Estimating Value-at-Risk with a Precision Measure by Combining Kernel Estimation with Historical Simulation

Authors: Butler J.S.¹; Schachter B.²

Source: Review of Derivatives Research, Volume 1, Number 4, February 1998 , pp. 371-390(20)

Publisher: Springer

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Abstract:

In this paper we propose an alternative way to implement the historical simulation approach to Value-at-Risk (VaR) measurement, employing a non-parametric kernel quantile estimator (Sheather and Marron, 1990) of the probability density function (pdf) of the returns on a portfolio. Then we derive an expression for the pdf of any order statistic of the return distribution. That pdf is not analytic, and we employ numerical integration to obtain the moments of the order statistic, the mean being the estimate of VaR, and the standard deviation allowing the construction of a confidence interval around the estimate. We apply this method to trading portfolios provided by a financial institution.

Keywords: value at risk; estimation; kernel

Language: English

Document Type: Regular paper

Affiliations: 1: Department of Economics and Business Administration, Vanderbilt University, Nashville, TN, USA 2: Chase Manhattan Bank, New York, NY, USA. E-mail barry.schacter@chase.com

Publication date: 1998-02-01