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For the first, people regularly compute VaR or CVaR over time and plot the results. For two and three, the documentation for the ETL function says that you can either calculate it using a Gaussian approach or Cornish-Fisher expansion. These are both analytical methods. The Gaussian approach uses only the mean and variance (effectively assuming that the ...

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In most of the literature on the information content of various volatility estimator the relevant question is whether a particular estimator can predict (is correlated) with future realized volatility. Hence, the testing regression would be $$RV(t,T) = \alpha + \beta VOL(t) + \epsilon(t)$$ where RV(t,T) is an estimate of the realized volatility from t to ...

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I think what you are missing is simply the Vega-Gamma relation in the Black-Scholes model. Namely: $$Vega = \frac{\partial v}{\partial \sigma} = \sigma(T-t)S^2 \frac{\partial^2 v}{\partial S^2} = \sigma \tau S^2 \Gamma$$ Plugging this into your coverage error, you get its expression in terms of the Vega which is the most natural measurement of your ...

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This is a very good question. In part, you can find a comparison by going to randommatrixportfolios.com and looking at the wealth charts for e.g. the Dow 30 portfolios, say, the 2-year data. You will note that portfolios based regressing the log-returns of price on the "signal" PCs (principal components) based on the Marcenko-Pastur noise cutoff and using ...

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