A risk measure commonly used in financial risk management, namely, Value-at-Risk (VaR), is studied. In particular, we find a\nVaR forecast for heteroscedastic processes such that its (conditional) coverage probability is close to the nominal. To do so, we pay\nattention to the effect of estimator variability such as asymptotic bias and mean square error. Numerical analysis is carried out to\nillustrate this calculation for the Autoregressive Conditional Heteroscedastic (ARCH) model, an observable volatility type model.\nIn comparison, we find VaR for the latent volatility model i.e., the Stochastic Volatility Autoregressive (SVAR) model. It is found\nthat the effect of estimator variability is significant to obtain VaR forecast with better coverage. In addition, we may only be able to\nassess unconditional coverage probability for VaR forecast of the SVAR model. This is due to the fact that the volatility process of\nthe model is unobservable.
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