Abstract :
Value-at-risk ~VaR! and expected shortfall ~ES! are now both widely used risk
measures+ However, users have not paid much attention to the estimation risk
issues, especially in the case of heteroskedastic financial time series+ The key
challenge arises from the fact that the estimated generalized autoregressive conditional
heteroskedasticity ~GARCH! innovations are not the true independent innovations+
The purpose of this work is to provide an analytical method to assess the
precision of conditional VaR and ES in the GARCH model estimated by the filtered
historical simulation ~FHS! method based on the asymptotic behavior of the
residual empirical distribution function in GARCH processes+ The proposed method
is evaluated by simulation and proved valid+
