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2015 | Modelowanie wielowymiarowych struktur danych i analiza ryzyka | 22--40
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Modeling of the extreme risk

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EV-VaR has some advantages over traditional parametric and nonparame- tric approach to VaR. Parametric approaches estimate VaR by fitting distribution to a set of observed returns. We used some statistics hypothesis and use statistical tests. We accommodate the mass of central observations, rather than the tail observation, that is more important for VaR purposes. Nonparametric and historical simulation approach estimate VaR by reading from a histogram of returns. But they give less efficient VaR estimates than EV approaches. The very important limitation is that methods tell us noting whatever about VaR beyond our sample range. EVT deals with the frequency and magnitude of very low probability events. Additionally, because extreme events are extreme, we have small data sets and this means that all estimators - quantile estimators, VaR and estimated probabilities associated with this extreme values - are very imprecise. However, EVT makes the best out of an inherently difficult problem, therefore marks a significant step forward in VaR estimation. Application of EVT requires an appreciation of strengths and limitations, but it can be useful. (fragment of text)
  • University of Economics in Katowice, Poland
  • Drees H. (2003), Extreme Quantile Estimation for Dependent Data with Applications to Finance, "Bernoulli", 9.
  • Drees H., Reiss R.-D. (1992), Tail Behavior in WickselTs Corpuscle Problem [in:] J. Galambos, I. Katai (eds.), Probability Theoiy and Applications, Kluwer, Dortrecht.
  • Jenkinson A.F. (1955), The Frequency Distribution of Annual Maximum (or Minimum) Values of Meteorological Elements, "Quarterly Journal of the Royal Meteorological Society", 81.
  • Mises R. von (1936), La distribution de la plus grande de n valeurs, "Rev. Math. Union Interbalcanique", 1. Reproduced in Selected Papers of Richard von Mises, "American Mathematical Society" 1964, 2.
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