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Statistics of Extreme Risks

  • Jürgen Franke
  • Wolfgang Härdle
  • Christian M. Hafner
Part of the Universitext book series (UTX)

Abstract

When we model returns using a GARCH process with normally distributed innovations, we have already taken into account the second stylized fact (see Chapter 12). The distribution of the random returns automatically has a leptokurtosis and larger losses occurring more frequently than under the assumption that the returns are normally distributed. If one is interested in the 95%-VaR of liquid assets, this approach produces the most useful results. For the extreme risk quantiles such as the 99%-VaR and for riskier types of investments the risk is often underestimated when the innovations are assumed to be normally distributed, since a higher probability of particularly extreme losses than a GARCH process ε t with normally distributed Z t can produce.

Keywords

Pareto Distribution Exceedance Probability Generalize Pareto Distribution Empirical Distribution Function Extremal Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Recommended Literature

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Jürgen Franke
    • 1
  • Wolfgang Härdle
    • 2
  • Christian M. Hafner
    • 3
  1. 1.University of KaiserslauternKaiserslauternGermany
  2. 2.CASE-Center for Applied Statistics and EconomicsHumboldt-Universität zu BerlinBerlinGermany
  3. 3.Econometric Institute, Faculty of EconomicsErasmus University RotterdamRotterdamThe Netherlands

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