ESTIMATION RISK IN GARCH VaR AND ES ESTIMATES

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+