Quality evaluation of the model-based forecasts of implied volatility index

Influence of volatility on financial market forecasts is very high. It appears as a specific factor which causes that financial instruments' prices are highly changeable which causes problems with accuracy of their forecasts. When the market is dynamically developing, regulation of its volatility forecasts and magnification of their accuracy have particular significance, even though calculating it is complex and its values are hard to be interchangeably determined. That is the reason why model-based forecasts and especially their accuracy should be constantly modified and improved to as precisely as possible. The aim of this paper is extended analysis of the implied volatility VIX index volatility forecasts quality by examining various errors of forecasts based on the GARCH class model which allows to decide whether model-based forecasts are sufficiently accurate. These forecasts are next compared with realised VVIX index quotes from the appropriate period of time. The VVIX is established as an estimator of volatility of VIX, because financial market and model-free implied volatility appear to be the most accurate representation of this unobservable variable. It is not only the problem with volatility itself. By estimating the appropriate volatility estimator for VIX index, the result is an unobservable variable of unobservable basic instrument - implied volatility index. The chosen periods consider both calm and fluctuating periods, market tendencies (analysis of quasi-stable ups or downs) and their interdependencies.