Adjusting VAR to correct sample volatility bias

David Frank proposes an adjustment to sample variance for the computation of value-at-risk

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In this article, we propose a simple adjustment that can be used when computing value-at-risk (RiskMetrics Group 1996) if a sample standard deviation of returns rather than the true standard deviation is employed. Using the sample standard deviation as if it were the true standard deviation (the usual procedure) results in VAR estimates that are biased downwards. We propose a correction for this bias by adjusting the VAR level itself, where the adjustment depends on

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