# Why is short term implied volatility typically higher?

Why do short term implieds move more than long term?

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Implied volatility represents the market expectation of "stuff happening in the future". Over long periods, all that stuff tends to cancel out a bit, so long-term vols are much more stable. In the short term, a single news item may be enough to drastically increase (or decrease) return uncertainty.

From a quant point of view, we think of volatility as "mean-reverting".

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I would not say that it has to do with mean reversion, but I think you elegantly described why iVol[t]*Sqrt(xxx/(T-t)) != iVol[t+i]*Sqrt(xxx/(T-t+i)), where xxx denotes the chosen annualization factor. Still, I am missing the math behind your answer. –  Matt Wolf Jan 8 '13 at 11:08

While everyone touched on the subject of short term volatility, I believe Jim Gatheral and Bruno Dupire provides a great explanation about the term structure of volatility. Generally, we see that the ATM implied vol have a term structure roughly of the form $\sqrt{\tau}$ and we see that the term structure of ATM skew has a term structure roughly of the form $a - b\sqrt{\tau}$ where you can get the coefficients from fitting your data. The reason that we see that shorter to maturity options typically are quoted at higher volatility is because of jumps (which is equivalent to > 0 excess kurt). The longer the maturity, the more and more gaussian the gamma of your option is and therefore the jump costs you less. Whereas for short term maturities, the gamma converges to a dirac delta function. This implies that if there were a jump, the slippage is much higher for shorter to maturity functions.

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I think your question is ambiguous, in the subject you ask why short term implied volatility is higher, in the body you ask why do short term "implieds" move more than long term, which indicates you are asking more about the short-term vol-of-vol.

For a), short term implied vols are not typically higher at the money. They might be at the wings, due to many reasons depending who you ask, but I typically favor the vol-of-vol-leading-to-kurtosis explanation. This explanation ALSO covers why ATM short-term vols are LOWER (higher peak of probability at-the-money due to the excess kurtosis).

For b), why is short-term vol-of-vol higher, I believe it's as mentioned above because on short time scales the variance of volatility overwhelms the mean-reversion of volatility.

It's worth pointing out that "implied volatility" is just a model output of market prices, so it gets a bit dangerous to try and understand why "it" does things, when its sometimes more fruitful to think, "why do traders demand higher prices for options in these regimes or those?"

I found Nassim Taleb's Dynamic Hedging a pretty good read for these sorts of questions.

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Please explain vol-of-vol-leading-to-kurtosis –  Steve Lorimer Jan 11 '13 at 1:13
are you not pointing out how the risk conversion to spot(underlying) is basically changing and being converted to outright just gamma/theta..at some point on the term structure near expiration you are just outright calling the terminal distribution. One thing i think is missing that you caught well is demand drives price.. Asking oneself.. why would the market demand prices like that... It would be thought that "gamma" exposure has a higher relative risk related to hedging.if Convexity effects had an order it would go up relative to time left to expiration.. Look at vola by delta as well –  cdcaveman Feb 13 '13 at 6:52

Actually, short term implied volatility is higher at high volatility periods and lower at low realized volatility periods. From a quantitative perspective, the explanation for this is usually that short-term implied volatility is more influenced by the recent realized volatility, while longer-term is more influenced by the long term average. From a market perspective, it probably has to do with squeezes and reaching for protection at the time of need (so it's higher then longer term) and option over-writing in the front during the quiet times.

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