Predicting extreme value at risk: Nonparametric quantile regression with refinements from extreme value theory

A framework is introduced allowing us to apply nonparametric quantile regression to Value at Risk (VaR) prediction at any probability level of interest. A monotonized double kernel local linear estimator is used to estimate moderate (1%) conditional quantiles of index return distributions. For extre...

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Bibliographic Details
Published in:Computational statistics & data analysis 2012-12, Vol.56 (12), p.4081-4096
Main Author: Schaumburg, Julia
Format: Article
Language:English
Subjects:
Estimators
Extreme value statistical applications
Extreme value theory
Extreme values
Mathematical models
Monotonization
Nonparametric quantile regression
Quantiles
Regression
Risk
Risk management
Value at risk
VAR
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Summary:A framework is introduced allowing us to apply nonparametric quantile regression to Value at Risk (VaR) prediction at any probability level of interest. A monotonized double kernel local linear estimator is used to estimate moderate (1%) conditional quantiles of index return distributions. For extreme (0.1%) quantiles, nonparametric quantile regression is combined with extreme value theory. The abilities of the proposed estimators to capture market risk are investigated in a VaR prediction study with empirical and simulated data. Possibly due to its flexibility, the out-of-sample forecasting performance of the new model turns out to be superior to competing models.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2012.03.016