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In a volatile market with uncertainty it's more likely that we see a volatility skew and not so much a smile. Therefore it must hold that, in chaotic markets, out-of-the-money calls and in-the-money puts are in greater demand than in-the-money calls and out-of-the-money puts.(am I correct?)

But how come OTM calls and ITM puts are more in demand in volatile markets?

Eg. the day after Brexit there is a skew for GBPUSD options

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  • $\begingroup$ I don't agree with the first sentence. Smile is a signal of the likelihood of outsize events (fat tails ). That's a feature of uncertain markets. $\endgroup$ – dm63 Aug 9 '16 at 0:50
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Actually, you are going to find that the vol premium on the wings is lower in volatile markets, purely due to the "cabinet effect" when vol is very low.

I think, however, that you are mixing up smile (aka kurtosis premium) with skew (risk direction premium). When a specific side of the vol surface moves that usually means people are trying to protect against a specific direction move, either due to perception or due to market position

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