Estimating Longer-Dated Volatility from VIX Moves
Summary
The document considers whether a spike in spot VIX implies an exponentially smaller change in implied volatility for options with longer expirations. It cautions that VIX and VIX futures are related measures, not direct readings of longer-dated option implied volatility: VIX represents the square root of a variance swap strike, while VIX futures represent forwards on that quantity.
One proposed approximation is to interpolate neighboring VIX futures contracts to create constant-maturity series, then regress changes in those series against changes in spot VIX. The described analysis covers maturities from one to six months and reports a decreasing relationship, but not an exponential one. A second answer emphasizes that the volatility surface does not move in parallel and recommends considering longer-dated contracts’ own traded levels. The discussion offers an empirical proxy, not a direct formula for option volatility, and gives no regression coefficients or detailed sample information.
Key ideas
- Spot VIX and VIX futures are related to variance swap measures but are not themselves longer-dated option implied volatilities.
- Constant-maturity VIX futures series can be formed by interpolating neighboring contract maturities.
- Regressing changes in those series against spot VIX changes provides one approximation of maturity-specific sensitivity.
- The described relationship declines with maturity but is not reported as exponential.
- Longer-dated implied volatility should also be assessed using the traded levels of those options.
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# Implied volatility for different expiration dates # Implied volatility for different expiration dates So VIX provides implied volatility for a 30-day time horizon. I would imagine that when VIX "spikes", the implied volatility of longer dated options would exponentially decay, due to a mean reverting nature of volatility. Is this true? Would some sort of exponential decay from a certain threshold provide a crude estimate of what the implied volatility would look like for T>30days dated options? Thanks! ## Answer by Chris Taylor (score 1) https://quant.stackexchange.com/a/82461 An interesting approximation is to regress changed in VIX futures against changes in VIX spot. This isn't exactly what you asked, since VIX levels are the square root of a variance swap strike, and VIX futures levels are forwards on the square root of a variance swap strike, rather than being implied volatilities. But it is related. It's straightforward to create constant maturity VIX futures levels by interpolating betgween adjacent contracts (e.g. if you have contracts with 40 days and 70 days to expiry, you can create a 60 day constant maturity VIX futures level by weighting these two contracts in the ratio 1/3, 2/3) and then regress these on changes in spot VIX. In the below chart I created constant maturity VIX futures with 1-6 months to expiry, and plotted the betas against changes in VIX spot. The relationship is not exponentially decreasing, but it is decreasing, as you would expect because the VIX displays mean reverting behaviour. ## Answer by boonga (score 0) https://quant.stackexchange.com/a/71980 agree, you won't have a parallel shift of the implied vol surface. Movement in the long dated implied vol levels will be certainly be less but you also need to look at the traded market levels of longer dated contracts on their own merit
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.