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Estimation and Application of the Tail Index
Název práce v češtině: Odhad a využití chvostového indexu
Název v anglickém jazyce: Estimation and Application of the Tail Index
Klíčová slova: Teorie extrémních hodnot, chvostový index, vlastnosti chvostů, risk
Klíčová slova anglicky: Extreme Value Theory, Tail Index, tail behaviour, risk
Akademický rok vypsání: 2014/2015
Typ práce: bakalářská práce
Jazyk práce: angličtina
Ústav: Institut ekonomických studií (23-IES)
Vedoucí / školitel: PhDr. Boril Šopov, M.Sc., LL.M.
Řešitel: skrytý - zadáno vedoucím/školitelem
Datum přihlášení: 04.06.2015
Datum zadání: 04.06.2015
Datum a čas obhajoby: 15.06.2016 08:00
Místo konání obhajoby: IES, m 314
Datum odevzdání elektronické podoby:12.05.2016
Datum proběhlé obhajoby: 15.06.2016
Oponenti: Mgr. Tomáš Zelený
 
 
 
Kontrola URKUND:
Zásady pro vypracování
Monte carlo simulation
Extreme value theory
GARCH models
Seznam odborné literatury
Artzner, P., Delbaen, F., Eber, J. M., and Health, D. (1999). Coherent measures of risk. Mathematical finance, 9(3), 203-228.
Drees, H., DeHaan, L., and Resnick, S. (2000). How to make a hill plot. The Annals of Statistics, pages 1833-1855.
Coles, S., Bawa, J., Trenner, L., and Dorazio, P. (2001). An introduction to statistical modeling of extreme values, volume 208. Springer.
Hill, B. M. (1975). A simple general approach to inference about the tail of a distribution. The Annals of Statistics, 3(5), 1163-1174.
McNeil, A., Frey, R., and Embrechts, P. (2005). Quantitative risk management. Princeton Series in Finance, Princeton, 10.
Resnick, S., and Starica, C. (1997). Smoothing the Hill estimator. Advances in Applied Probability, pages 271-293.
Předběžná náplň práce
Recently it has been shown that a good performance of models in periods with extreme events is of a great importance. Since financial returns do not seem to be normally distributed, the Extreme Value Theory and its theorems could serve to deal with this issue. The main interest of this study is application of Extreme Value Theory and estimation of the so called Tail Index. From the tail index inference can be made about the heaviness of tails. It is therefore a suitable tool to be used in financial risk management. The estimation of tail index by the original Hill's method will be described. Then its disadvantages will be stated and graphical methods of threshold selection will be discussed. In the empirical part several stocks will be chosen and the theory will be applied to the log-return series. The stylized facts of financial time series will be taken into account and analysed properly.
Then the tail index will be computed for each series based on the Hill’s method and other appropriately chosen procedures which will be considered based on better objectivity compared to Hill’s method. The tail index will be computed also for subsamples of shorter time span to see whether the tail characteristics change over time.
 
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