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I could see that the short-term options' IV raises on earnings announcements when longer-term options' IV does not react too much.

So I had this doubt, "Is the volatility of short-term options' IV higher than longer-term options' IV"?

Edit: The questions in other words,

  1. Is the graph of short-term options' IV more responsive/sensitive to the events (news/announcements) than the long-term options' IV graph?

  2. Does the price change of the actual underlying impact short-term options IV differently than long term options' IV?

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No. Not really. The term-structure of options IV can change shapes through the year. Sometimes short-term options have a higher IV sometimes long-term options have a higher IV.

You can take a look at figure 1 from Egloff Leippold Wu (2012). They show for the aggregate market different shapes of the term-structure of IV (measured as the Variance Swap Rate) at different points in time. But the pattern is also true for individual stocks.

enter image description here

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    $\begingroup$ CAVEAT : It can be deceiving to use variance swap rates (expected realised variances) as proxy for the behaviour of IV. What I mean is that, for instance, the term structure of variance swap rates can be monotonically increasing while ATM implied volatilities can be decreasing. Variance swap rates and ATM volatility are related but through skewness/kurtosis. Thus, it really depends on how the latter evolve through time. See quant.stackexchange.com/a/24966/19887. It also depends on what you call IV. At the money IV, OTM IV ? $\endgroup$ – Quantuple Mar 31 '16 at 13:03
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    $\begingroup$ Agreed . Given that he did not specifiy exactly what he mean by IV, I took this simpler root. But I agree with your caveat. $\endgroup$ – phdstudent Mar 31 '16 at 14:31
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Yes.

Implied vol is (very loosely speaking) the risk neutral expectation of the realized volatility over the life of the option.

A 10Y implied vol is an average over 10 years, and therefore is relatively immune to short term spikes. It is slowly varying, relative to a 1M vol which only captures spikes in short term sentiment.

When the Vix (which is short term) went to over 150% in the crisis of 2008-9, you would not expect it to last for many months. Therefore the longer term vols did not spike in that extent.

It is essentially the same logic that applies to yield curves, where the 30Y rate moves in a much less volatile than the 1Y rate. The former reflects long term fundamentals, while the latter assesses the next business cycle and central bank responses.

Re (2) in your edit:

Implied vol skews are much more pronounced for short term options (when you have moneyness on the x-axis). After all, a 10% move is big over a day or a week, but not a big deal over two years. Also, just due to the law of large numbers distributions become more Gaussian in the long run, and the smile flattens out somewhat.

Every stock/vol surface will have some degree of 'stickiness' associated with it: Say, for example, that the spot is 100, and (strike, vol) pairs look like that (90, 40%), (100 ATM, 30%), (110, 25%). If now the spot moves down to 95, there are three effects in play:

  1. Sticky moneyness: The ATM spot level is now 95, and the whole skew will have the tendency to be carried with the declining spot to the left, in order for the ATM option to keep vol of 30%. When you use time series of ATM implied vols, this is what you implicitly assume. The option with strike 90 will see its implied vol going down to 35%, and so on.

  2. Sticky strike: The skew stays where it is in terms of strikes. Since options are contractually defined in terms of strikes, the implied vols of individual options do not change (even though you now observe the ATM vol to go up, from 30% to 35%).

In reality every stock, index or FX will exhibit a mix of moneyness and strike strickiness. As a rule of thumb, I would say the sticky strike dominates over short term moves for equities.

The above move (or not move) the skew left and right. But you also have:

  1. Spot/vol correlation: Realised vol is correlated with spot. This does not refer to any particular option, and will move the whole skew up or down. It just says that if the spot drops by 5% the world is more volatile by 2% (and the time value of all options increases, so to speak).

As long term skews are much flatter, spot/vol correlation becomes more important over stickiness.

This is my toy understanding and decomposition: spot/vol correlation (up/down) and stickiness (left/right). It is not uncommon for people to confuse left/right for up/down and conclude that there more negative spot/vol correlation than there really is. Especially when they use short term vols like the Vix.

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Just a small addition to excellent responses above - traders' rule of thumb is that vol term structure moves proportional to inverse sqrt of time to expiration.

Source: Dynamic Hedging by Taleb

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  • $\begingroup$ ATM volatility that is, isn't it @onlyvix.blogspot.com? Because IV on the wings can evolve significantly differently. $\endgroup$ – Quantuple Mar 31 '16 at 16:09
  • $\begingroup$ Don't have the book in front of me, and I believe the statement was made about ATM. But IMO it also makes sense (as far as rules of thumb go) for any fixed log-moneyness. $\endgroup$ – onlyvix.blogspot.com Apr 3 '16 at 14:17

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