Динаміка параметрів α-стійкого процесу Леві для розподілів прибутковостей фінансових часових рядів

Abstract

Modem market economy of any country cannot successfully behave without the existence of the effective financial market. In the conditions of growing financial market, it is necessary to use modern risk-management methods, which take non-gaussian distributions into consideration. It is known, that financial and economic time series return’s distributions demonstrate so-called «heavy tails», which interrupts the modeling o f these processes with classical statistical methods. One o f the models, that is able to describe processes with «heavy tails», are the а -stable Levi processes. They can slightly simulate the dynamics of the asset prices, because it consists o f two components: the Brownian motion component and jump component. In the current work the usage of model parameters estimation procedure is proposed, which is based on the characteristic functions and is applied for the moving window for the purpose of financial-economic system’ s state monitoring.