A nonparametric approach to calculating value-at-risk

A method to estimate an extreme quantile that requires no distributional assumptions is presented. The approach is based on transformed kernel estimation of the cumulative distribution function (cdf). The proposed method consists of a double transformation kernel estimation. We derive optimal bandwidth selection methods that have a direct expression for the smoothing parameter. The bandwidth can accommodate to the given quantile level. The procedure is useful for large data sets and improves quantile estimation compared to other methods in heavy tailed distributions. Implementation is straightforward and R programs are available.

► We estimate an extreme quantile without distributional assumptions. ► The proposed method consists of a double transformation kernel estimation. ► Optimal bandwidth has a direct expression for a given quantile level. ► Improves quantile estimation compared to other methods in heavy tailed distributions. ► Sample size needs to be large and implementation in R is available from the authors.