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Traders keep telling me this (and sounds very trivial/straightforward), but I don't know why (intuition and mathematically). Could someone help?

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I can address the intuition. Let’s say you are long a forward starting option, meaning an option that gets struck ATM at some future date. You choose to hedge by selling a currently ATM option. Then the underlying market moves. Now you are still long the ATM forward option but short a (now) OTM option. Since OTM options are short vol of vol , you are now short vol of vol. This scenario will occur throughout the life of the forward starting option.

This description is most valid in stochastic vol models.

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  • $\begingroup$ Thanks! Could you please clarify: 1) Why OTM options are short vol of vol? 2) If OTM options are short vol of vol, and you short an OTM option, isn't it the case that you are long vol of vol? $\endgroup$ Commented Feb 11 at 3:28
  • $\begingroup$ Clarification : OTM options are long vol of vol, so if you are short then you are short vol of vol. sorry if wasn’t clear. $\endgroup$ Commented Feb 12 at 3:49

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