This paper presents a general Bayesian estimator for Value-at-Risk and applies it in analysing bank VaR time-series. The estimator optimally incorporates estistimation risk into VaR by integrating over the posterior of each unknown variables. It is shown that Bayesian VaR estimates are uniformly larger in magnitude (more conservative) than usual “plug-in” estimates, which ignore parameter uncertainty. An unusual finding of empirical VaR analysis is that commercial banks’ appear to consistently overstate their VaR level (“the Capital Charge puzzle”). Using a sample of 5 international banks’ daily VaR and trading revenue, I test whether parameter uncertainty reconciles the apparent overstatement using Bayesia

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Bayesian estimation　estimation risk　parameter uncertainty　bank　
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VaR Methods——Monte Carlo