Advertisement

Statistics of Extreme Risks

  • Jürgen FrankeEmail author
  • Wolfgang Karl Härdle
  • Christian Matthias Hafner
Chapter
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 stylised fact (see Chapter 13.). 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 there is a higher probability of particularly extreme losses than a GARCH process "t with normally distributed Zt can produce.

Keywords

Pareto Distribution Exceedance Probability Generalise Pareto Distribution Extremal Index Gumbel Distribution 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jürgen Franke
    • 1
    Email author
  • Wolfgang Karl Härdle
    • 2
    • 3
  • Christian Matthias Hafner
    • 4
  1. 1.FB MathematikTU KaiserslauternKaiserslauternGermany
  2. 2.Ladislaus von Bortkiewicz Chair of Statistics C.A.S.E. Centre for Applied Statistics and Economics School of Business and EconomicsHumboldt-Universität zu BerlinBerlinGermany
  3. 3.Graduate Institute of StatisticsNational Central UniversityJhongliTaiwan
  4. 4.Inst. StatistiqueUniversité Catholique de LouvainLeuven-la-NeuveBelgium

Personalised recommendations