# Implied volatility in parametric VaR

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?

• Which stock index? – rbm Apr 10 '17 at 14:28

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: