I understand how to calculate the parametric VaR of a stock and an option separately. But I don't understand how one can calculate the VaR of a portfolio of a stock and an option on that stock using the parametric method.

Would the method for multiple stocks be correct here? i.e.,

$ VaR(portfolio) = -\sqrt{w^{T}\Sigma w} \times z \times V, $

where $w$ = weights, $\Sigma$ = covariance matrix for stock and option, $z$ = $2.327$ for $1\%$ $VaR$ and $V$ = portfolio value.

This doesn't seem correct to me as the delta of the option is not involved...

Additionally, how do you extend this to have multiple stock-option pairs in the same portfolio?

  • $\begingroup$ In a parametric setting this would be done with a single risk factor approach on the net delta, normally. Whether or not that's suitable with and without the inclusion of gamma is a separate matter though $\endgroup$ – Bram Nov 13 '17 at 18:21

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