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Nonparametric estimation of \(100(1-p)\%\) expected shortfall: \(p\to 0\) as sample size is increased. (English) Zbl 1462.62209

Summary: Expected shortfall (ES) is a well-known measure of extreme loss associated with a risky asset or portfolio. For any \(0<p<1\), the \(100(1-p)\) percent ES is defined as the mean of the conditional loss distribution, given the event that the loss exceeds \((1-p)\)th quantile of the marginal loss distribution. Estimation of ES based on asset return data is an important problem in finance. Several nonparametric estimators of the expected shortfall are available in the literature. Using Monte Carlo simulations, we compare the accuracy of these estimators under the condition that \(p\to 0\) as \(n\) for several asset return time series models, where \(n\) is the sample size. Not much seems to be known regarding the properties of the ES estimators under this condition. For \(p\) close to zero, the ES measures an extreme loss in the right tail of the loss distribution of the asset or portfolio. Our simulations and real-data analysis provide insight into the effect of varying \(p\) with \(n\) on the performance of nonparametric ES estimators.

MSC:

62G05 Nonparametric estimation
62G32 Statistics of extreme values; tail inference
62P20 Applications of statistics to economics
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