We apply order statistics to the setting of VaR estimation. Here techniques like historical and Monte Carlo simulation rely on using the k-th heaviest loss to estimate the quantile of the profit and loss distribution of a portfolio of assets. We show that when the k-th heaviest loss is used the expected quantile and its error will be independent of the portfolio composition and the return functions of the assets in the portfolio. This is not the case when a linear combination of simulated losses is used. Furthermore, we briefly demonstrate how order statistics can be applied to pricing options depending on the quantile of a distribution.
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