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Title: A Large Deviations Analysis of Quantile Estimation with Application to Value at Risk
Authors: Jin, Xing
Fu, Michael C.
Type: Article
Keywords: simulation
quantile estimation
large deviations
value at risk
Issue Date: 1-Jul-2005
Abstract: Quantile 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.
Appears in Collections:Decision, Operations & Information Technologies Research Works

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