Title: Reduced bias kernel value-at-risk estimation
Authors: Frederico Caeiro - NOVA.ID.FCT - Universidade Nova de Lisboa (Portugal) [presenting]
Ligia Henriques-Rodrigues - University of Sao Paulo (Brazil)
Abstract: The aim is the estimation of the value-at-risk (VaR) at a small level $q\in]0,1[$. The VaR is a key measure in risk market, and represents the size of the loss that occurs with a probability $q$. For heavy right-tails, the classical VaR estimators are the Weissman-Hill estimators, based on an intermediate number $k$ of top order statistics. Semi-parametric reduced-bias (RB) VaR-estimation procedures based on Kernel estimators of the extreme value index (EVI) are put forward. Under convenient restrictions on the underlying model, these Weissman-Kernel RB VaR-estimators are consistent and asymptotically normal for adequate $k$, the number of top order statistics to be used. The adequate VaR procedures are then applied to the standardized log-returns of the Bovespa stock market index.