Modely predikce volatility a Value at Risk

The thesis compares volatility forecasting models in the calculation of Value at Risk (VaR). Eleven models are evaluated, from historical simulation and the RiskMetrics EWMA to GARCH-family specifications with normal, Student-t and skewed-t innovations, filtered historical simulation and GARCH-EVT. The models are tested on daily returns of six instruments (S&P 500, DAX, EUR/USD, gold, WTI oil and Bitcoin) over 2001–2026, at the 5, 1 and 0.1 percent levels and at horizons of 1, 5 and 30 trading days. Forecasts are assessed with coverage backtests, the tick loss and the Basel traffic light. Conditional normality fails at every tail level, whereas a GARCH filter with an estimated tail is well calibrated on nearly all instruments. GJR-t attains the lowest quantile loss at the 1 percent level and IGARCH-t is most dependable in the far tail. Square-root-of-time scaling distorts 30-day VaR. The decisive modelling choice is the innovation distribution rather than the variance dynamics.