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volatility smiles


Active Member

I read something in Hull that I just cannot wrap my head around and I was hoping you may have an easy way of clearing this up. When talking about the greek letters, it says:

"The volatility smile complicates the calculation of the Greek letters. Assume that the relationship between the implied volatility and K/S for an option with a certain maturity stays the same." I believe this is referring to the sticky delta rule. So far it sounds perfectly plausible.

And then it includes a note that says:

"It is interesting to note that this natural model is internally consistent only when the volatility smile is flat for all maturities".

If the volatility smile is flat, there is no smile, so what the heck is going on? Sticky delta usually means that there is a smile and that the smile "moves" with the price of the underlying so this concept seems absolutely inconsistent with what is being described here.



New Member
oh.. reread it like three times and now i think i understand.

the stickyness rules are not internally consistent. It is only consistent when the volatility smile is flat.

he is just saying here that it is only consistent when the smile is flat.. but this also means that these stickyness rules have lost their use.