Statistical Methods in Finance 2016

Abstract

Nonparametric Estimation of 100(1-p) Percent Expected Shortfall: p close to zero

by Shantanu Dutta

Expected shortfall (ES) is a well known measure of market risk 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. For p close to zero, the ES measures an extreme loss in the right tail of the loss distribution. Not much seems to be known regarding the properties of the ES estimators under this condition. Using Monte-Carlo simulations we compare the accuracy of these estimators under the condition that p is close to zero 0, for several important asset return time series models. Our simulations and real data analysis provide important insight into the effect of varying p with n on the performance of nonparametric ES estimators.

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