Why VIX Differs from At-the-Money SPX Implied Volatility
Summary
The document explains why the VIX should not be expected to equal a quoted at-the-money implied volatility for SPX or SPY options. The key distinction is that VIX represents a variance-swap-style measure derived from a broad range of SPX option strikes, while an at-the-money quote reflects volatility at a particular strike and expiry. As a result, the two measures summarize different parts of the options market and can have different levels.
The answer describes the theoretical variance calculation as a weighted integration across strikes, approximated in practice using available option quotes and numerical weights. It notes that the calculation uses out-of-the-money puts and calls and that downside options receive additional weight, consistent with the equity return distribution. The document offers a conceptual explanation, not a numerical derivation or a full account of the VIX methodology; it also does not specify the exact quote conventions behind the question’s SPX or SPY implied-volatility figure.
Key ideas
- VIX is a broad, variance-swap-style measure and is not simply the at-the-money implied volatility.
- The theoretical variance measure aggregates option prices across strikes with appropriate weights.
- The practical calculation approximates the strike integration using listed options and numerical weights.
- Downside options contribute meaningfully to the measure, so the result can differ from an at-the-money quote.
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# How is VIX different from SPY/SPX IV? # How is VIX different from SPY/SPX IV? Maybe I should have read the CBOE whitepaper but I never did... Now I cannot find it. I was looking at SPY/SPX just a moment ago and noticed that spot VIX doesn't match with SPY or SPX IV. Why not? I always thought that is what VIX was. I can see current spot VIX at 10.71 at the moment while SPY/SPX IV is at 8.4% EDIT!! this is just further info based on accepted answer. SPY option chains look like someone thinking the world is gonna end. ## Answer by FinanceGuyThatCantCode (score 3, accepted) https://quant.stackexchange.com/a/34057 What is your definition of SPX IV? ATM? ATM vol will be less than VIX. VIX is calculated by pricing a variance swap on SPX. A variance swap is priced theoretically using all strikes from 0 to infinity appropriately weighted - the final formula is an integral across all of the strikes. The VIX calculation uses the discrete strikes that are available in the market with weights that you would get from doing a numerical integration based on the strikes in the market. I believe the cutoff strikes for the calculation occur on both the put and call side at the strike where two consecutive strikes have no bid. Look up variance swaps on wikipedia - at the bottom there is a link to an Emannuel Derman paper that goes over the theory of variance swaps. Variance swaps levels are nice because it is not strike dependent for the options and gives extra weight to downside moves which is sensible given the terminal distribution of equities. The CBOE paper: https://www.cboe.com/micro/vix/vixwhite.pdf Wikipedia variance swaps: https://en.wikipedia.org/wiki/Variance_swap Derman's paper: http://www.emanuelderman.com/writing/entry/more-than-you-ever-wanted-to-know-about-volatility-swaps-the-journal-of-der
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.