Journal of Probability and Statistics
Volume 2010 (2010), Article ID 754851, 26 pages
Research Article

Local Likelihood Density Estimation and Value-at-Risk

1CREST and University of Toronto, Canada
2York University, Canada

Received 5 October 2009; Accepted 9 March 2010

Academic Editor: Ričardas Zitikis

Copyright © 2010 Christian Gourieroux and Joann Jasiak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a new nonparametric method for computing the conditional Value-at-Risk, based on a local approximation of the conditional density function in a neighborhood of a predetermined extreme value for univariate and multivariate series of portfolio returns. For illustration, the method is applied to intraday VaR estimation on portfolios of two stocks traded on the Toronto Stock Exchange. The performance of the new VaR computation method is compared to the historical simulation, variance-covariance, and J. P. Morgan methods.