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Im looking at a call butterfly spread where i am long one ITM and OTM call option, and short two ATM call options. Also i have a time spread where i am long December put and short November put.

Now lets say implied volatility goes up. I have read online that delta increases for the OTM one but decreases for the ITM one, but nevertheless im not sure about the ATM one and if this affect would basically cancel each other out. Also, its not clear how delta would be impacted since its the change of option price relative to underlying price but here vol is just changing, with no mention of underlying price.

So overall, does anyone know how and why implied volatility increase impact the delta and gamma for a butterfly spread? What about a time spread?

Appreciate anyone who can help answer.

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  • $\begingroup$ The question and answers are not specifically for butterflies but since it's just a combination of individual legs, the answer to your question will also simply be the sum of the individual deltas. In reality, you will never have IV change without spot changing, so this is a purely theoretical question. $\endgroup$
    – AKdemy
    Oct 8, 2023 at 17:02
  • $\begingroup$ @AKdemy thank you for your response. i saw that post. but im still not sure about ATM options. what about those? $\endgroup$
    – SnG
    Oct 8, 2023 at 19:04
  • $\begingroup$ When S=K, log(S/K)=0 and if your read my answers you should see that $1/2∗σ^2∗t−log(S/K)$ is what matters. Therefore, the effect for ATM is clear. It's also specifically addressed in the last section of my answer. $\endgroup$
    – AKdemy
    Oct 8, 2023 at 19:20

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