Abstract
The usual market risk metrics, such as Value at Risk (VaR) or Expected Shortfall (ES), are estimated pointwise. From a statistical viewpoint, VaR is a quantile and ES is a conditional expectation of the loss distribution, which can be modeled parametrically or non-parametrically. However, a point estimator is only as good as its precision; therefore any risk estimation should be accompanied with some indication of its precision. In this paper confidence intervals for the estimators of both metrics, under the most commonly used distributions: Normal and empirical, were calculated. The usefulness of the intervals lies in the possibility of drawing a decision equivalent to backtesting from the very first risk estimation, without having to wait to gather a sample of risk estimates
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