Modeling of statistical regularities in financial markets by generalized variance gamma distributions

Some aspects of the application of generalized variance gamma distributions for modeling statistical regularities in financial markets are discussed. The paper describes elementary properties of generalized 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.