Variance reduced Value at Risk Monte-Carlo simulations
Monte-Carlo simulations of the risk measure Value at Risk inherently involve standard errors that depend on the sample size N. In this article, we present a variance reduction technique for the estimation of loss probabilities using importance sampling. For a given sample size N, the method reduces the empirical variance of these loss probabilities by more than two orders of magnitude. Thus, it yields more accurate estimators than a standard Monte-Carlo simulation.
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