Informatics and Applications
2015, Volume 9, Issue 4, pp 14-28
MODELING OF STATISTICAL REGULARITIES IN FINANCIAL MARKETS BY GENERALIZED VARIANCE GAMMA DISTRIBUTIONS
- V. Yu. Korolev
- A. Yu. Korchagin
- I. A. Sokolov
Abstract
Some aspects of the application of generalized variance gamma distributions for modeling statistical regularities in financial markets are discussed. The paper describes elementary properties ofgeneralized variance gamma distributions as special normal variance-mean mixtures in which mixing distributions are the generalized gamma laws. Limit theorems for sums of a random number of independent random variables are presented that are analogs of the law of large numbers and the central limit theorem. These theorems give grounds for the possibility of using generalized variance gamma distributions as asymptotic approximations. The paper presents
the results of practical fitting of generalized variance gamma distributions to real data concerning the behavior of financial indexes as well as of fitting generalized gamma distributions to the observed intensities of information flows in contemporary financial information systems. The results of comparison of generalized gamma models with generalized hyperbolic models demonstrate the superiority of the former over the latter. The methods for parameter estimation of generalized gamma models are also discussed as well as their application for predicting processes in financial markets.
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[+] About this article
Title
MODELING OF STATISTICAL REGULARITIES IN FINANCIAL MARKETS BY GENERALIZED VARIANCE GAMMA DISTRIBUTIONS
Journal
Informatics and Applications
2015, Volume 9, Issue 4, pp 14-28
Cover Date
2015-02-30
DOI
10.14357/19922264150402
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
random sum; normal mixture; normal variance-mean mixture; generalized hyperbolic distribution; generalized variance-gamma distribution; generalized gamma distribution; law of large numbers; central limit theorem
Authors
V. Yu. Korolev  ,  ,
A. Yu. Korchagin , and I. A. Sokolov 
Author Affiliations
Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University,
1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
Institute of Informatics Problems, Federal Research Center “Computer Sciences and Control” of the Russian
Academy of Sciences, 44-2 Vavilov Str.,Moscow 119333, Russian Federation
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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