Metody předvídání volatility

In this masterthesis we have reviewed and explained the most important developments that have emerged in the area of volatility forecasting during the last several decades. These include the concepts of realized volatility, stochastic volatility, long-memory modeling, heterogenous volatility, as well as implied volatility and model-free volatility. Further we have applied several of the most popular volatility models for the purpose of volatility forecasting of the EUR/USD foreign exchange rate in the period of the last 5 years. The evaluated models were the models EWMA, GARCH, FIGARCH, ARIMA-RV, ARFIMA-RV, HAR-RV, as well as implied volatility and model-free volatility. The most succesfull models on the one-day forecast horizon were the option-based models (when adjusted for the effect of the volatility premium), while on the longer horizons (weekly and monthly) they were rivalled by the ARFIMA model. From the time-series models the most succesfull ones were the long-memory realized volatility models (ARFIMA and HAR) which over-performed the GARCH and EWMA types of models substantially. The better performance of long-memory models over the short-memory ones was most striking especially on the monthly forecast horizons. Atrough the option-based models were generally the most succesfull ones, we found out that they still did not contain all of the information contained in the time-series models. So we constructed several hybrid models (using option forecasts as well as time-series forecasts) that archieved better results than any of the separate models alone.