A study of stable models of stock markets

Since the middle of the last century, financial engineering has become very popular among mathematicians and analysts. Stochastic methods were widely applied in financial engineering. Gaussian models were the first to be applied, but it has been noticed out that they inadequately describe the behavior of financial series. Since the classical Gaussian models were taken with more and more criticism and eventually have lost their positions, new models were proposed. Stable models attracted special attention; however their adequacy in real market should be justified. Nowadays, they have become an extremely powerful and versatile tool in financial modeling. Stock market modeling problems are considered in this paper. Adequacy and efficiency of the chosen model are demonstrated. The parameters of stable laws are estimated by the maximal likelihood method. Multifractality and self-similarity hypotheses are tested and the Hurst analysis is made as well.