ESTIMATION RISK IN GARCH VaR AND ES ESTIMATES
研究了GARCH模型中条件VaR和ES估计的精度问题，提出基于过滤历史模拟的分析方法，通过模拟验证其有效性。
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.