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I have read that volatility smiles didn't show up for equity options until 1987. Can some one give me an example(s) of what markets now still don't have volatility smiles and what an explanation for them not having equity smiles would be? thanks

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There are tons of market where vol smile doesn't exist - either because no one makes a market on the call/put options (private equity, physical real estate comes to mind) or only the ATM option gets traded infrequently. You can't have volatility smile without a vol market.

On the other hand (and maybe more relevant to what you are trying to get at), if only ATM option market exists for the underlying asset, and someone wants a bespoke/one-off price on a strike other than ATM, then you can also call transactions like this "not priced off of a vol smile". Lets say you want to buy effectively a 25 delta call (keep in mind you are unlikely to have priced delta precisely). Market maker could price this at ATM vol, and tag on an "extra" which expresses his views on what realized vol + friction cost to trade this look like, so that he could hedge himself, and still satisfy your demand as a client.

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  • $\begingroup$ Thanks that's helpful but I'm also trying to figure out are there any regularly traded markets that regularly trade ATM and ITM/OTM options and don't have a volatility smile? And if those exist, why would that be? $\endgroup$ – doru Apr 15 '16 at 23:42
  • $\begingroup$ "Why would that be?". Different stochastic process for the underlying? I.e. deviation from geometric brownian motion assumed by Black Scholes? $\endgroup$ – Alex C Apr 16 '16 at 0:58
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    $\begingroup$ @doru i think the quick answer would be: probably not. Assuming realized vol move differently at OTM strikes, if the market maker prices no smile in he would be quickly arbed out of business. $\endgroup$ – Larasing Apr 16 '16 at 1:09
  • $\begingroup$ @AlexC I'm asking what markets don't have a volatility smile and why they don't have a volatility smile while other markets do have a volatility smile not why volatility smiles exist $\endgroup$ – doru Apr 16 '16 at 2:25
  • $\begingroup$ In many markets (esp. stock indexes) the actual volatility of the market varies as the market level goes up or down. The $\sigma$ of the underlying is not constant like BS assumed. And Fischer Black was one of the first to discover this. But this "leverage effect" is stronger or weaker in diff mkts. $\endgroup$ – Alex C Apr 16 '16 at 13:21

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