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A nonparametric approach to calculating value-at-risk. (English) Zbl 1284.62635

Summary: 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.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62G05 Nonparametric estimation
91B30 Risk theory, insurance (MSC2010)

Software:

QRM
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References:

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