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

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Author Info
J. S. Butler (Vanderbilt University, Nashville, TN, USA)
Barry Schachter (Office of the Comptroller of the Currency, Washington, DC, USA)

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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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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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Find related papers by JEL classification:
G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Mortgages
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

References listed on IDEAS
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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:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
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  2. Xiongwei Ju & Neil D. Pearson, 1998. "Using Value-at-Risk to Control Risk Taking: How Wrong Can you Be?," Finance 9810002, EconWPA. [Downloadable!]
  3. Jon Danielsson & Casper G. De Vries, 2000. "Value-at-Risk and Extreme Returns," Annales d'Economie et de Statistique, ADRES, issue 60, pages 11, Octobre-D. [Downloadable!]
    Other versions:
  4. Jose A. Lopez, 1997. "Regulatory evaluation of value-at-risk models," Research Paper 9710, Federal Reserve Bank of New York. [Downloadable!]
    Other versions:
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