Before revision:  Unfortunately, because the relevant severities are heavy-tailed AND the quantiles being estimated are so high, VaR is a convex function of the severity parameters, so all widely-used estimators will generate biased capital estimates due to Jensen's Inequality.
After revision:  Unfortunately, because the relevant severities are heavy-tailed AND the quantiles being estimated are so high, VaR always appears to be a convex function of the severity parameters, so all widely-used estimators will generate biased capital estimates due to Jensen's Inequality.