Improving Value-At-Risk Estimates By Combining Kernel Estimation With Historical Simulation
AbstractIn 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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Date of creation: 16 May 1996
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Find related papers by JEL classification:
- G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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