Improving Value-at-Risk Estimates by Combining Kernel Estimation with Historical Simulation
Posted: 26 Jun 1998
Date Written: April 1996
Abstract
In this paper we develop a means to improve the performance of one of the more popular methods for Value-at-Risk measurement, the historical simulation approach. The procedure we employ is the following: First, the density of the return on a portfolio is estimated using a non- parametric method, called a Gaussian kernel. Second, we derive an expression for the density of any order statistic of the return distribution. Finally, because the density is not analytic, we employ Gauss-Legendre integration to obtain the moments of the density of the order statistic, the mean being our Value-at-Risk estimate, and the standard deviation providing us with the unique ability to construct a confidence interval around the estimate. We apply this method to trading portfolios provided by a financial institution.
JEL Classification: G21, G11
Suggested Citation: Suggested Citation