Predicting extreme VaR: Nonparametric quantile regression with refinements from extreme value theory - Julia Schaumburg (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2010)
This paper studies the performance of nonparametric quantile regression as a tool to predict Value at Risk (VaR). The approach is flexible as it requires no assumptions on the form of return distributions. A monotonized double kernel local linear estimator is applied to estimate moderate (1%) conditional quantiles of index return distributions. For extreme (0.1%) quantiles, where particularly few data points are available, we propose to combine nonparametric quantile regression with extreme value theory. The out-of-sample forecasting performance of our methods turns out to be clearly superior to different specifications of the Conditionally Autoregressive VaR (CAViaR) models.
Keywords: C14; C22; C52; C53; 330; Value at Risk; nonparametric quantile regression; risk management; extreme value theory; monotonization; CAViaR; Value at Risk; Prognoseverfahren; Regression; Nichtparametrisches Verfahren; Extremwertanalyse; Theorie