How Option Implied Volatility Varies Across Expiries and Spot Moves

# Sensitivity of short-term vs long term options' IV


# Sensitivity of short-term vs long term options' IV












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,

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

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

## Answer by phdstudent (score 3)

https://quant.stackexchange.com/a/25133

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.

## Answer by Kiwiakos (score 3)

https://quant.stackexchange.com/a/25135

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:





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:

- 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.

## Answer by onlyvix.blogspot.com (score 1)

https://quant.stackexchange.com/a/25165

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