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A Large Deviations Analysis of Quantile Estimation with Application to Value at Risk

dc.contributor.authorJin, Xing
dc.contributor.authorFu, Michael C.
dc.date.accessioned2005-07-01T12:31:49Z
dc.date.available2005-07-01T12:31:49Z
dc.date.issued2005-07-01T12:31:49Z
dc.identifier.urihttp://hdl.handle.net/1903/2301
dc.description.abstractQuantile estimation has become increasingly important, particularly in the financial industry, where Value-at-Risk has emerged as a standard measurement tool for controlling portfolio risk. In this paper we apply the theory of large deviations to analyze various simulation-based quantile estimators. First, we show that the coverage probability of the standard quantile estimator converges to one exponentially fast with sample size. Then we introduce a new quantile estimator that has a provably faster convergence rate. Furthermore, we show that the coverage probability for this new estimator can be guaranteed to be 100% with sufficiently large, but finite, sample size. Numerical experiments on a VaR example illustrate the potential for dramatic variance reduction.en
dc.format.extent364407 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.subjectsimulationen
dc.subjectquantile estimationen
dc.subjectlarge deviationsen
dc.subjectvalue at risken
dc.titleA Large Deviations Analysis of Quantile Estimation with Application to Value at Risken
dc.typeArticleen
dc.relation.isAvailableAtRobert H. Smith School of Businessen_us
dc.relation.isAvailableAtDecision & Information Technologiesen_us
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_us
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_us


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