We quantify and endogenize the model risk associated with quantile estimates using a maximum
entropy distribution (MED) as benchmark. Moment-based MEDs cannot have heavy
tails, however generalized beta generated distributions have attractive properties for popular
applications of quantiles. These are MEDs under three simple constraints on the parameters
that explicitly control tail weight and peakness. Model risk arises because analysts are constrained to use a model distribution that is not the MED. Then the model’s  quantile differs from the  quantile of the MED so the tail probability under the MED associated with the model’s alpha quantile is not alpha, it is a random variable, alpha-hat. Model risk is endogenized by parameterizing the uncertainty about alpha-hat, whence the quantile becomes a generated random variable. To obtain a point model-risk-adjusted quantile, the generated distribution is used to adjust the model’s  quantile for any systematic bias and uncertai

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model risk　estimation error　maximum entropy　beta distribution　GARCH　RiskMetrics　
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VaR Methods——Properties of VaR