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In index options, there was not much of a smile (on the put-side) until the 1987 market crash.

I'm wondering if the same applies to single name stocks? That is, do price crashes in individual stocks trigger smiles in their option surfaces?

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Yes, it is very very common that implied vol, and particularty that of OTM puts, increases after crashes, even after limited losses.

A market maker will have a tendency to increase its volatility on the left side of a smile if a stock price drops, because the risk inherent to that stock is considered higher.

Hope it helps.

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  • $\begingroup$ Thanks much. Are there any references, studies, or papers that document this? $\endgroup$ Jun 15 at 16:06
  • $\begingroup$ You can have a look at the following sources : - sr-sv.com/modelling-the-relation-between-volatility-and-returns/…. -link $\endgroup$
    – Amaumox
    Jun 16 at 9:13
  • $\begingroup$ I think the "notion" that you are referring to is the "volatility leverage effect". Check it out on google, you will find plenty of references. $\endgroup$
    – Amaumox
    Jun 16 at 9:16

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