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In a lot of literature, they like to compare the performance of buying an option, and then delta hedging either at that options implied volatility (IV) or the true future volatility. This is under the BSM framework.

My question is for the former case. Let's assume the option IV is 20% and the true future volatility is 30%. We buy the option at 20% IV and delta hedge using 20% IV. As we move forward in time, if the option that we bought has an IV that changes, let's say now it is at 25% IV. Do we now delta hedge at 25% IV or do we continue to hedge at 20% IV? The literature never makes this part clear.

Thanks!

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  • $\begingroup$ Strictly speaking in the BSM framework IV never changes, so there is no "adjusting" for changes. But in empirical work that tests hedging strategies (and in real world hedging) they usually do adjust for changing IV. $\endgroup$
    – Alex C
    Commented Aug 9, 2019 at 12:38
  • $\begingroup$ Thanks! This is exactly what I wanted to know. $\endgroup$
    – confused
    Commented Aug 9, 2019 at 13:27
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    $\begingroup$ Yes, if you hedge for anything other than the IV embedded in the option at any/every point in time, you're not delta-hedged! You might be almost-correctly directionally hedged, but you'll have delta (ie price) exposure on the books. And beta/delta usually trumps gamma/theta/vega in the risk mix... $\endgroup$
    – demully
    Commented Aug 9, 2019 at 20:11
  • $\begingroup$ @demully Awesome, thank you as well! $\endgroup$
    – confused
    Commented Aug 20, 2019 at 15:47
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    $\begingroup$ It's a good question. It actually depends on what you want to achieve. Some good pointers are raised in Wilmott's article "Which free lunch would you like today, sir?" (docplayer.net/…) $\endgroup$
    – Quantuple
    Commented Jan 6, 2020 at 12:26

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You need to hedge dynamically (ie, with changes in IV/delta) to accurately hedge your position. This also winds up being a potential risk for a covered option position if there are big moves or general lack of liquidity, since it can be more difficult and also more important to hedge at those times given large market moves.

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