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Does anyone have a good reference on how to derive time weighted vega for options? The only literature I found was in this presentation:

http://www.topquants.nl/wordpress/wp-content/uploads/2015/01/Van-Gulik-Risk-management-at-Optiver.pdf

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Unfortunately, I don't quite understand how the author got from step 2 to 3. Why is perfect correlation assumed? I did the derivation for $\rho = 1$, and I did not seem to get the 3rd equation. Also, it is also unclear on why there needs to be a floor for the time conversion in the 4th equation.

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The "floor" is a cap on the wVega so that near expiries aren't weighted too highly. An example would be the vega of options on their day of expiry: capped at a maximum of 3 * vega despite sqrt(T_scale/t) approaching infinity.

For your first question they're just making an approximation of the risk they have. They use the wVega to measure their exposure to a shift in vols across the term structure. Any shift in vols is unlikely to follow this precisely: vols could go up in one expiry and down in another. They've introduced a term in step 2 to allow them to cancel out that other term. This yields a rough estimate of their pnl when vols go up or down.

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  • $\begingroup$ For your first question they're just making an approximation of the risk they have. They use the wVega to measure their exposure to a shift in vols across the term structure. Any shift in vols is unlikely to follow this precisely: vols could go up in one expiry and down in another. They've introduced a term in step 2 to allow them to cancel out that other term. This yields a rough estimate of their pnl when vols go up or down. $\endgroup$
    – louvred
    Nov 13, 2021 at 20:48

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