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I'm calculating 1-day parametric VaR estimates for a stock index under the simple assumption that the returns are normally distributed. My question is, what is your opinion of using a volatility index such as the VIX as an input for the expected volatility of the underlying stock index?

The (annualized) volatility index level would be re-scaled at the daily level (e.g. ${\sqrt{1/360}}\,VIX$). I recognize that VIX is an expectation over one month which is longer than the one-day VaR risk horizon. Are there some other fundamental problems?

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  • $\begingroup$ Which stock index? $\endgroup$
    – rbm
    Commented Apr 10, 2017 at 14:28

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The idea of the parametric VaR is to fit a parametric distribution to historical data. In your case, the historical data is your daily returns.

Starting from this, you have to make an assumption on this historical returns distribution. The most obvious choice is to assume a normal distribution, which is entirely determined by the mean (average of your historical returns distribution) and the variance (standard deviation of your daily historical returns distribution).

Once you have fully parameterized your distribution, there exists a closed-form solution for the VaR at any quantile $\alpha$. Here is a post mentioning this formula:

Parametric/Analytical VaR

Hope this helps

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  • $\begingroup$ I would be grateful to the one that put a down vote on my answer without any reason. Thanks $\endgroup$
    – JejeBelfort
    Commented Apr 27, 2017 at 15:38

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