Stabilní rozdělení a finanční aplikace

Abstract

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).

Title: Stable distributions and application to finance Author: Vadym Omelchenko Department: Department of Probability and Mathematical Statistics Supervisor: Prof. Lev Klebanov, DrSc. Supervisor's e-mail address: Lev.Klebanov@mff.cuni.cz Abstract: This work deals with the theory of the stable distributions, their parameter estimation, and their financial application. There arc given the methods of characteristic function and method of projections, which is rel- ative to ML-methodology, for estimation of the parameters of stable dis- tributions. We compare these methods with the conventional estimators. The quality of estimators is verified by the simulation of the sample having stable distribution with known parameters and comparing the estimates of these parameters with their real values. The aim of this work is estima- tion of parameters of the stable laws which iy applicable for modification of AHCH/GAHCH models with stable innovations. Keywords: stable distribution, ARGII/GARCII models, characteristic func- tion (CF) based estimators, maximum likelihood projection (MLP) estima- tors.