Models of the Dynamics of the Volatility Indices

Five volatility indices of different countries are analyzed in this study. They are VIX (USA), VDAX (Germany), VXJ (Japan), VFTSE (UK) and RVI (Russia). This paper investigates the properties of the volatility index and such models for forecasting the profitability of volatility index like ARMA-model, GARCH-model and regression models. The empirical analysis consists of two parts. The first one covers the period between 2003 and 2016, the second – 2013-2016. The models ARCH and GARCH, which take the volatility clustering into account, are applicable for all volatility indices. The current value of the Japanese index gives the highest contribution into the current value of the German index of volatility. Also, there is relationship between VXJ and American volatility index, while the inverse relationship is not detected. In the second period (2013-2016) ARMA-models are built for such indexes like VIX, VDAX and VFTSE. GARCH (1,1)-model is applicable just for the Japanese volatility index and cannot be used for the Russian index. Various regression models are constructed for this index. The results show that the Russian index depends on European and Japanese indexes of volatility. Models, which include the indicator of the economic crisis in 2014, reject the hypothesis about the contribution of the economic crisis to the profitability of the Russian volatility index.