I've noticed that for a given strike price, the shorter expiration dates of options have more pronounced volatilities

why is that?

  • $\begingroup$ Are you looking at any class of options in particular? $\endgroup$ – Phil H Feb 17 '14 at 10:52
  • 1
    $\begingroup$ "more pronounced volatilities" - with relation to what? Which volatilities do you compare to which? $\endgroup$ – sashkello Feb 18 '14 at 1:26
  • $\begingroup$ in relation to options with the exact same strike price and underlying asset just of a later month or expiry $\endgroup$ – user7265 Feb 18 '14 at 3:08

You have to remember that implied volatility comes from a "wrong" model to give the right answer. Option prices are determined by supply and demand (subject to a few arbitrage bounds). A higher implied volatility for OTM/ITM options relative to ATM options simply means that the prices of these options are higher than the Black-Scholes model would imply (using constant ATM implied volatility as the volatility of the underlying price diffusion).

The Black-Scholes model makes several strong assumptions, none of which are true. The implied volatility smile is simply an expression of "how wrong" the model is relative to market prices. For short maturities, Black-Scholes option for OTM options are basically zero. The reason is that the stock price is modeled as a (continuous) diffusion and therefore there is only a very small chance that the money will finish in the money. Market participants, on the other hand, may think that the probability is actually much higher because prices do jump and change rapidly within small time frames. Hence, the pronounced shape of the implied volatility smile at short maturities.


To expand on pbr142,

If the implied volatility (vis. Black & Scholes) is persistently higher for short-expiry contracts away from the money, the problem is the model, not the thing that's modeled. The price of a contract at a given point in time is the "correct" price at that point in time (or we should move this to philosophy.stackexchange.com). So how come these contracts aren't described as well by a simple, closed-form (at least in Europe) model? Some possibilities:

  • Informed trading. Since the premium is so much lower, the potential long-side reward/penalty for being right/wrong is significantly greater/lower for a pronounced move. Conversely, without some perceived edge (which can come in the form of non-public information, better research, or a better model), a trader is less likely to go long, since her time to react is less and premium decay is greater. The short side of the contract (probably also more likely to be a market maker) has to guard against this posibility. Indeed, insider trading is often revealed by large, anomalous OTM-short-expiry positions. If informed traders have an observed tendency to cluster in to these types of contracts, smart sellers should insist on a greater premium. My guess is that this accounts for the bulk of the difference.
  • Greater short-side risk of ruin. While smooth probability distributions may turn out to model risk pretty well on an infinite time horizon (we'll have to wait a bit to find out), they don't have a great track record with extreme events in the here-and-now. For any given extreme event (which isn't trying to hear about sigma), the maximum potential loss on the short side approaches parity on a per-contract basis. On a cost/benefit basis, it's therefore much greater. This should condition a greater premium. Additionally, while it might be possible to eek out a degree of distributional independence with a smart portfolio strategy under normal conditions, anecdotal evidence (we've only had thirteen-ish bubbles since we started keeping track, according to Goldman, who seems to know a thing or two) suggests that under extreme conditions, independence falls away. So offsetting extreme risk is much trickier.
  • Behavioral features. I mostly included this one to have three bullet points, but it's probably true. What's the implied volatility of a lottery ticket?

Black & Scholes or similar implied volatility can still be a helpful descriptive parameter, particularly on a comparative basis. It is usefully wrong.


What you suggest is mainly true in times of stress. The shorter maturity deals are priced with larger implied volatility to incorporate the short term volatility in the market.

  • $\begingroup$ The situation is in reverse for the period of relative calm (in fact, it is more often the case, when the "contango" is observed). $\endgroup$ – sashkello Feb 18 '14 at 1:28
  • $\begingroup$ As far as I know this also has some mathematical background. Short maturity out the money options would be almost worthless in the B&S model. Still the market often gives you positive prices. If you back out the implied vol from these it has to be quite large, so that the price makes sense in B&S setting. $\endgroup$ – Probilitator Feb 18 '14 at 9:28

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