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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?

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    $\begingroup$ 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. $\endgroup$ Nov 26 '21 at 14:11
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    $\begingroup$ 5% OTM option is priced higher in dollar terms, lower in IV terms compared to the other and vice versa. $\endgroup$
    – noob2
    Nov 26 '21 at 14:17
  • $\begingroup$ 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)? $\endgroup$
    – TRex
    Nov 26 '21 at 14:29
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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.

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  • $\begingroup$ 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)? $\endgroup$
    – TRex
    Nov 26 '21 at 14:24
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    $\begingroup$ IV calculation takes into account $K$, which is different for the two options, not only $p$. $\endgroup$
    – noob2
    Nov 26 '21 at 14:27
  • $\begingroup$ 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) $\endgroup$
    – TRex
    Nov 26 '21 at 14:39
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    $\begingroup$ Put it this way; if both options had the same IV, would you expect them to have the same price? $\endgroup$ Nov 26 '21 at 14:58
  • $\begingroup$ yeh I get the point now! $\endgroup$
    – TRex
    Nov 26 '21 at 15:09

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