# Confusion with the equity option skew

In general out of the money (OTM) equity options have higher implied volatility (IV) than at the money (ATM) options. So assuming we have two put options (5% OTM and 10% OTM). Skew reveals that 10% OTM will have higher IV i.e. more expensive. If that be the case why would one not buy 5% OTM option instead for less + get higher protection?! am I missing something here?

• What do you mean with 'less'? The 5% OTM put is in terms of option premium more expensive than the 10% OTM. Otherwise there would be arbitrage.
– user34971
Nov 26, 2021 at 14:11
• 5% OTM option is priced higher in dollar terms, lower in IV terms compared to the other and vice versa. Nov 26, 2021 at 14:17
• question is if the IV is calc'd back from dollar premium shouldn't higher dollar value for 5% OTM result in higher implied value (compared to 10% OTM)?
– TRex
Nov 26, 2021 at 14:29

It’s relatively more expensive compared to the BS price with flat volatility. The option premium of the 5% OTM put is higher than the 10% OTM put.

• thanks, still confused - isn't IV calculated back from the market premium? so if that be the case shouldn't higher option premium of 5% OTM result in higher implied vols for that option? (contrary to what skew implies)?
– TRex
Nov 26, 2021 at 14:24
• IV calculation takes into account $K$, which is different for the two options, not only $p$. Nov 26, 2021 at 14:27
• yes agree, but if the market convention is to define richness (or cheapness) of options using their IVs. wouldn't that imply that 10% OTM is richer than 5% OTM as its IV is higher? (although its over way around if you look at the dollar value)
– TRex
Nov 26, 2021 at 14:39
• Put it this way; if both options had the same IV, would you expect them to have the same price? Nov 26, 2021 at 14:58
• yeh I get the point now!
– TRex
Nov 26, 2021 at 15:09