Time-Weighted Vega and Expiry Caps in Options Risk

Summary

The discussion explains time-weighted vega as a rough measure of exposure to volatility shifts across option expiries. Its construction permits some volatility changes at different maturities to offset one another, so the measure approximates portfolio profit and loss under broad volatility moves rather than describing every possible term-structure change.

A floor in the time conversion limits the weight assigned to near-expiry options, whose unbounded scaling could otherwise make their vega count disproportionately. The example given is a maximum weighting of three times ordinary vega on expiration day. The response does not derive the weighting formula or resolve the question about perfect correlation algebraically; it characterizes the assumptions as an approximation and points to a separate reference. Use the explanation as intuition for the risk measure, not as a complete derivation or a general model of volatility movements.

Key ideas

• Time-weighted vega approximates exposure to volatility shifts across expiries.
• The measure allows volatility moves at different maturities to offset in its risk estimate.
• A floor on time conversion limits the influence of options close to expiration.
• The explanation offers intuition but does not provide a full derivation of the formula.

Tags

# Options Weighted Vega Derivation


# Options Weighted Vega Derivation












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

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.

## Answer by louvred (score 2)

https://quant.stackexchange.com/a/68758

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.