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

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  • J. S. Butler

    (Vanderbilt University, Nashville, TN, USA)

  • Barry Schachter

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

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 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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Bibliographic Info

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.).
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Cited by:
  1. Jose A. Lopez, 1997. "Regulatory evaluation of value-at-risk models," Research Paper 9710, Federal Reserve Bank of New York.
  2. Xiongwei Ju & Neil D. Pearson, 1998. "Using Value-at-Risk to Control Risk Taking: How Wrong Can you Be?," Finance 9810002, EconWPA.
  3. Luis Fernando Melo Velandia & Oscar Reinaldo Becerra Camargo, 2005. "Medidas De Riesgo, Caracteristicas Y Técnicas De Medición: Una Aplicación Del Var Y El Es A La Tasa Interbancaria De Colombia," BORRADORES DE ECONOMIA 003198, BANCO DE LA REPÚBLICA.
  4. Agata Gemzik-Salwach, 2012. "The Use Of A Value At Risk Measure For The Analysis Of Bank Interest Margins," "e-Finanse", University of Information Technology and Management, Institute of Financial Research and Analysis, vol. 8(4), pages 15-29, February.

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