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Majewska Justyna (University of Economics in Katowice, Poland)
Applications of extreme value mixture models to the global stock exchanges
Prace Naukowe / Uniwersytet Ekonomiczny w Katowicach. Modelowanie wielowymiarowych struktur danych i analiza ryzyka, 2015, s. 65-81, tab., wykr., bibliogr. 7 poz.
Słowa kluczowe
Zarządzanie ryzykiem, Modele matematyczne, Modele ekonometryczne, Giełda
Risk management, Mathematical models, Econometric models, Stock exchange
During the last decade financial markets have realized the importance of monitoring the risk. The classical variance does not provide us information "if things go wrong, how wrong they can be". Measures which are the functions of extreme quantiles of the data distribution allows us to answer this question. But the first task is to identify which values are extreme. In practice this is done by graphical methods or by other ad hoc methods that impose an arbitrary threshold (5%, 10%, ...). The threshold selection is a challenging area in the extreme value literature. In some cases, it is likely that there are multiple suitable thresholds in some datasets. Different threshold choice may result in different tail behavior and corresponding with different return levels. This chapter reviews the key historical threshold estimation approaches for extreme value applications and the latest developments. There is a certain focus on recently developed mixture model approach, which deals with both estimation and formal uncertainty quantification. We also present an empirical application where the extreme values of financial indexes of major stock markets are identified via presented methods. (fragment of text)
Dostępne w
Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie
Biblioteka Główna Uniwersytetu Ekonomicznego w Katowicach
Biblioteka Główna Uniwersytetu Ekonomicznego w Poznaniu
Biblioteka Główna Uniwersytetu Ekonomicznego we Wrocławiu
  1. Behrens C.N., Lopes H.F., Gamerman D. (2004), Bayesian Analysis of Extreme Events with Threshold Estimation, "Statistical Modelling", 4(3).
  2. Coles S. (2001), An Introduction to Statistical Modeling of Extreme Values, Springer Series in Statistics, Springer-Verlag, London.
  3. Embrechts P., Kluppelberg C., Mikosch T. (1997), Modelling Extremal Events for Insurance and Finance. Applications of Mathematics, Springer-Verlag, New York.
  4. Embrechts P., Lindskog F., McNeil A. (2003), Handbook of Heavy Tailed Distributions in Finance, Chapter 8, Modelling Dependence With Copulas And Applications To Risk Management, Handbooks in Finance, Elsevier.
  5. Scarrott C.J., MacDonald A.E. (2012), A Review of Extreme Value Threshold Estimation and Uncertainty Quantification, "REVSTAT Statistical Journal", 10 (1).
  6. [www 1]
  7. [www 2]
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