In the Basel regulation the required capital of a financial institution is based on conditional measures of the risk of its future equity value such as Value-at-Risk, or Expected Shortfall. In Basel 2 the uncertainty on this equity value is captured by means of changes in asset prices (market...

We consider joint estimation of conditional Value-at-Risk (VaR) at several levels, in the framework of general conditional heteroskedastic models. The volatility is estimated by Quasi-Maximum Likelihood (QML) in a first step, and the residuals are used to estimate the innovations quantiles in a...

Standard risk measures, such as the Value-at-Risk (VaR), or the Expected Shortfall, have to be estimated and their estimated counterparts are subject to estimation uncertainty. Replacing, in the theoretical formulas, the true parameter value by an estimator based on n observations of the Profit...