectors in the 2000's decade," Applied Financial Economics, Taylor & Francis Journals, vol. 22(24), pages 2085-2100, December.
    18. Beran, Jan & Schell, Dieter, 2012. "On robust tail index estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3430-3443.
    19. Riedel, Christoph & Wagner, Niklas, 2015. "Is risk higher during non-trading periods? The risk trade-off for intraday versus overnight market returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 39(C), pages 53-64.

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    More about this item

    Keywords

    fat tails; tail index; stationary marginal distribution; GARCH; Hill estimator; foreign exchange;
    All these keywords.

    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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