Score-driven models for Value at Risk and Expected Shortfall

The aim of this thesis is volatility estimation and estimates’ comparison of financial risk measures, which are specially Value at Risk (VaR) and Expected Shortfall (ES) for four world market price indices. Models of conditional heteroskedasticity are utilized. Generalized Autoregressive Score (GAS) models are applied since they are able to describe the probability density of observations in a more complex way than Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. Furthermore, they lead to more adequate estimates. VaR and ES estimates are backtested using rolling windows, which calculate one-step ahead predictions based on estimated parameters of GAS model. Parameters can be estimated in each step or in every k-step. The main contribution of this thesis is to study the impact of the length of the refit step of parameters for rolling windows in GAS models followed by comparison of estimated values of VaR and ES using Dynamic quantile (DQ) test and calculating the loss functions. The results showed that the length of the refit step does not significantly influence estimates of VaR and ES for GAS models with the Student’s t distribution. However, it underestimates values of VaR and ES significantly in the periods of price shocks for GAS models with the Gaussian distribution.