Econometric Modeling of Volatility on the Macedonian Stock Exchange

Abstract

For proper valuation of risk to which the portfolio of financial assets is exposed, it is necessary to forecast the second moments of financial time series, that is variabilities. The empirical investigations show that financial time series are heteroskedastic, i.e. their volatility is not constant in time. For that reason the appropriate mathematical methods were developed which take this effect into account. In this paper we study one particular member of GARCH family of models that successfully describe heteroscedasticity, i.e. GARCH (1,1) model. We show the significance of the model parameters and also make the connection between the frequently used EWMA (exponentially weighted moving average) model which is a special case of IGARCH model (integrated GARCH). Using the maximum likelihood method we calculate the model parameters for Alkaloid ordinary shares, Komercijalna banka shares, Macedonian stock exchange share price index (MIB) and index S and P500. By using these models we show how one can improve risk-forecasting process