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Statistics of Extreme Risks

  • Szymon Borak
  • Wolfgang Karl Härdle
  • Brenda López-Cabrera
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. The random returns automatically have a leptokurtic distribution and larger losses occur 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 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 extreme losses can be produced.

References

  1. Breiman, L. (1973). Statistics: With a view towards application. Boston: Houghton Mifflin Company.Google Scholar
  2. Cizek, P., Härdle, W., & Weron, R. (2011). Statistical tools in finance and insurance (2nd ed.). Berlin/Heidelberg: Springer.Google Scholar
  3. Feller, W. (1966). An introduction to probability theory and its application (Vol. 2). New York: Wiley.Google Scholar
  4. Franke, J., Härdle, W., & Hafner, C. (2011). Statistics of financial markets (3rd ed.). Berlin/ Heidelberg: Springer.Google Scholar
  5. Härdle, W., & Simar, L. (2012). Applied multivariate statistical analysis (3rd ed.). Berlin: Springer.Google Scholar
  6. Härdle, W., Müller, M., Sperlich, S., & Werwatz, A. (2004). Nonparametric and semiparametric models. Berlin: Springer.Google Scholar
  7. Harville, D. A. (2001). Matrix algebra: Exercises and solutions. New York: Springer.Google Scholar
  8. Klein, L. R. (1974). A textbook of econometrics (2nd ed., 488 p.). Englewood Cliffs: Prentice Hall.Google Scholar
  9. MacKinnon, J. G. (1991). Critical values for cointegration tests. In R. F. Engle & C. W. J. Granger (Eds.), Long-run economic relationships readings in cointegration (pp. 266–277). New York: Oxford University Press.Google Scholar
  10. Mardia, K. V., Kent, J. T., & Bibby, J. M. (1979). Multivariate analysis. Duluth/London: Academic.Google Scholar
  11. RiskMetrics. (1996). J.P. Morgan/Reuters (4th ed.). RiskMetricsTM.Google Scholar
  12. Serfling, R. J. (2002). Approximation theorems of mathematical statistics. New York: Wiley.Google Scholar
  13. Tsay, R. S. (2002). Analysis of financial time series. New York: Wiley.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Szymon Borak
    • 1
  • Wolfgang Karl Härdle
    • 1
  • Brenda López-Cabrera
    • 1
  1. 1.Humboldt-Universität zu Berlin Ladislaus von Bortkiewicz Chair of StatisticsC.A.S.E. Centre for Applied Statistics and Economics School of Business and EconomicsBerlinGermany

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