Improving Value-at-Risk Estimates by Combining Kernal Estimation with Historical Simulation

by J.S. Butler and Barry Schachter

OCC Working Paper 96-1, August 1996.

Abstract

In this paper we develop an improvement on 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 nonparametric 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 ability to construct a confidence interval around the estimate. We apply this method to trading portfolios provided by a financial institution.

Disclaimer

As with all OCC Working Papers, the opinions expressed in this paper are those of the author alone, and do not necessarily reflect the views of the Office of the Comptroller of the Currency or the Department of the Treasury.

Any whole or partial reproduction of material in this paper should include the following citation: Butler and Schachter, "Improving Value-at-Risk Estimates by Combining Kernal Estimation with Historical Simulation," Office of the Comptroller of the Currency, E&PA Working Paper 96-1, August 1996.