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Stabilní rozdělení a finanční aplikace
Omelchenko, Vadym ; Klebanov, Lev (vedoucí práce) ; Branda, Martin (oponent)
Nazev pracc: Stabihn rozdeleni a iinancnf aplikacc Autor: Vadyni Oinclchcnko pravdipodobnosti a mateuiaticke statistiky Vedoucf diplomove praee: Prof. Lev Klebanov, DrSc. e-mail vedonci'ho: Lev.Klebanov@raff.cuni.cz Abstrakt: Tato prace so zabyva teorii' stabilnieh rn^deleni. mrt.odami odhadu jcjicb pararnctrii a j(;jich miancni a])likaci. Byly siinineny vseobecne znamc odhady a navrzeny inct.ody odliadn ()arainctm na zakladn r-harakt^risticko furikc',0 a projekcrii inctody. kt(^r;i jc niodifikaci metody inaximalni vcrohodnosti. Kvalit.a odbadfi sc zjisfovala s pouiocf siiuulaci naliodnelio vybcni zc sta- bihn'lio rozdeleni so znamymi paranictry a. porovnam" odhadu parametru s jcjich skutcrnymi hodnotami. Jadrcin teto ])rac;c jsou odhady parauictru ata- bilni'ch rozdeleni, coz jc aplikovat(^lnc ]>ro modifikaee modcln typu AR.CH/ GARCH sc stabilnf inovaci. Kh'cova slova: stabilnf rozdeleni, ARCH/GARCH moclely. odhady zalozene na charakteristicke funkci (CF), odhady zalozene na jjrojekcrii metode, pfi'bnzne odhadnni ML (MLP).
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Stabilní rozdělení a finanční aplikace
Omelchenko, Vadym ; Branda, Martin (oponent) ; Klebanov, Lev (vedoucí práce)
Nazev pracc: Stabihn rozdeleni a iinancnf aplikacc Autor: Vadyni Oinclchcnko pravdipodobnosti a mateuiaticke statistiky Vedoucf diplomove praee: Prof. Lev Klebanov, DrSc. e-mail vedonci'ho: Lev.Klebanov@raff.cuni.cz Abstrakt: Tato prace so zabyva teorii' stabilnieh rn^deleni. mrt.odami odhadu jcjicb pararnctrii a j(;jich miancni a])likaci. Byly siinineny vseobecne znamc odhady a navrzeny inct.ody odliadn ()arainctm na zakladn r-harakt^risticko furikc',0 a projekcrii inctody. kt(^r;i jc niodifikaci metody inaximalni vcrohodnosti. Kvalit.a odbadfi sc zjisfovala s pouiocf siiuulaci naliodnelio vybcni zc sta- bihn'lio rozdeleni so znamymi paranictry a. porovnam" odhadu parametru s jcjich skutcrnymi hodnotami. Jadrcin teto ])rac;c jsou odhady parauictru ata- bilni'ch rozdeleni, coz jc aplikovat(^lnc ]>ro modifikaee modcln typu AR.CH/ GARCH sc stabilnf inovaci. Kh'cova slova: stabilnf rozdeleni, ARCH/GARCH moclely. odhady zalozene na charakteristicke funkci (CF), odhady zalozene na jjrojekcrii metode, pfi'bnzne odhadnni ML (MLP).
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Elliptical Stable Distributions
Omelchenko, Vadym
The elliptical stable distributions represent a symmetric subfamily of the stable distributions. Their advantage contrary to the general stable distributions consists in their easy-to-use property and the highest resemblance to the normal distribution. They enable an easy representation of the dependence structure of the margins by means of a matrix Q the same as in case of the normal distribution. In general, the dependence structure between margins is given in form of a spectral measure which can be even continuous. The computations and approximations require so much time that it just the fact that many practitioners avoid using general stable distributions. The general stable distributions possess so many additional properties that they barely take after the multivariate normal distribution. But the multi-variate elliptical stable distributions can be easily simulated and the estimation of their parameters can be obtained by methods whose preciseness is almost the same as the one of the maximum likelihood methodology.
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