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Improving Value-At-Risk Estimates By Combining Kernel Estimation With Historical Simulation

  • J. S. Butler

    (Vanderbilt University, Nashville, TN, USA)

  • Barry Schachter

    (Office of the Comptroller of the Currency, Washington, DC, USA)

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 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 ability to construct a confidence interval around the estimate. We apply this method to trading portfolios provided by a financial institution.

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Paper provided by EconWPA in its series Finance with number 9605001.

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Date of creation: 16 May 1996
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Handle: RePEc:wpa:wuwpfi:9605001
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  1. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
  2. Paul H. Kupiec & James M. O'Brien, 1995. "The use of bank trading risk models for regulatory capital purposes," Finance and Economics Discussion Series 95-11, Board of Governors of the Federal Reserve System (U.S.).
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