National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Stable distribution and application to finance
Omelchenko, Vadym ; Branda, Martin (referee) ; Klebanov, Lev (advisor)
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.
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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