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If we know the options Implied Volatility (IV) skew for an equity, is it possible to calculate the probability of the equity moving, given a move in the IV?

We can define IV skew as the difference between IV at delta 0.25 compared to IV at delta 0.75.

Contango
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The skew alone is not enough. You can see this by noting the one-to-one correspondence between volatility skew and terminal probability distributions, which is independent of price and volatility dynamics. (See my answer at How to derive the implied probability distribution from B-S volatilities? for a derivation of that dependence)

Now, if you choose a non-Black-Scholes model (such as the Heston model) and calibrate it, then you can use that model to compute, say, the maximum likelihood equity price given a certain level of implied volatility.

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Brian B
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  • Very interesting. We have developed a model that can accurately predict IV in all of the market regimes we have tested it in, back to 2002. Would you be interested in collaborating to produce a method of using this same equation to predict the underlying? Preliminary results show that this is definitely possible with SPX/VIX. – Contango Aug 21 '11 at 22:31