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All throughout my MFE I was told that implied volatility for close to expiry ATM options is a reasonable estimate for current volatility and tracks realised vol pretty well. Then why does VIX measure 30-day expected volatility?

Is VIX not supposed to be measuring current vol, but the average vol throughout the month?

So is it correct to say: implied vol for the SPX options expiring in 3-4 days is currently sitting at ~6%, whilst the VIX is 13.5%. So currently vol is around 6%, but the average vol throughout the month might be around 13.5%?

Bonus: If SPX options are cash-settled and don't pay dividends, does that mean their dividend yield is 0% wrt the Black-Sholes formula, or do you have to use the SPY dividend yield.

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Bonus: Dividend yield concerns the underlying, not the option. It is a cost of carry no arbitrage logic that is used to price options and as such you need to take dividends into account.

The VIX index is basically the discrete analog of the square root of the theoretical fair variance swap strike. You can find details here.

The calculation window was a choice made based on liquidity in the market. It is not the only index though. There is a 1d, 9D, 3m, 6m, 1y index. You can find them all here.

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  • $\begingroup$ I know you can use a put and a call pair to compute the forward rate traders are using to price their options, but how are traders deciding future dividend % and dates? If a 2 month expiry option expires 2 days before the EX date then that would affect the price, as the owner of the delta hedged stock won’t receive the dividend. Seeing as the underwriter has no idea when this date is, how do they go about this? $\endgroup$
    – THATS MY QUANT MY QUANTITATIVE
    Commented Nov 23, 2023 at 2:36
  • $\begingroup$ That's a lot of questions in one go. Did no one ever discuss this topic during your studies? It's quite an important one. This answer mentions how dividends are treated. For indices it's simpler because you have so many firms. For single stocks it's often a discrete model. There are also dividend Futures and you can imply them from option prices. $\endgroup$
    – AKdemy
    Commented Nov 23, 2023 at 2:59
  • $\begingroup$ My undergrad was in physics and my MFE program was more math theory heavy (PDE, martingales, measure theory etc) than finance heavy. Realistically, it was more-so a master's of mathematics program with a sprinkle of finance, so I have quite big gaps in my basic finance knowledge. Thanks for the recommendation, though - I'll have a read. $\endgroup$
    – THATS MY QUANT MY QUANTITATIVE
    Commented Nov 23, 2023 at 3:21
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This question was asked the day before Thanksgiving ? Then an option that expires in 3-4 days is Friday ? Or Monday ? It doesn’t much matter, the point is that the market doesn’t expect much action in the next few days due to Thanksgiving holiday and the lack of data announcements. In contrast, over the next month we have payrolls, CPI and Fed meeting. Hence higher expected vol.

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  • $\begingroup$ NFP: December 8, CPI: December 12, Fed: December 13. $\endgroup$
    – nbbo2
    Commented Nov 23, 2023 at 15:30

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